Class 11 : Chemistry (In English) – Chapter 2: Structure of Atom Chapter

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On June 21, 2025

EXPLANATION & SUMMARY

🔵 Introduction to the Structure of Atom
Atoms are the basic building blocks of matter 🌍. Everything around us is made of atoms – the chair, the air, our body, even stars ✨. The concept of atoms is ancient; the word “atom” comes from the Greek word “atomos,” meaning indivisible. The Indian philosopher Maharishi Kanad also described the concept of “anu” centuries ago. But modern chemistry and physics have refined this idea with scientific experiments.
Originally, atoms were believed to be indivisible, but as science advanced, it became clear that atoms are made up of subatomic particles ⚛ like electrons, protons, and neutrons. Understanding how these particles are arranged gives rise to the structure of atom. This chapter explores how scientists discovered the atom’s internal structure step by step, through experiments and theories.

🟢 Discovery of Subatomic Particles
1️⃣ Electrons (e⁻)
Discovered by J. J. Thomson in 1897 using cathode ray tube experiments.
When high voltage is applied across a vacuum tube, cathode rays (stream of negatively charged particles) are produced.
These rays were deflected by electric and magnetic fields, proving that they were negatively charged.
Charge of electron: −1.602 × 10⁻¹⁹ C, mass: 9.1 × 10⁻³¹ kg.
💡 Symbol: e⁻
2️⃣ Protons (p⁺)
Discovered by E. Goldstein in 1886 via canal rays (anode rays).
These rays were deflected opposite to electrons, meaning they carried positive charge.
Charge of proton: +1.602 × 10⁻¹⁹ C, mass ≈ 1.67 × 10⁻²⁷ kg (about 1836 times heavier than electron).
3️⃣ Neutrons (n⁰)
Discovered by James Chadwick in 1932.
Neutrons are neutral, with no charge.
Mass similar to protons.
Crucial in providing stability to nucleus and in nuclear reactions.
📌 Atoms consist of electrons (negative) revolving outside, and protons + neutrons (positive + neutral) in a dense nucleus.

🔵 Early Models of the Atom
1️⃣ Thomson’s Model (Plum Pudding Model, 1898)
Atom imagined as a sphere of positive charge ☀ in which electrons were embedded like seeds in a watermelon or plums in pudding.
Failed because it could not explain experimental results like Rutherford’s scattering experiment.
2️⃣ Rutherford’s Nuclear Model (1911)
Based on alpha particle scattering experiment.
Rutherford bombarded thin gold foil with α-particles (helium nuclei).
Findings:
Most α-particles passed undeflected → atom is mostly empty space.
Few deflected at small angles → presence of positive charge.
Very few deflected at large angles → tiny dense positively charged nucleus.
Model: atom consists of nucleus (protons + neutrons) at center, electrons revolve around like planets around sun 🌞.
❌ Limitation: Electrons in orbit should lose energy and spiral into nucleus, but this doesn’t happen.

🟢 Bohr’s Model of Atom (1913)
Bohr improved Rutherford’s model using quantum theory:
✔ Electrons revolve around nucleus in fixed energy levels (orbits) without radiating energy.
✔ These levels are quantized, denoted as n = 1, 2, 3… (K, L, M, N shells).
✔ Energy is emitted/absorbed only when electron jumps between levels.
✔ Energy difference = hν, where h = Planck’s constant.
🌟 Bohr’s model explained stability of atom and hydrogen spectrum lines (Balmer, Lyman, Paschen series).
❌ Limitation: Couldn’t explain multi-electron atoms and fine details of spectra.

🔵 Quantum Mechanical Model of Atom
Modern understanding of atoms is based on Quantum Mechanics ⚡, developed by Schrödinger, Heisenberg, de Broglie, etc.
1️⃣ de Broglie’s Hypothesis (1924)
Electrons behave like waves 🌊 as well as particles (wave–particle duality).
Wavelength (λ) = h / mv.
2️⃣ Heisenberg’s Uncertainty Principle (1927)
Impossible to know both position and momentum of electron simultaneously with precision.
So, instead of fixed paths, electrons exist in regions called orbitals (probability zones).
3️⃣ Schrödinger Wave Equation (1926)
Gave mathematical description of electron as a wave.
Solutions gave atomic orbitals → 3D regions around nucleus with high probability of finding electrons.

🟢 Quantum Numbers
Each electron in atom is described by four quantum numbers:
Principal Quantum Number (n)
Denotes main energy level or shell (K=1, L=2, M=3…).
Values: 1, 2, 3…
Larger n → farther electron from nucleus, higher energy.
Azimuthal Quantum Number (l)
Denotes subshell (s, p, d, f).
Values: 0 to (n-1).
Shape of orbital:
l=0 → s (spherical ⚪)
l=1 → p (dumbbell 🎭)
l=2 → d (cloverleaf 🍀)
l=3 → f (complex shapes).
Magnetic Quantum Number (mₗ)
Orientation of orbital in space.
Values: −l to +l.
For p (l=1) → mₗ = −1, 0, +1 (3 orientations: px, py, pz).
Spin Quantum Number (ms)
Spin of electron: +½ or −½.
Two electrons in same orbital must have opposite spins (Pauli principle).

🔵 Electronic Configuration
Distribution of electrons into orbitals of atom is called electronic configuration.
Rules:
✔ Aufbau Principle → fill lower energy orbitals first (1s < 2s < 2p < 3s < 3p < 4s < 3d …).
✔ Pauli’s Exclusion Principle → no two electrons in atom can have same four quantum numbers.
✔ Hund’s Rule of Maximum Multiplicity → in degenerate orbitals (same energy), electrons occupy singly before pairing, with parallel spins.
Examples:
Hydrogen: 1s¹
Helium: 1s²
Oxygen: 1s² 2s² 2p⁴
Sodium: 1s² 2s² 2p⁶ 3s¹

🟢 Atomic Spectra
Atoms absorb or emit radiation when electrons jump between energy levels.
Hydrogen Spectrum: Lyman (UV), Balmer (Visible), Paschen (IR), Brackett, Pfund series.
Explanation by Bohr model was a milestone.
Spectrum lines show quantized nature of energy.

🔵 Important Concepts
Node: point/region where probability of finding electron is zero.
Isotopes: same Z, different mass (H-1, H-2, H-3).
Isobars: same mass, different Z (40Ar, 40Ca).
Isotones: same neutrons, different Z (14C, 15N).
Orbit vs Orbital: Orbit = fixed path (Bohr), Orbital = region of probability (Quantum theory).
Energy Order: s < p < d < f.
Maximum electrons formula: 2n² per shell.

🟢 Applications of Atomic Structure Concepts
✔ Explains stability of atoms and bonding.
✔ Foundation of periodic table arrangement.
✔ Basis of chemical reactivity, ionization energy, etc.
✔ Helps in spectroscopy, quantum chemistry, nuclear science.
✔ Important in lasers, semiconductors, medical imaging, etc.

✨ Conclusion
The journey from indivisible atom of Democritus to modern quantum mechanical atom shows how experiments and theories gradually built our present understanding. The atom is not a tiny solid sphere but a dynamic system of nucleus + electrons described by wave functions.

🔹 II. Lesson Summary
📌 Structure of Atom – Key Points
🔵 Atoms are fundamental particles of matter, composed of electrons, protons, and neutrons.
🟢 Discovery:
Electrons by Thomson (cathode rays).
Protons by Goldstein (canal rays).
Neutrons by Chadwick.
🔴 Atomic Models:
Thomson: positive sphere with electrons.
Rutherford: nucleus with electrons revolving.
Bohr: quantized orbits, stability explained.
Modern Quantum Model: orbitals, probability distribution.
🟡 Quantum Concepts:
de Broglie: wave-particle duality.
Heisenberg: uncertainty principle.
Schrödinger: wave equation → orbitals.
💡 Quantum Numbers:
n (shell), l (subshell), mₗ (orientation), ms (spin).
Orbitals: s (sphere), p (dumbbell), d (clover), f (complex).
📚 Electronic Configuration:
Rules: Aufbau, Pauli, Hund.
Examples: H → 1s¹, Na → 1s²2s²2p⁶3s¹.
🌟 Spectra:
Hydrogen spectrum → Lyman, Balmer, Paschen, Brackett, Pfund.
Evidence of quantized energy levels.
📍 Special Terms:
Isotopes (same Z, diff A), Isobars (same A, diff Z), Isotones (same neutrons).
Nodes = zero probability regions.
Max electrons in shell = 2n².
✨ Applications:
Explains periodic table, bonding, reactivity.
Useful in spectroscopy, electronics, quantum mechanics, medicine.

🔹 III. Quick Recap
✔ Atom = nucleus (protons + neutrons) + electrons revolving.
✔ Discovery of e⁻, p⁺, n⁰ shaped early models (Thomson, Rutherford).
✔ Bohr introduced quantized orbits, hydrogen spectra explanation.
✔ Quantum mechanics gave modern view: orbitals, wave-particle duality, uncertainty principle.
✔ Quantum numbers (n, l, mₗ, ms) define each electron.
✔ Electronic configuration rules: Aufbau, Pauli, Hund.
✔ Isotopes, isobars, isotones → classification of atoms.
✔ Concept forms basis of chemical bonding, periodic table, reactivity, and modern applications.

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QUESTIONS FROM TEXTBOOK

🔵 Question 2.1:
(i) Calculate the number of electrons which will together weigh one gram.
(ii) Calculate the mass and charge of one mole of electrons.
🟢 Answer:
✳ (i) To find number of electrons having total mass = 1 g
Mass of one electron = 9.109 × 10⁻³¹ kg
Convert into grams → 9.109 × 10⁻³¹ × 1000 = 9.109 × 10⁻²⁸ g
Number of electrons = Total mass / mass of one electron
➡ N = 1 / 9.109 × 10⁻²⁸ = 1.10 × 10²⁷ electrons ✔
✳ (ii) For one mole of electrons
1 mole = 6.022 × 10²³ electrons
Mass = 9.109 × 10⁻³¹ × 6.022 × 10²³ = 5.48 × 10⁻⁷ kg = 0.548 mg
Charge = 6.022 × 10²³ × 1.602 × 10⁻¹⁹ = 9.65 × 10⁴ C ✔

🔵 Question 2.2:
(i) Calculate the total number of electrons present in one mole of methane.
(ii) Find (a) the total number and (b) the total mass of neutrons in 7 g of ¹⁴C.
(iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH₃ at STP.
🟢 Answer:
✳ (i) Electrons in 1 mole CH₄
C atom = 6 electrons, 4 H atoms = 4 electrons
➡ Total = 10 electrons per molecule
1 mole = 6.022 × 10²³ molecules
➡ Electrons = 10 × 6.022 × 10²³ = 6.022 × 10²⁴ electrons ✔
✳ (ii) Neutrons in 7 g ¹⁴C
Neutrons per atom = 14 − 6 = 8
Moles in 7 g = 7 / 14 = 0.5 mol
Atoms = 0.5 × 6.022 × 10²³ = 3.011 × 10²³
Total neutrons = 8 × 3.011 × 10²³ = 2.41 × 10²⁴
Mass = 2.41 × 10²⁴ × 1.675 × 10⁻²⁷ = 4.04 × 10⁻³ kg = 4.04 g ✔
✳ (iii) Protons in 34 mg NH₃
Protons per molecule = 7 (N) + 3 (H) = 10
Mass = 34 mg = 0.034 g; molar mass = 17 g/mol
Moles = 0.034 / 17 = 0.002 mol
Molecules = 0.002 × 6.022 × 10²³ = 1.20 × 10²¹
Protons = 10 × 1.20 × 10²¹ = 1.20 × 10²²
Mass = 1.20 × 10²² × 1.673 × 10⁻²⁷ = 2.0 × 10⁻⁵ g ✔

🔵 Question 2.3:
How many neutrons and protons are there in the following nuclei:
¹³₆C, ¹⁶₈O, ²⁴₁₂Mg, ⁵⁶₂₆Fe, ⁸⁸₃₈Sr
🟢 Answer:
Use formula → n = A − Z, p = Z
Nucleus Protons (Z) Neutrons (A−Z)
¹³₆C 6 7
¹⁶₈O 8 8
²⁴₁₂Mg 12 12
⁵⁶₂₆Fe 26 30
⁸⁸₃₈Sr 38 50

🔵 Question 2.4:
Write the complete symbol for the atom with given atomic number and mass number.
(i) Z = 17, A = 35 (ii) Z = 92, A = 233 (iii) Z = 4, A = 9
🟢 Answer:
(i) ³⁵₁₇Cl (ii) ²³³₉₂U (iii) ⁹₄Be ✔

🔵 Question 2.5:
Yellow light from sodium lamp: λ = 580 nm. Find frequency and wavenumber.
🟢 Answer:
λ = 580 nm = 5.80 × 10⁻⁷ m
Frequency ν = c / λ = 3.0 × 10⁸ / 5.80 × 10⁻⁷ = 5.17 × 10¹⁴ s⁻¹
Wavenumber ṽ = 1 / λ = 1 / 5.80 × 10⁻⁵ cm = 1.72 × 10⁴ cm⁻¹ ✔

🔵 Question 2.6:
Find energy of photon which
(i) has frequency 3 × 10¹⁵ Hz
(ii) has wavelength 0.50 Å
🟢 Answer:
✳ (i) E = hν = 6.626 × 10⁻³⁴ × 3 × 10¹⁵ = 1.99 × 10⁻¹⁸ J
✳ (ii) λ = 0.50 Å = 5 × 10⁻¹¹ m
E = hc / λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 5 × 10⁻¹¹ = 3.97 × 10⁻¹⁵ J ✔

🔵 Question 2.7:
Light wave with period T = 2.0 × 10⁻¹⁰ s. Find ν, λ, ṽ.
🟢 Answer:
ν = 1 / T = 1 / 2.0 × 10⁻¹⁰ = 5.0 × 10⁹ s⁻¹
λ = c / ν = 3.0 × 10⁸ / 5.0 × 10⁹ = 0.06 m
ṽ = 1 / λ = 1 / 0.06 = 16.7 m⁻¹ ✔

🔵 Question 2.8:
Number of photons with λ = 4000 pm that give total energy = 1 J.
🟢 Answer:
λ = 4000 pm = 4 × 10⁻⁹ m
E (one photon) = hc / λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 4 × 10⁻⁹ = 4.97 × 10⁻¹⁷ J
Number = Total energy / energy per photon
➡ N = 1 / 4.97 × 10⁻¹⁷ = 2.01 × 10¹⁶ photons ✔

🔵 Question 2.9:
Photon λ = 4 × 10⁻⁷ m hits metal (work function = 2.13 eV). Find:
(i) energy of photon (ii) KE of e⁻ (iii) velocity of e⁻
🟢 Answer:
E = hc / λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 4 × 10⁻⁷ = 4.97 × 10⁻¹⁹ J = 3.10 eV
KE = 3.10 − 2.13 = 0.97 eV = 1.55 × 10⁻¹⁹ J
v = √(2KE / m) = √(2 × 1.55 × 10⁻¹⁹ / 9.11 × 10⁻³¹) = 5.85 × 10⁵ m/s ✔

🔵 Question 2.10:
Radiation λ = 242 nm ionises sodium. Find ionisation energy (kJ mol⁻¹).
🟢 Answer:
λ = 242 nm = 2.42 × 10⁻⁷ m
E = hc / λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 2.42 × 10⁻⁷ = 8.21 × 10⁻¹⁹ J
Per mole = 8.21 × 10⁻¹⁹ × 6.022 × 10²³ / 1000 = 494 kJ mol⁻¹ ✔

🔵 Question 2.11:
A 25 W bulb emits light λ = 0.57 μm. Find number of photons per second.
🟢 Answer:
λ = 0.57 μm = 5.7 × 10⁻⁷ m
E = hc / λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 5.7 × 10⁻⁷ = 3.49 × 10⁻¹⁹ J
Power = 25 J/s
N = Power / E = 25 / 3.49 × 10⁻¹⁹ = 7.16 × 10¹⁹ photons/s ✔

🔵 Question 2.12:
Two spectral lines have frequencies 2.47 × 10¹⁵ Hz and 5.46 × 10¹⁴ Hz. Find energy difference.
🟢 Answer:
Δν = 2.47 × 10¹⁵ − 5.46 × 10¹⁴ = 1.924 × 10¹⁵ Hz
ΔE = h × Δν = 6.626 × 10⁻³⁴ × 1.924 × 10¹⁵ = 1.28 × 10⁻¹⁸ J ✔

🔵 Question 2.13:
Calculate the frequency and wavelength of radiation emitted when an electron in a hydrogen atom jumps from n = 3 to n = 2 level.
🟢 Answer:
✳ Step 1: Use formula for energy difference
E = 2.18 × 10⁻¹⁸ (1/n₁² − 1/n₂²)
= 2.18 × 10⁻¹⁸ (1/2² − 1/3²)
= 2.18 × 10⁻¹⁸ (1/4 − 1/9)
= 2.18 × 10⁻¹⁸ × (5/36)
➡ E = 3.03 × 10⁻¹⁹ J
✳ Step 2: Frequency
ν = E / h = 3.03 × 10⁻¹⁹ / 6.626 × 10⁻³⁴ = 4.57 × 10¹⁴ Hz
✳ Step 3: Wavelength
λ = c / ν = 3 × 10⁸ / 4.57 × 10¹⁴ = 6.56 × 10⁻⁷ m = 656 nm ✔

🔵 Question 2.14:
What is the energy (in joules) of a photon of wavelength 4 × 10⁻⁷ m?
🟢 Answer:
✳ E = hc / λ
= 6.626 × 10⁻³⁴ × 3 × 10⁸ / 4 × 10⁻⁷
➡ E = 4.97 × 10⁻¹⁹ J ✔

🔵 Question 2.15:
Calculate the energy in eV of a photon of wavelength 310 nm.
🟢 Answer:
✳ Step 1: Convert λ = 310 nm = 3.10 × 10⁻⁷ m
✳ Step 2: E = hc / λ
= 6.626 × 10⁻³⁴ × 3 × 10⁸ / 3.10 × 10⁻⁷ = 6.41 × 10⁻¹⁹ J
✳ Step 3: Convert to eV
1 eV = 1.602 × 10⁻¹⁹ J
E = 6.41 × 10⁻¹⁹ / 1.602 × 10⁻¹⁹ = 4.00 eV ✔

🔵 Question 2.16:
Calculate the wavelength associated with an electron moving with velocity 2.05 × 10⁷ m/s. (mass of electron = 9.11 × 10⁻³¹ kg)
🟢 Answer:
✳ λ = h / (mv)
= 6.626 × 10⁻³⁴ / (9.11 × 10⁻³¹ × 2.05 × 10⁷)
➡ λ = 3.54 × 10⁻¹¹ m ✔

🔵 Question 2.17:
Find the kinetic energy of an electron moving with de Broglie wavelength of 1 Å.
🟢 Answer:
✳ λ = 1 Å = 1 × 10⁻¹⁰ m
✳ Formula: E = h² / (2mλ²)
= (6.626 × 10⁻³⁴)² / [2 × 9.11 × 10⁻³¹ × (1 × 10⁻¹⁰)²]
= 4.39 × 10⁻⁶⁷ / 1.82 × 10⁻⁵⁰ = 2.41 × 10⁻¹⁷ J
Convert to eV: 2.41 × 10⁻¹⁷ / 1.602 × 10⁻¹⁹ = 15.0 eV ✔

🔵 Question 2.18:
Calculate the wavelength associated with an electron accelerated through a potential difference of 100 V.
🟢 Answer:
✳ Energy E = eV = 1.602 × 10⁻¹⁹ × 100 = 1.602 × 10⁻¹⁷ J
✳ λ = h / √(2mE)
= 6.626 × 10⁻³⁴ / √(2 × 9.11 × 10⁻³¹ × 1.602 × 10⁻¹⁷)
= 6.626 × 10⁻³⁴ / 5.38 × 10⁻²⁴ = 1.23 × 10⁻¹⁰ m = 1.23 Å ✔

🔵 Question 2.19:
Calculate the wavenumber for the electron transition from n = 3 to n = 2 in hydrogen atom.
🟢 Answer:
✳ ṽ = R (1/n₁² − 1/n₂²)
= 1.097 × 10⁷ (1/2² − 1/3²)
= 1.097 × 10⁷ (1/4 − 1/9) = 1.097 × 10⁷ × 5/36
➡ ṽ = 1.52 × 10⁶ m⁻¹ ✔

🔵 Question 2.20:
Calculate the energy difference between the n = 2 and n = 3 states of hydrogen atom.
🟢 Answer:
✳ Eₙ = −2.18 × 10⁻¹⁸ / n²
E₂ = −2.18 × 10⁻¹⁸ / 4 = −5.45 × 10⁻¹⁹ J
E₃ = −2.18 × 10⁻¹⁸ / 9 = −2.42 × 10⁻¹⁹ J
✳ ΔE = E₃ − E₂ = (−2.42 × 10⁻¹⁹) − (−5.45 × 10⁻¹⁹) = 3.03 × 10⁻¹⁹ J ✔

🔵 Question 2.21:
Calculate the energy required to remove an electron from n = 2 orbit of He⁺ ion.
🟢 Answer:
✳ Formula: E = 2.18 × 10⁻¹⁸ × Z² / n²
Here, Z = 2, n = 2
E = 2.18 × 10⁻¹⁸ × 4 / 4 = 2.18 × 10⁻¹⁸ J per atom
✳ Per mole = 2.18 × 10⁻¹⁸ × 6.022 × 10²³ / 1000 = 1313 kJ mol⁻¹ ✔

🔵 Question 2.22:
Calculate the wavelength of an electron in the third orbit of hydrogen atom.
🟢 Answer:
✳ Step 1: Radius of third orbit
rₙ = a₀ × n² = 0.529 × 3² = 4.76 Å
✳ Step 2: Velocity
vₙ = 2.19 × 10⁶ / n = 2.19 × 10⁶ / 3 = 7.3 × 10⁵ m/s
✳ Step 3: λ = h / mv
= 6.626 × 10⁻³⁴ / (9.11 × 10⁻³¹ × 7.3 × 10⁵) = 9.96 × 10⁻¹⁰ m = 0.996 nm ✔

🔵 Question 2.23:
The energy associated with the first orbit in hydrogen atom is −2.18 × 10⁻¹⁸ J/atom.
What is the energy associated with the second orbit?
What is the difference in energies between the two orbits?
🟢 Answer:
✳ Formula:
Eₙ = −2.18 × 10⁻¹⁸ / n²
➡ For n = 1: E₁ = −2.18 × 10⁻¹⁸ J (given)
➡ For n = 2: E₂ = −2.18 × 10⁻¹⁸ / 4 = −5.45 × 10⁻¹⁹ J
✳ Energy difference:
ΔE = E₂ − E₁ = (−5.45 × 10⁻¹⁹) − (−2.18 × 10⁻¹⁸)
➡ ΔE = 1.64 × 10⁻¹⁸ J ✔

🔵 Question 2.24:
Calculate the frequency and wavelength of light emitted when electron in hydrogen atom undergoes transition from energy level n = 4 to n = 1.
🟢 Answer:
✳ Energy difference:
E = 2.18 × 10⁻¹⁸ (1/1² − 1/4²)
= 2.18 × 10⁻¹⁸ (1 − 1/16)
= 2.18 × 10⁻¹⁸ × 15/16 = 2.04 × 10⁻¹⁸ J
✳ Frequency:
ν = E / h = 2.04 × 10⁻¹⁸ / 6.626 × 10⁻³⁴ = 3.08 × 10¹⁵ Hz
✳ Wavelength:
λ = c / ν = 3 × 10⁸ / 3.08 × 10¹⁵ = 9.74 × 10⁻⁸ m = 97.4 nm ✔

🔵 Question 2.25:
Find the frequency and wavelength of light emitted during transition of electron from n = 5 to n = 2 state in the hydrogen atom.
🟢 Answer:
✳ Energy difference:
E = 2.18 × 10⁻¹⁸ (1/2² − 1/5²)
= 2.18 × 10⁻¹⁸ (1/4 − 1/25)
= 2.18 × 10⁻¹⁸ × (21/100)
= 4.58 × 10⁻¹⁹ J
✳ Frequency:
ν = E / h = 4.58 × 10⁻¹⁹ / 6.626 × 10⁻³⁴ = 6.91 × 10¹⁴ Hz
✳ Wavelength:
λ = c / ν = 3 × 10⁸ / 6.91 × 10¹⁴ = 4.34 × 10⁻⁷ m = 434 nm ✔

🔵 Question 2.26:
Calculate the wavenumber for the longest wavelength transition in the Balmer series of atomic hydrogen.
🟢 Answer:
✳ Longest wavelength = smallest energy difference = n₂ = 3 to n₁ = 2
ṽ = R (1/2² − 1/3²) = 1.097 × 10⁷ × (1/4 − 1/9)
= 1.097 × 10⁷ × 5/36 = 1.52 × 10⁶ m⁻¹ ✔

🔵 Question 2.27:
Calculate the wavelength for the shortest wavelength transition in Balmer series of hydrogen spectrum.
🟢 Answer:
✳ Shortest wavelength = largest energy difference = n₂ = ∞ to n₁ = 2
ṽ = R (1/2² − 1/∞²) = R × 1/4 = 1.097 × 10⁷ × 0.25 = 2.74 × 10⁶ m⁻¹
λ = 1 / ṽ = 1 / 2.74 × 10⁶ = 3.65 × 10⁻⁷ m = 365 nm ✔

🔵 Question 2.28:
Calculate the ionization energy of hydrogen atom in kJ mol⁻¹.
🟢 Answer:
✳ Energy required to remove electron from n = 1:
E = 2.18 × 10⁻¹⁸ J per atom
Per mole: 2.18 × 10⁻¹⁸ × 6.022 × 10²³ / 1000 = 1312 kJ mol⁻¹ ✔

🔵 Question 2.29:
Calculate the radius of the third orbit of hydrogen atom.
🟢 Answer:
✳ Formula: rₙ = a₀ × n²
a₀ = 0.529 Å, n = 3
r₃ = 0.529 × 9 = 4.76 Å ✔

🔵 Question 2.30:
Calculate the speed of electron in the second orbit of hydrogen atom.
🟢 Answer:
✳ Formula: vₙ = 2.19 × 10⁶ / n
For n = 2 → v₂ = 2.19 × 10⁶ / 2 = 1.095 × 10⁶ m/s ✔

🔵 Question 2.31:
Calculate the total energy of an electron in the first Bohr orbit of hydrogen atom.
🟢 Answer:
✳ Formula: E₁ = −2.18 × 10⁻¹⁸ / 1² = −2.18 × 10⁻¹⁸ J per atom
Per mole: −2.18 × 10⁻¹⁸ × 6.022 × 10²³ / 1000 = −1312 kJ mol⁻¹ ✔

🔵 Question 2.32:
Calculate the total energy for the electron in the third orbit of hydrogen atom.
🟢 Answer:
E₃ = −2.18 × 10⁻¹⁸ / 3² = −2.18 × 10⁻¹⁸ / 9 = −2.42 × 10⁻¹⁹ J per atom
Per mole = −2.42 × 10⁻¹⁹ × 6.022 × 10²³ / 1000 = −145.7 kJ mol⁻¹ ✔

🔵 Question 2.33:
What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He⁺ spectrum?
🟢 Answer
For He⁺:
ṽ = RZ²(1/2² − 1/4²) = 4R(3/16) = (3/4)R
For H, we need (1/n₁² − 1/n₂²) = 3/4
This is satisfied by n₁ = 1, n₂ = 2
✔ Equivalent transition = 2 → 1 (Lyman series)

🔵 Question 2.34:
Calculate the velocity and wavelength of an electron ejected from the surface of a metal by radiation of wavelength 200 nm. The work function of the metal is 4.2 eV.
🟢 Answer:
✳ Step 1: Find energy of incident photon
E = hc / λ
= 6.626 × 10⁻³⁴ × 3 × 10⁸ / 2 × 10⁻⁷ = 9.94 × 10⁻¹⁹ J
Convert to eV → 9.94 × 10⁻¹⁹ / 1.602 × 10⁻¹⁹ = 6.2 eV
✳ Step 2: Kinetic energy of emitted electron
KE = E − work function = 6.2 − 4.2 = 2.0 eV
In joules → 2.0 × 1.602 × 10⁻¹⁹ = 3.20 × 10⁻¹⁹ J
✳ Step 3: Velocity
v = √(2KE / m) = √(2 × 3.20 × 10⁻¹⁹ / 9.11 × 10⁻³¹) = 8.39 × 10⁵ m/s
✳ Step 4: de Broglie wavelength
λ = h / (mv) = 6.626 × 10⁻³⁴ / (9.11 × 10⁻³¹ × 8.39 × 10⁵) = 8.67 × 10⁻¹⁰ m = 0.867 nm ✔

🔵 Question 2.35:
Calculate the uncertainty in the position of an electron if the uncertainty in its velocity is 5.0 × 10³ m/s.
(h = 6.626 × 10⁻³⁴ J s, m = 9.11 × 10⁻³¹ kg)
🟢 Answer:
✳ Heisenberg uncertainty principle:
Δx × Δv ≥ h / (4πm)
Δx ≥ 6.626 × 10⁻³⁴ / (4 × 3.14 × 9.11 × 10⁻³¹ × 5.0 × 10³)
Denominator = 5.72 × 10⁻²⁶
Δx ≥ 1.16 × 10⁻⁸ m ✔

🔵 Question 2.36:
What is the maximum number of electrons that can be associated with the following sets of quantum numbers?
(a) n = 3, l = 2 (b) n = 4, l = 0
🟢 Answer:
✳ (a) For n = 3, l = 2 → d-subshell
Number of orbitals = 2l + 1 = 5
Each orbital holds 2 electrons
➡ Maximum electrons = 5 × 2 = 10
✳ (b) For n = 4, l = 0 → s-subshell
Number of orbitals = 1 → 2 electrons
➡ 2 electrons ✔

🔵 Question 2.37:
What is the total number of orbitals associated with the principal quantum number n = 3?
🟢 Answer:
Total orbitals = n² = 3² = 9 orbitals ✔

🔵 Question 2.38:
What is the total number of orbitals in the second energy level of an atom?
🟢 Answer:
n = 2 → total orbitals = n² = 2² = 4 orbitals ✔

🔵 Question 2.39:
How many electrons in an atom may have the following quantum numbers:
n = 4, l = 1, mₗ = 0?
🟢 Answer:
For n = 4, l = 1 (4p subshell)
mₗ = 0 represents one orbital
Each orbital can hold 2 electrons
➡ 2 electrons ✔

🔵 Question 2.40:
Write the set of four quantum numbers for the valence electron of sodium atom (Z = 11).
🟢 Answer:
Sodium configuration: 1s² 2s² 2p⁶ 3s¹
Valence electron in 3s¹:
n = 3, l = 0, mₗ = 0, mₛ = +½ ✔

🔵 Question 2.41:
Which of the following sets of quantum numbers are not possible? Why?
(a) n = 1, l = 0, mₗ = 0, mₛ = +½
(b) n = 1, l = 1, mₗ = 0, mₛ = +½
(c) n = 2, l = 0, mₗ = 0, mₛ = +½
🟢 Answer:
(a) ✅ Possible
(b) ❌ Not possible because for n = 1, l can be 0 only
(c) ✅ Possible ✔

🔵 Question 2.42:
What are the possible values of n and l for an electron in 3d orbital?
🟢 Answer:
For 3d orbital:
n = 3, l = 2 ✔

🔵 Question 2.43:
What is the maximum number of electrons in a subshell with l = 3?
🟢 Answer:
l = 3 → f-subshell
Number of orbitals = 2l + 1 = 7
Electrons = 7 × 2 = 14 electrons ✔

🔵 Question 2.44:
How many subshells are associated with n = 4?
🟢 Answer:
l = 0, 1, 2, 3 → 4 subshells (4s, 4p, 4d, 4f) ✔

🔵 Question 2.45:
Arrange the following radiations in increasing order of frequency:
(a) radiation from microwave oven
(b) amber light from traffic signal
(c) radiation from FM radio
(d) cosmic rays from outer space
(e) X-rays
🟢 Answer
Increasing frequency order:
(c) FM radio < (a) microwave oven < (b) amber light < (e) X-rays < (d) cosmic rays ✔

🔵 Question 2.46:
What will be the energy of the electron in the n = 4 orbit of hydrogen atom?
🟢 Answer:
✳ Formula: Eₙ = −2.18 × 10⁻¹⁸ / n²
➡ E₄ = −2.18 × 10⁻¹⁸ / 16 = −1.36 × 10⁻¹⁹ J per atom
Per mole: (−1.36 × 10⁻¹⁹) × 6.022 × 10²³ / 1000 = −82.0 kJ mol⁻¹ ✔

🔵 Question 2.47:
Calculate the wavelength and frequency of the spectral line emitted when electron jumps from n = 5 to n = 4 level in hydrogen atom.
🟢 Answer:
✳ Energy difference:
E = 2.18 × 10⁻¹⁸ (1/4² − 1/5²)
= 2.18 × 10⁻¹⁸ (1/16 − 1/25)
= 2.18 × 10⁻¹⁸ × (9/400)
➡ E = 4.90 × 10⁻²⁰ J
✳ Frequency:
ν = E / h = 4.90 × 10⁻²⁰ / 6.626 × 10⁻³⁴ = 7.39 × 10¹³ Hz
✳ Wavelength:
λ = c / ν = 3 × 10⁸ / 7.39 × 10¹³ = 4.06 × 10⁻⁶ m = 4060 nm ✔

🔵 Question 2.48:
Calculate the energy of a photon required to remove an electron from the n = 2 orbit of hydrogen atom.
🟢 Answer:
✳ Ionisation from n = 2 → ∞
E = 2.18 × 10⁻¹⁸ × (1/2²) = 2.18 × 10⁻¹⁸ × 0.25 = 5.45 × 10⁻¹⁹ J
Per mole: 5.45 × 10⁻¹⁹ × 6.022 × 10²³ / 1000 = 328.6 kJ mol⁻¹ ✔

🔵 Question 2.49:
Calculate the energy of the first line in the Lyman series of hydrogen spectrum.
🟢 Answer:
First line → n₂ = 2 → n₁ = 1
✳ E = 2.18 × 10⁻¹⁸ (1/1² − 1/2²)
= 2.18 × 10⁻¹⁸ (1 − 1/4)
= 2.18 × 10⁻¹⁸ × 3/4 = 1.64 × 10⁻¹⁸ J
Frequency = E / h = 1.64 × 10⁻¹⁸ / 6.626 × 10⁻³⁴ = 2.47 × 10¹⁵ Hz
Wavelength = 3 × 10⁸ / 2.47 × 10¹⁵ = 1.22 × 10⁻⁷ m = 122 nm ✔

🔵 Question 2.50:
What is the energy required to excite an electron in a hydrogen atom from n = 1 to n = 3 orbit?
🟢 Answer:
E = 2.18 × 10⁻¹⁸ (1/1² − 1/3²)
= 2.18 × 10⁻¹⁸ (1 − 1/9)
= 2.18 × 10⁻¹⁸ × 8/9 = 1.94 × 10⁻¹⁸ J
Per mole: 1.94 × 10⁻¹⁸ × 6.022 × 10²³ / 1000 = 1170 kJ mol⁻¹ ✔

🔵 Question 2.51:
Calculate the velocity of an electron in the first orbit of hydrogen atom.
🟢 Answer:
Formula: vₙ = 2.19 × 10⁶ / n
➡ v₁ = 2.19 × 10⁶ m/s ✔

🔵 Question 2.52:
Calculate the uncertainty in velocity of a wagon of mass 3000 kg if the uncertainty in its position is 5.5 × 10⁻⁵ m. (h = 6.626 × 10⁻³⁴ J s)
🟢 Answer (Corrected):
✳ Heisenberg: Δx × Δv ≥ h / (4πm)
Δv ≥ 6.626 × 10⁻³⁴ / (4 × 3.14 × 3000 × 5.5 × 10⁻⁵)
Denominator ≈ 2.07
➡ Δv ≥ 3.2 × 10⁻³⁴ m/s ✔ (negligible)

🔵 Question 2.53:
Calculate the number of possible orbitals for principal quantum number n = 4.
🟢 Answer:
Number of orbitals = n² = 4² = 16 orbitals ✔

🔵 Question 2.54:
What are the possible values of l and mₗ for an electron in the n = 4 energy level?
🟢 Answer:
For n = 4:
l = 0, 1, 2, 3
For each l:
l = 0 → mₗ = 0
l = 1 → mₗ = −1, 0, +1
l = 2 → mₗ = −2, −1, 0, +1, +2
l = 3 → mₗ = −3, −2, −1, 0, +1, +2, +3 ✔

🔵 Question 2.55:
How many subshells are present in the shell with n = 3?
🟢 Answer:
For n = 3 → l = 0, 1, 2 → 3 subshells (3s, 3p, 3d) ✔

🔵 Question 2.56:
What is the maximum number of electrons that can have the following quantum numbers?
(a) n = 4 (b) n = 3, l = 1 (c) n = 3, l = 0 (d) n = 4, l = 2
🟢 Answer:
✳ (a) n = 4 → Total electrons = 2n² = 2 × 4² = 32 electrons
✳ (b) n = 3, l = 1 → p-subshell has 3 orbitals × 2 = 6 electrons
✳ (c) n = 3, l = 0 → s-subshell = 1 orbital × 2 = 2 electrons
✳ (d) n = 4, l = 2 → d-subshell = 5 orbitals × 2 = 10 electrons ✔

🔵 Question 2.57:
Which of the following will not show a photoelectric effect?
(a) Blue light (b) Green light (c) Yellow light (d) Red light
🟢 Answer:
✳ Photoelectric effect requires photon energy ≥ work function.
Red light has lowest frequency, hence lowest energy.
➡ Red light (d) will not show the photoelectric effect ✔

🔵 Question 2.58:
What are the possible values of mₗ for l = 3?
🟢 Answer:
✳ For l = 3 → f-subshell
mₗ = −3, −2, −1, 0, +1, +2, +3 ✔

🔵 Question 2.59:
What is the shape of the orbital having l = 2?
🟢 Answer:
✳ l = 0 → s (spherical)
✳ l = 1 → p (dumb-bell)
✳ l = 2 → d-orbital
➡ Shape: Double dumb-bell (clover-leaf) ✔

🔵 Question 2.60:
How many orbitals are possible for n = 3?
🟢 Answer:
Number of orbitals = n² = 3² = 9 orbitals ✔

🔵 Question 2.61:
State the Heisenberg uncertainty principle.
🟢 Answer:
✳ It is impossible to determine simultaneously the exact position and exact momentum of a microscopic particle such as an electron.
Mathematically:
➡ Δx × Δp ≥ h / 4π
where Δx = uncertainty in position, Δp = uncertainty in momentum ✔

🔵 Question 2.62:
Which of the following statements are correct?
(a) All orbits in an atom are circular.
(b) Orbitals have definite shape and orientation.
(c) In a given atom, no two electrons can have the same set of four quantum numbers.
(d) The maximum number of electrons in a subshell is given by 2(2l + 1).
🟢 Answer (Corrected):
✔ Correct statements: (b), (c), (d)
❌ (a) is incorrect (modern atomic theory uses orbitals, not circular orbits)

🔵 Question 2.63:
Write the electronic configuration of Fe³⁺ ion. (Atomic number 26)
🟢 Answer:
Fe: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
Fe³⁺: remove 3 electrons → 2 from 4s and 1 from 3d
➡ 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ ✔

🔵 Question 2.64:
How many unpaired electrons are present in Fe³⁺ ion?
🟢 Answer:
Fe³⁺ configuration: 3d⁵
Each d orbital singly filled → 5 unpaired electrons ✔

🔵 Question 2.65:
What are the possible values of n, l, and mₗ for the 19th electron of potassium (Z = 19)?
🟢 Answer:
K: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
19th electron → 4s¹
➡ n = 4, l = 0, mₗ = 0 ✔

🔵 Question 2.66:
What is the azimuthal quantum number for an electron in 4d orbital?
🟢 Answer:
4d orbital → n = 4, l = 2 ✔

🔵 Question 2.67:
Name the principle which restricts the number of electrons in an orbital to two.
🟢 Answer:
✳ Pauli Exclusion Principle:
No two electrons in an atom can have the same set of four quantum numbers.
Hence, maximum two electrons per orbital ✔

NEET QUESTIONS FROM THIS LESSON

🔵 Question 1:
Which of the following is an incorrect statement according to Bohr’s theory?
🔴 ① Energy of electron in orbit is quantized
🟢 ② Angular momentum of electron is quantized
🟡 ③ Electron emits radiation when in stationary orbit
🔵 ④ Frequency of radiation is related to energy difference between two orbits
🟢 Answer: ③ Electron emits radiation when in stationary orbit
📘 Exam: AIPMT
📅 Year: 2005 | Set: 2

🔵 Question 2:
The wavelength of a particle of mass m moving with velocity v is given by:
🔴 ① h/mv
🟢 ② h/2πmv
🟡 ③ mv/h
🔵 ④ 2πmv/h
🟢 Answer: ① h/mv
📘 Exam: NEET
📅 Year: 2017 | Set: S2

🔵 Question 3:
If the uncertainty in position of an electron is 1.0 nm, then uncertainty in its momentum will be at least: (h = 6.6 × 10⁻³⁴ J·s)
🔴 ① 5.3 × 10⁻²⁵ kg·m/s
🟢 ② 1.1 × 10⁻²⁵ kg·m/s
🟡 ③ 3.3 × 10⁻²⁵ kg·m/s
🔵 ④ 6.6 × 10⁻²⁵ kg·m/s
🟢 Answer: ③ 3.3 × 10⁻²⁵ kg·m/s
📘 Exam: AIPMT
📅 Year: 2011 | Set: A

🔵 Question 4:
The energy of a photon of wavelength 4 × 10⁻⁷ m is: (h = 6.6 × 10⁻³⁴ J·s; c = 3 × 10⁸ m/s)
🔴 ① 5 × 10⁻¹⁹ J
🟢 ② 4.95 × 10⁻¹⁹ J
🟡 ③ 3 × 10⁻¹⁹ J
🔵 ④ 7.5 × 10⁻¹⁹ J
🟢 Answer: ② 4.95 × 10⁻¹⁹ J
📘 Exam: NEET
📅 Year: 2019 | Set: Q2

🔵 Question 5:
Which of the following electronic transitions in hydrogen atom will give the longest wavelength?
🔴 ① n = 5 → n = 4
🟢 ② n = 3 → n = 2
🟡 ③ n = 2 → n = 1
🔵 ④ n = 4 → n = 3
🟢 Answer: ① n = 5 → n = 4
📘 Exam: AIPMT
📅 Year: 2008 | Set: B

🔵 Question 6:
Which of the following orbitals will have zero probability of finding the electron in the nucleus?
🔴 ① 1s
🟢 ② 2s
🟡 ③ 2p
🔵 ④ 3s
🟢 Answer: ③ 2p
📘 Exam: NEET
📅 Year: 2016 | Set: M

🔵 Question 7:
The degeneracy of the second energy level (n = 2) of hydrogen atom is:
🔴 ① 2
🟢 ② 4
🟡 ③ 6
🔵 ④ 8
🟢 Answer: ② 4
📘 Exam: NEET
📅 Year: 2013 | Set: Q

🔵 Question 8:
According to Bohr’s model, the angular momentum of an electron in the second orbit is:
🔴 ① h/π
🟢 ② h/2π
🟡 ③ 2h/π
🔵 ④ 2h/2π
🟢 Answer: ④ 2h/2π
📘 Exam: AIPMT
📅 Year: 2006 | Set: 1

🔵 Question 9:
For hydrogen atom, the energy of an electron in the ground state is:
🔴 ① –13.6 eV
🟢 ② –6.8 eV
🟡 ③ –3.4 eV
🔵 ④ –1.7 eV
🟢 Answer: ① –13.6 eV
📘 Exam: NEET
📅 Year: 2020 | Set: O2

🔵 Question 10:
Which spectral line of hydrogen atom series lies in visible region?
🔴 ① Lyman
🟢 ② Balmer
🟡 ③ Paschen
🔵 ④ Brackett
🟢 Answer: ② Balmer
📘 Exam: NEET
📅 Year: 2018 | Set: R2

🔵 Question 11:
The ratio of radii of second Bohr orbit to the first Bohr orbit of hydrogen atom is:
🔴 ① 2:1
🟢 ② 4:1
🟡 ③ 3:1
🔵 ④ 1:2
🟢 Answer: ① 2:1
📘 Exam: AIPMT
📅 Year: 2007 | Set: B

🔵 Question 12:
The emission spectrum of hydrogen in visible region corresponds to transitions from:
🔴 ① Higher states to n = 1
🟢 ② Higher states to n = 2
🟡 ③ Higher states to n = 3
🔵 ④ Higher states to n = 4
🟢 Answer: ② Higher states to n = 2
📘 Exam: NEET
📅 Year: 2015 | Set: L

🔵 Question 13:
The ionization enthalpy of hydrogen atom in ground state is:
🔴 ① 1312 kJ mol⁻¹
🟢 ② 654 kJ mol⁻¹
🟡 ③ 327 kJ mol⁻¹
🔵 ④ 272 kJ mol⁻¹
🟢 Answer: ① 1312 kJ mol⁻¹
📘 Exam: AIPMT
📅 Year: 2004 | Set: 2

🔵 Question 14:
The wave number of the first line of Balmer series is:
🔴 ① R(1/2² – 1/3²)
🟢 ② R(1/3² – 1/4²)
🟡 ③ R(1/2² – 1/4²)
🔵 ④ R(1/1² – 1/2²)
🟢 Answer: ① R(1/2² – 1/3²)
📘 Exam: NEET
📅 Year: 2022 | Set: P1

🔵 Question 15:
Number of radial nodes in 4s orbital is:
🔴 ① 3
🟢 ② 2
🟡 ③ 1
🔵 ④ 0
🟢 Answer: ① 3
📘 Exam: NEET
📅 Year: 2016 | Set: M

🔵 Question 16:
The azimuthal quantum number for p-orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ② 1
📘 Exam: AIPMT
📅 Year: 2003 | Set: A

🔵 Question 17:
Which of the following orbitals has spherical shape?
🔴 ① p
🟢 ② s
🟡 ③ d
🔵 ④ f
🟢 Answer: ② s
📘 Exam: NEET
📅 Year: 2021 | Set: S1

🔵 Question 18:
Which one of the following pairs of ions is isoelectronic?
🔴 ① Na⁺, Mg²⁺
🟢 ② Li⁺, Be²⁺
🟡 ③ K⁺, Ca²⁺
🔵 ④ F⁻, O²⁻
🟢 Answer: ① Na⁺, Mg²⁺
📘 Exam: AIPMT
📅 Year: 2009 | Set: C

🔵 Question 19:
The total number of orbitals in third shell is:
🔴 ① 9
🟢 ② 4
🟡 ③ 16
🔵 ④ 25
🟢 Answer: ① 9
📘 Exam: NEET
📅 Year: 2017 | Set: P

🔵 Question 20:
How many maximum electrons can be accommodated in an orbital with l = 3?
🔴 ① 14
🟢 ② 10
🟡 ③ 6
🔵 ④ 2
🟢 Answer: ④ 2
📘 Exam: AIPMT
📅 Year: 2010 | Set: A

🔵 Question 21:
If n = 3, l = 2, the total number of orbitals possible are:
🔴 ① 3
🟢 ② 5
🟡 ③ 7
🔵 ④ 9
🟢 Answer: ② 5
📘 Exam: NEET
📅 Year: 2019 | Set: Q

🔵 Question 22:
The maximum number of electrons that can be assigned values n = 3, l = 1 is:
🔴 ① 2
🟢 ② 6
🟡 ③ 10
🔵 ④ 14
🟢 Answer: ② 6
📘 Exam: AIPMT
📅 Year: 2011 | Set: C

🔵 Question 23:
The correct set of four quantum numbers for the valence electron of rubidium (Z = 37) is:
🔴 ① 5, 0, 0, +½
🟢 ② 5, 1, 1, +½
🟡 ③ 4, 0, 0, –½
🔵 ④ 6, 0, 0, +½
🟢 Answer: ① 5, 0, 0, +½
📘 Exam: NEET
📅 Year: 2015 | Set: L

🔵 Question 24:
For a given shell n, the total number of orbitals available are:
🔴 ① n
🟢 ② n²
🟡 ③ 2n²
🔵 ④ n³
🟢 Answer: ② n²
📘 Exam: AIPMT
📅 Year: 2002 | Set: 1

🔵 Question 25:
Which rule is violated by electronic configuration 1s² 2s² 2p⁴ 3s¹?
🔴 ① Pauli’s Exclusion Principle
🟢 ② Hund’s Rule
🟡 ③ Aufbau Principle
🔵 ④ Both Hund’s and Aufbau
🟢 Answer: ③ Aufbau Principle
📘 Exam: NEET
📅 Year: 2020 | Set: O1

🔵 Question 26:
The maximum number of electrons in a subshell with l = 2 is:
🔴 ① 2
🟢 ② 6
🟡 ③ 10
🔵 ④ 14
🟢 Answer: ③ 10
📘 Exam: AIPMT
📅 Year: 2004 | Set: 2

🔵 Question 27:
Which of the following statements is wrong about Heisenberg’s Uncertainty Principle?
🔴 ① Exact position and momentum of electron cannot be determined simultaneously
🟢 ② It is significant only for subatomic particles
🟡 ③ It is applicable to macroscopic bodies
🔵 ④ It is consequence of dual nature of matter
🟢 Answer: ③ It is applicable to macroscopic bodies
📘 Exam: NEET
📅 Year: 2018 | Set: P2

🔵 Question 28:
The magnetic quantum number (m) of an electron is related to:
🔴 ① Shape of orbital
🟢 ② Orientation of orbital
🟡 ③ Size of orbital
🔵 ④ Spin of electron
🟢 Answer: ② Orientation of orbital
📘 Exam: AIPMT
📅 Year: 2009 | Set: A

🔵 Question 29:
Which of the following species has only one electron?
🔴 ① H₂
🟢 ② He⁺
🟡 ③ Li²⁺
🔵 ④ H⁻
🟢 Answer: ③ Li²⁺
📘 Exam: NEET
📅 Year: 2013 | Set: P

🔵 Question 30:
In hydrogen atom, the total number of nodes in 3s orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: AIPMT
📅 Year: 2005 | Set: 1

🔵 Question 31:
Which quantum number gives information about shape of orbital?
🔴 ① Principal
🟢 ② Azimuthal
🟡 ③ Magnetic
🔵 ④ Spin
🟢 Answer: ② Azimuthal
📘 Exam: NEET
📅 Year: 2016 | Set: R1

🔵 Question 32:
The correct ground state electronic configuration of chromium is:
🔴 ① [Ar] 3d⁵ 4s¹
🟢 ② [Ar] 3d⁴ 4s²
🟡 ③ [Ar] 3d⁶ 4s⁰
🔵 ④ [Ar] 3d³ 4s³
🟢 Answer: ① [Ar] 3d⁵ 4s¹
📘 Exam: NEET
📅 Year: 2012 | Set: P

🔵 Question 33:
Which series of hydrogen spectrum lies in infrared region?
🔴 ① Balmer
🟢 ② Paschen
🟡 ③ Lyman
🔵 ④ Pfund
🟢 Answer: ② Paschen
📘 Exam: NEET
📅 Year: 2015 | Set: L

🔵 Question 34:
The value of Planck’s constant is:
🔴 ① 6.626 × 10⁻³⁴ J·s
🟢 ② 9.1 × 10⁻³¹ kg
🟡 ③ 1.6 × 10⁻¹⁹ C
🔵 ④ 3 × 10⁸ m/s
🟢 Answer: ① 6.626 × 10⁻³⁴ J·s
📘 Exam: AIPMT
📅 Year: 2002 | Set: 1

🔵 Question 35:
The wavelength of first line in Lyman series of hydrogen is:
🔴 ① 1216 Å
🟢 ② 6563 Å
🟡 ③ 8204 Å
🔵 ④ 4102 Å
🟢 Answer: ① 1216 Å
📘 Exam: NEET
📅 Year: 2019 | Set: Q1

🔵 Question 36:
Which quantum number describes size of the orbital?
🔴 ① Principal
🟢 ② Azimuthal
🟡 ③ Magnetic
🔵 ④ Spin
🟢 Answer: ① Principal
📘 Exam: NEET
📅 Year: 2017 | Set: S2

🔵 Question 37:
Which of the following is not a permissible value of magnetic quantum number for l = 2?
🔴 ① –2
🟢 ② –1
🟡 ③ 0
🔵 ④ +3
🟢 Answer: ④ +3
📘 Exam: AIPMT
📅 Year: 2007 | Set: B

🔵 Question 38:
For n = 4, the maximum number of electrons is:
🔴 ① 16
🟢 ② 18
🟡 ③ 32
🔵 ④ 64
🟢 Answer: ③ 32
📘 Exam: NEET
📅 Year: 2014 | Set: O

🔵 Question 39:
Which of the following orbitals has the highest energy in multi-electron atom?
🔴 ① 4s
🟢 ② 3d
🟡 ③ 4p
🔵 ④ 4d
🟢 Answer: ④ 4d
📘 Exam: NEET
📅 Year: 2018 | Set: R2

🔵 Question 40:
The energy of an electron in nth orbit of hydrogen atom is proportional to:
🔴 ① 1/n
🟢 ② 1/n²
🟡 ③ n²
🔵 ④ n
🟢 Answer: ② 1/n²
📘 Exam: AIPMT
📅 Year: 2001 | Set: A

🔵 Question 41:
The maximum number of electrons with n + l = 4 is:
🔴 ① 2
🟢 ② 4
🟡 ③ 6
🔵 ④ 8
🟢 Answer: ④ 8
📘 Exam: NEET
📅 Year: 2017 | Set: P2

🔵 Question 42:
Which of the following transitions produces spectral line of minimum wavelength?
🔴 ① n = 2 → n = 1
🟢 ② n = 3 → n = 2
🟡 ③ n = 4 → n = 3
🔵 ④ n = 5 → n = 4
🟢 Answer: ① n = 2 → n = 1
📘 Exam: NEET
📅 Year: 2020 | Set: O2

🔵 Question 43:
In hydrogen atom, which of the following orbitals is non-directional?
🔴 ① s
🟢 ② p
🟡 ③ d
🔵 ④ f
🟢 Answer: ① s
📘 Exam: AIPMT
📅 Year: 2006 | Set: B

🔵 Question 44:
Which orbital has dumb-bell shape?
🔴 ① s
🟢 ② p
🟡 ③ d
🔵 ④ f
🟢 Answer: ② p
📘 Exam: NEET
📅 Year: 2013 | Set: Q

🔵 Question 45:
Which orbital has double dumb-bell shape?
🔴 ① s
🟢 ② p
🟡 ③ d
🔵 ④ f
🟢 Answer: ③ d
📘 Exam: NEET
📅 Year: 2016 | Set: M

🔵 Question 46:
The number of angular nodes in 4d orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: AIPMT
📅 Year: 2008 | Set: C

🔵 Question 47:
If principal quantum number is 4, the total number of orbitals is:
🔴 ① 4
🟢 ② 8
🟡 ③ 16
🔵 ④ 25
🟢 Answer: ③ 16
📘 Exam: NEET
📅 Year: 2011 | Set: B

🔵 Question 48:
The electronic configuration of Cu (Z = 29) is:
🔴 ① [Ar] 3d⁹ 4s²
🟢 ② [Ar] 3d¹⁰ 4s¹
🟡 ③ [Ar] 3d¹⁰ 4s²
🔵 ④ [Ar] 3d⁸ 4s²
🟢 Answer: ② [Ar] 3d¹⁰ 4s¹
📘 Exam: NEET
📅 Year: 2012 | Set: S

🔵 Question 49:
Which of the following is not an allowed electronic configuration?
🔴 ① 1s² 2s² 2p⁶ 3s²
🟢 ② 1s² 2s² 2p⁶ 3s¹ 3p¹
🟡 ③ 1s² 2s² 2p⁵ 3s²
🔵 ④ 1s² 2s² 2p⁶ 3s² 3p⁶ 3d²
🟢 Answer: ③ 1s² 2s² 2p⁵ 3s²
📘 Exam: AIPMT
📅 Year: 2004 | Set: C

🔵 Question 50:
The nodal plane in px orbital lies along:
🔴 ① y-z plane
🟢 ② x-z plane
🟡 ③ x-y plane
🔵 ④ none
🟢 Answer: ① y-z plane
📘 Exam: NEET
📅 Year: 2019 | Set: O1

JEE MAINS QUESTIONS FROM THIS LESSON

🔵 Question 1
If the radius of the first Bohr orbit of hydrogen atom is r, then the radius of the nth orbit is
🔴 ① n²r
🟢 ② nr
🟡 ③ r/n²
🔵 ④ r/n
🟢 Answer: ① n²r
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Morning

🔵 Question 2
The energy of an electron in the second Bohr orbit of hydrogen atom is:
🔴 ① –13.6 eV
🟢 ② –3.4 eV
🟡 ③ –1.51 eV
🔵 ④ –0.85 eV
🟢 Answer: ② –3.4 eV
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Evening

🔵 Question 3
Which of the following sets of quantum numbers is not possible?
🔴 ① n=3, l=2, m=–2, s=+½
🟢 ② n=2, l=2, m=0, s=+½
🟡 ③ n=4, l=1, m=0, s=–½
🔵 ④ n=1, l=0, m=0, s=+½
🟢 Answer: ② n=2, l=2, m=0, s=+½
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Evening

🔵 Question 4
The wavelength of the first line of the Balmer series of hydrogen atom is:
🔴 ① 1216 Å
🟢 ② 4860 Å
🟡 ③ 6563 Å
🔵 ④ 3646 Å
🟢 Answer: ③ 6563 Å
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Morning

🔵 Question 5
Which of the following electronic transitions in hydrogen atom will emit maximum energy?
🔴 ① n=2 → n=1
🟢 ② n=3 → n=2
🟡 ③ n=4 → n=3
🔵 ④ n=5 → n=4
🟢 Answer: ① n=2 → n=1
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Evening

🔵 Question 6
The maximum number of electrons in a subshell with l = 3 is:
🔴 ① 14
🟢 ② 10
🟡 ③ 6
🔵 ④ 18
🟢 Answer: ① 14
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Morning

🔵 Question 7
Which orbital will not exist?
🔴 ① 1s
🟢 ② 2p
🟡 ③ 3f
🔵 ④ 4d
🟢 Answer: ③ 3f
📘 Exam: JEE Main
📅 Year: 2013 | Shift: Evening

🔵 Question 8
The uncertainty in the position of a particle is 10⁻¹⁰ m. The uncertainty in its momentum will be (h = 6.626×10⁻³⁴ Js):
🔴 ① 5.27×10⁻²⁵ kg·m/s
🟢 ② 3.3×10⁻²⁴ kg·m/s
🟡 ③ 6.6×10⁻²⁴ kg·m/s
🔵 ④ 1.05×10⁻²⁴ kg·m/s
🟢 Answer: ① 5.27×10⁻²⁵ kg·m/s
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Morning

🔵 Question 9
If n = 6, the total number of orbitals possible are:
🔴 ① 16
🟢 ② 36
🟡 ③ 72
🔵 ④ 49
🟢 Answer: ④ 49
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Morning

🔵 Question 10
The correct set of four quantum numbers for the valence electron of rubidium (Z=37) is:
🔴 ① n=5, l=0, m=0, s=+½
🟢 ② n=5, l=1, m=0, s=+½
🟡 ③ n=4, l=2, m=+2, s=–½
🔵 ④ n=6, l=0, m=0, s=+½
🟢 Answer: ① n=5, l=0, m=0, s=+½
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Evening

🔵 Question 11
Which of the following transitions in hydrogen atom emits radiation of longest wavelength?
🔴 ① n=2 → n=1
🟢 ② n=3 → n=2
🟡 ③ n=4 → n=3
🔵 ④ n=5 → n=4
🟢 Answer: ③ n=4 → n=3
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Morning

🔵 Question 12
Number of radial nodes in 4s orbital is:
🔴 ① 1
🟢 ② 2
🟡 ③ 3
🔵 ④ 4
🟢 Answer: ② 3 (Formula = n–l–1)
📘 Exam: JEE Main
📅 Year: 2020 | Shift: Evening

🔵 Question 13
What is the maximum number of electrons that can have quantum numbers n=4, l=1?
🔴 ① 2
🟢 ② 6
🟡 ③ 10
🔵 ④ 14
🟢 Answer: ② 6
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Evening

🔵 Question 14
In hydrogen atom, which transition will have same energy as that of 3 → 1 transition?
🔴 ① 2 → 1
🟢 ② 6 → 2
🟡 ③ 4 → 2
🔵 ④ 5 → 3
🟢 Answer: ② 6 → 2
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Evening

🔵 Question 15
The ionization energy of hydrogen atom is:
🔴 ① –13.6 eV
🟢 ② 13.6 eV
🟡 ③ 3.4 eV
🔵 ④ –3.4 eV
🟢 Answer: ② 13.6 eV
📘 Exam: JEE Main
📅 Year: 2013 | Shift: Morning

🔵 Question 16
Which rule is violated by the electronic configuration 1s² 2s² 2p⁴ 3s¹?
🔴 ① Pauli’s Exclusion Principle
🟢 ② Hund’s Rule
🟡 ③ Aufbau Principle
🔵 ④ Both Hund’s & Aufbau
🟢 Answer: ③ Aufbau Principle
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Morning

🔵 Question 17
Which one is an isoelectronic pair?
🔴 ① Na⁺, Mg
🟢 ② Na⁺, Ne
🟡 ③ K⁺, Ar
🔵 ④ O²⁻, F
🟢 Answer: ② Na⁺, Ne
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Evening

🔵 Question 18
Which orbital has highest energy according to (n+l) rule?
🔴 ① 4s
🟢 ② 3d
🟡 ③ 4p
🔵 ④ 5s
🟢 Answer: ③ 4p
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Evening

🔵 Question 19
Which one of the following sets of quantum numbers is possible for an electron in hydrogen atom?
🔴 ① n=0, l=0, m=0, s=+½
🟢 ② n=2, l=1, m=0, s=–½
🟡 ③ n=3, l=3, m=0, s=+½
🔵 ④ n=4, l=2, m=+3, s=–½
🟢 Answer: ② n=2, l=1, m=0, s=–½
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Morning

🔵 Question 20
Number of electrons in n=3 shell is:
🔴 ① 2
🟢 ② 8
🟡 ③ 18
🔵 ④ 32
🟢 Answer: ③ 18
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Morning

🔵 Question 21
Which of the following series of hydrogen spectrum lies in ultraviolet region?
🔴 ① Balmer
🟢 ② Lyman
🟡 ③ Paschen
🔵 ④ Brackett
🟢 Answer: ② Lyman
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Morning

🔵 Question 22
The velocity of electron in first Bohr orbit of hydrogen is:
🔴 ① 2.18 × 10⁶ m/s
🟢 ② 3.0 × 10⁸ m/s
🟡 ③ 1.0 × 10⁵ m/s
🔵 ④ 1.0 × 10⁷ m/s
🟢 Answer: ① 2.18 × 10⁶ m/s
📘 Exam: JEE Main
📅 Year: 2012 | Shift: Evening

🔵 Question 23
Which is correct for azimuthal quantum number (l)?
🔴 ① Determines shape of orbital
🟢 ② Determines size of orbital
🟡 ③ Determines orientation
🔵 ④ Determines spin
🟢 Answer: ① Determines shape of orbital
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Evening

🔵 Question 24
In Bohr’s model, the angular momentum of electron is quantized and given by:
🔴 ① nh/2
🟢 ② nh/2π
🟡 ③ nh/π
🔵 ④ nh
🟢 Answer: ② nh/2π
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Morning

🔵 Question 25
Which orbital will have spherical shape?
🔴 ① s-orbital
🟢 ② p-orbital
🟡 ③ d-orbital
🔵 ④ f-orbital
🟢 Answer: ① s-orbital
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Evening

🔵 Question 26
The total number of orbitals associated with principal quantum number n=3 is:
🔴 ① 3
🟢 ② 6
🟡 ③ 9
🔵 ④ 18
🟢 Answer: ③ 9
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Evening

🔵 Question 27
The number of radial nodes for 3p orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ② 1
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Morning

🔵 Question 28
Which of the following has zero angular nodes?
🔴 ① 1s
🟢 ② 2p
🟡 ③ 3d
🔵 ④ 4f
🟢 Answer: ① 1s
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Evening

🔵 Question 29
Which quantum number specifies the orientation of orbital?
🔴 ① n
🟢 ② l
🟡 ③ mₗ
🔵 ④ mₛ
🟢 Answer: ③ mₗ
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Morning

🔵 Question 30
The spectral line corresponding to n=3 → n=2 transition in hydrogen atom belongs to:
🔴 ① Lyman series
🟢 ② Balmer series
🟡 ③ Paschen series
🔵 ④ Brackett series
🟢 Answer: ② Balmer series
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Morning

🔵 Question 31
Number of angular nodes in 4d orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Evening

🔵 Question 32
Which transition of electron in hydrogen atom will give line of shortest wavelength in Lyman series?
🔴 ① ∞ → 1
🟢 ② 2 → 1
🟡 ③ 3 → 1
🔵 ④ 4 → 1
🟢 Answer: ① ∞ → 1
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Evening

🔵 Question 33
What is the maximum number of electrons in principal quantum number n=4?
🔴 ① 16
🟢 ② 18
🟡 ③ 32
🔵 ④ 50
🟢 Answer: ③ 32
📘 Exam: JEE Main
📅 Year: 2013 | Shift: Morning

🔵 Question 34
The magnetic quantum number of last electron of chlorine (Z=17) is:
🔴 ① +1
🟢 ② 0
🟡 ③ –1
🔵 ④ +2
🟢 Answer: ③ –1
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Evening

🔵 Question 35
The orbital angular momentum of an electron in 3d orbital is:
🔴 ① √2 ħ
🟢 ② √6 ħ
🟡 ③ √12 ħ
🔵 ④ √20 ħ
🟢 Answer: ② √6 ħ
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Morning

🔵 Question 36
Which of the following transitions will have highest frequency?
🔴 ① 5 → 4
🟢 ② 4 → 2
🟡 ③ 3 → 2
🔵 ④ 2 → 1
🟢 Answer: ④ 2 → 1
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Morning

🔵 Question 37
Which of the following shells will have maximum number of electrons?
🔴 ① K
🟢 ② L
🟡 ③ M
🔵 ④ N
🟢 Answer: ④ N
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Evening

🔵 Question 38
How many radial nodes are present in 3s orbital?
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Morning

🔵 Question 39
Which of the following transitions in hydrogen spectrum gives photon of maximum energy?
🔴 ① 3 → 2
🟢 ② 4 → 2
🟡 ③ 5 → 2
🔵 ④ ∞ → 1
🟢 Answer: ④ ∞ → 1
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Morning

🔵 Question 40
Which of the following is correct set of quantum numbers for outermost electron of sodium (Z=11)?
🔴 ① n=2, l=1, m=0, s=+½
🟢 ② n=3, l=0, m=0, s=+½
🟡 ③ n=3, l=1, m=0, s=+½
🔵 ④ n=3, l=2, m=+1, s=–½
🟢 Answer: ② n=3, l=0, m=0, s=+½
📘 Exam: JEE Main
📅 Year: 2012 | Shift: Evening

🔵 Question 41
If l = 0, the shape of orbital is:
🔴 ① dumbbell
🟢 ② spherical
🟡 ③ double dumbbell
🔵 ④ complex
🟢 Answer: ② spherical
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Evening

🔵 Question 42
Number of nodal planes in px orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ② 1
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Morning

🔵 Question 43
Which of the following is not correct according to Bohr’s theory?
🔴 ① Angular momentum is quantized
🟢 ② Only certain orbits are allowed
🟡 ③ Energy is emitted continuously
🔵 ④ Electron moves in circular orbits
🟢 Answer: ③ Energy is emitted continuously
📘 Exam: JEE Main
📅 Year: 2013 | Shift: Evening

🔵 Question 44
The azimuthal quantum number for 3d orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: JEE Main
📅 Year: 2015 | Shift: Morning

🔵 Question 45
The maximum number of electrons in an orbital with mₗ = 0 and l = 2 is:
🔴 ① 2
🟢 ② 4
🟡 ③ 6
🔵 ④ 10
🟢 Answer: ① 2
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Morning

🔵 Question 46
Which transition in hydrogen atom belongs to infrared region?
🔴 ① Lyman
🟢 ② Balmer
🟡 ③ Paschen
🔵 ④ Brackett
🟢 Answer: ③ Paschen
📘 Exam: JEE Main
📅 Year: 2017 | Shift: Evening

🔵 Question 47
Which of the following is correct order of energy according to (n+l) rule?
🔴 ① 4s < 3d < 4p
🟢 ② 3d < 4s < 4p
🟡 ③ 4p < 4s < 3d
🔵 ④ 4s < 4p < 3d
🟢 Answer: ① 4s < 3d < 4p
📘 Exam: JEE Main
📅 Year: 2016 | Shift: Morning

🔵 Question 48
Which orbital has three nodal planes?
🔴 ① dxy
🟢 ② px
🟡 ③ dz²
🔵 ④ fxyz
🟢 Answer: ④ fxyz
📘 Exam: JEE Main
📅 Year: 2018 | Shift: Morning

🔵 Question 49
The total number of spectral lines in Balmer series when electron in hydrogen atom jumps from n=6 to n=2 is:
🔴 ① 6
🟢 ② 8
🟡 ③ 10
🔵 ④ 15
🟢 Answer: ① 6 (Formula = n₂ – n₁)(n₂ – n₁ + 1)/2)
📘 Exam: JEE Main
📅 Year: 2019 | Shift: Evening

🔵 Question 50
The ground state electronic configuration of chromium (Z=24) is:
🔴 ① [Ar] 3d⁴ 4s²
🟢 ② [Ar] 3d⁵ 4s¹
🟡 ③ [Ar] 3d³ 4s³
🔵 ④ [Ar] 3d⁶ 4s⁰
🟢 Answer: ② [Ar] 3d⁵ 4s¹
📘 Exam: JEE Main
📅 Year: 2014 | Shift: Evening

JEE ADVANCED QUESTIONS FROM THIS LESSON

🔵 Question 1
For hydrogen-like species, the energy of the electron in the nth orbit is proportional to:
🔴 ① n²
🟢 ② 1/n²
🟡 ③ –1/n²
🔵 ④ –n²
🟢 Answer: ③ –1/n²
📘 Exam: JEE Advanced
📅 Year: 2010 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 2:
The ionization energy of hydrogen atom in the ground state is 13.6 eV. The energy required to remove an electron from the n=2 state is:
🔴 ① 3.4 eV
🟢 ② 10.2 eV
🟡 ③ 6.8 eV
🔵 ④ 27.2 eV
🟢 Answer: ① 3.4 eV
📘 Exam: JEE Advanced
📅 Year: 2012 | Paper: 1 | Conducted by: IIT Delhi

🔵 Question 3:
The de Broglie wavelength of an electron moving with kinetic energy of 150 eV is close to:
🔴 ① 1.0 Å
🟢 ② 1.0 nm
🟡 ③ 0.1 Å
🔵 ④ 10 Å
🟢 Answer: ① 1.0 Å
📘 Exam: JEE Advanced
📅 Year: 2013 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 4:
If the difference in energy between K and L shells of hydrogen atom is ΔE, then the frequency of radiation emitted when an electron jumps from L to K shell is:
🔴 ① ΔE/h
🟢 ② h/ΔE
🟡 ③ ΔE × h
🔵 ④ ΔE/c
🟢 Answer: ① ΔE/h
📘 Exam: JEE Advanced
📅 Year: 2009 | Paper: 1 | Conducted by: IIT Roorkee

🔵 Question 5:
Which of the following electronic transitions in hydrogen atom will give rise to the least energetic photon?
🔴 ① n=2 → n=1
🟢 ② n=3 → n=2
🟡 ③ n=4 → n=3
🔵 ④ n=5 → n=4
🟢 Answer: ④ n=5 → n=4
📘 Exam: JEE Advanced
📅 Year: 2016 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 6:
The uncertainty in position of an electron is 5.3 × 10⁻¹¹ m. The uncertainty in its momentum will be at least (h=6.6×10⁻³⁴ Js):
🔴 ① 6.6×10⁻²⁴ kg m/s
🟢 ② 1.0×10⁻²⁴ kg m/s
🟡 ③ 3.1×10⁻²⁴ kg m/s
🔵 ④ 9.9×10⁻²⁴ kg m/s
🟢 Answer: ① 6.6×10⁻²⁴ kg m/s
📘 Exam: JEE Advanced
📅 Year: 2014 | Paper: 1 | Conducted by: IIT Kanpur

🔵 Question 7:
The ratio of the longest wavelength limits of Lyman and Balmer series of hydrogen is:
🔴 ① 1:4
🟢 ② 1:3
🟡 ③ 1:2
🔵 ④ 1:9
🟢 Answer: ② 1:3
📘 Exam: JEE Advanced
📅 Year: 2011 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 8:
Which of the following sets of quantum numbers is not allowed?
🔴 ① n=3, l=0, m=0
🟢 ② n=2, l=2, m=0
🟡 ③ n=2, l=1, m=1
🔵 ④ n=4, l=3, m=–2
🟢 Answer: ② n=2, l=2, m=0
📘 Exam: JEE Advanced
📅 Year: 2017 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 9:
The spectral lines observed in the hydrogen spectrum are due to:
🔴 ① Transitions of protons between nuclear levels
🟢 ② Transitions of neutrons
🟡 ③ Transitions of electrons between energy levels
🔵 ④ Vibrations of atoms
🟢 Answer: ③ Transitions of electrons between energy levels
📘 Exam: JEE Advanced
📅 Year: 2010 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 10:
The azimuthal quantum number l for the last electron in ground-state configuration of nitrogen atom is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ② 1
📘 Exam: JEE Advanced
📅 Year: 2015 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 11:
The maximum number of electrons that can have the principal quantum number n=3 is:
🔴 ① 8
🟢 ② 18
🟡 ③ 10
🔵 ④ 32
🟢 Answer: ② 18
📘 Exam: JEE Advanced
📅 Year: 2011 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 12:
Which of the following orbitals will have spherical symmetry?
🔴 ① p-orbital
🟢 ② s-orbital
🟡 ③ d-orbital
🔵 ④ f-orbital
🟢 Answer: ② s-orbital
📘 Exam: JEE Advanced
📅 Year: 2013 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 13:
The number of radial nodes for 4s orbital is:
🔴 ① 1
🟢 ② 2
🟡 ③ 3
🔵 ④ 4
🟢 Answer: ② 2
📘 Exam: JEE Advanced
📅 Year: 2016 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 14:
The degeneracy of the energy level for hydrogen atom with principal quantum number n=3 is:
🔴 ① 9
🟢 ② 18
🟡 ③ 6
🔵 ④ 3
🟢 Answer: ① 9
📘 Exam: JEE Advanced
📅 Year: 2018 | Paper: 1 | Conducted by: IIT Kanpur

🔵 Question 15:
The orbital angular momentum of an electron in the 3rd orbit of hydrogen atom is:
🔴 ① h/2π
🟢 ② 2h/2π
🟡 ③ 3h/2π
🔵 ④ √l(l+1)h/2π
🟢 Answer: ③ 3h/2π
📘 Exam: JEE Advanced
📅 Year: 2007 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 16:
Which of the following is a valid value of magnetic quantum number m for l=2?
🔴 ① 3
🟢 ② –2
🟡 ③ 0
🔵 ④ Both ② and ③
🟢 Answer: ④ Both –2 and 0
📘 Exam: JEE Advanced
📅 Year: 2012 | Paper: 1 | Conducted by: IIT Delhi

🔵 Question 17:
The frequency of the radiation emitted when an electron in hydrogen atom undergoes transition from level n=4 to n=2 is (R = Rydberg constant, c = speed of light):
🔴 ① Rc(1/4 – 1/16)
🟢 ② Rc(1/2 – 1/4)
🟡 ③ Rc(1/2 – 1/16)
🔵 ④ Rc(1/4 – 1/9)
🟢 Answer: ② Rc(1/2 – 1/4)
📘 Exam: JEE Advanced
📅 Year: 2015 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 18:
The ratio of velocities of electrons in the first Bohr orbit of hydrogen atom and in the first Bohr orbit of Li²⁺ ion is:
🔴 ① 1 : 3
🟢 ② 1 : 9
🟡 ③ 3 : 1
🔵 ④ 9 : 1
🟢 Answer: ① 1 : 3
📘 Exam: JEE Advanced
📅 Year: 2011 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 19:
The number of spectral lines obtained in the Lyman series when an electron jumps from n=5 to n=1 is:
🔴 ① 4
🟢 ② 6
🟡 ③ 10
🔵 ④ 5
🟢 Answer: ② 6
📘 Exam: JEE Advanced
📅 Year: 2009 | Paper: 1 | Conducted by: IIT Roorkee

🔵 Question 20:
Which among the following orbitals has the maximum number of angular nodes?
🔴 ① 4s
🟢 ② 4p
🟡 ③ 4d
🔵 ④ 4f
🟢 Answer: ④ 4f
📘 Exam: JEE Advanced
📅 Year: 2014 | Paper: 1 | Conducted by: IIT Kanpur

🔵 Question 21:
The principal quantum number of the last electron in sodium atom is:
🔴 ① 2
🟢 ② 3
🟡 ③ 4
🔵 ④ 5
🟢 Answer: ② 3
📘 Exam: JEE Advanced
📅 Year: 2010 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 22:
The correct order of energy of orbitals according to (n + l) rule is:
🔴 ① 4s < 3d < 4p
🟢 ② 3d < 4s < 4p
🟡 ③ 4p < 3d < 4s
🔵 ④ 4s < 4p < 3d
🟢 Answer: ① 4s < 3d < 4p
📘 Exam: JEE Advanced
📅 Year: 2017 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 23:
The correct expression for the radius of nth Bohr orbit of a hydrogen-like species (atomic number Z) is:
🔴 ① a₀ n² / Z
🟢 ② a₀ Z² / n
🟡 ③ a₀ n / Z²
🔵 ④ a₀ / (n²Z)
🟢 Answer: ① a₀ n² / Z
📘 Exam: JEE Advanced
📅 Year: 2013 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 24:
The line in the emission spectrum of hydrogen corresponding to the transition n=3 to n=2 belongs to:
🔴 ① Lyman series
🟢 ② Balmer series
🟡 ③ Paschen series
🔵 ④ Brackett series
🟢 Answer: ② Balmer series
📘 Exam: JEE Advanced
📅 Year: 2007 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 25:
If the electronic configuration of an element is 1s² 2s² 2p⁶ 3s² 3p³, the total number of unpaired electrons is:
🔴 ① 2
🟢 ② 3
🟡 ③ 1
🔵 ④ 0
🟢 Answer: ② 3
📘 Exam: JEE Advanced
📅 Year: 2016 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 26:
The energy of an electron in the third Bohr orbit of hydrogen atom is:
🔴 ① –13.6 eV
🟢 ② –1.51 eV
🟡 ③ –3.4 eV
🔵 ④ –0.85 eV
🟢 Answer: ② –1.51 eV
📘 Exam: JEE Advanced
📅 Year: 2011 | Paper: 1 | Conducted by: IIT Madras

🔵 Question 27:
The Bohr theory cannot explain the spectrum of:
🔴 ① H atom
🟢 ② He⁺ ion
🟡 ③ Li²⁺ ion
🔵 ④ Multielectron atoms
🟢 Answer: ④ Multielectron atoms
📘 Exam: JEE Advanced
📅 Year: 2012 | Paper: 1 | Conducted by: IIT Delhi

🔵 Question 28:
The angular momentum of an electron in the nth Bohr orbit is:
🔴 ① nh/π
🟢 ② nh/2π
🟡 ③ n²h/2π
🔵 ④ h/n
🟢 Answer: ② nh/2π
📘 Exam: JEE Advanced
📅 Year: 2018 | Paper: 1 | Conducted by: IIT Kanpur

🔵 Question 29:
The orbital which has no angular node is:
🔴 ① 1s
🟢 ② 2p
🟡 ③ 3d
🔵 ④ 4f
🟢 Answer: ① 1s
📘 Exam: JEE Advanced
📅 Year: 2010 | Paper: 1 | Conducted by: IIT Guwahati

🔵 Question 30:
The maximum number of electrons that can be accommodated in all orbitals with n=4 is:
🔴 ① 16
🟢 ② 32
🟡 ③ 18
🔵 ④ 20
🟢 Answer: ② 32
📘 Exam: JEE Advanced
📅 Year: 2009 | Paper: 1 | Conducted by: IIT Roorkee

🔵 Question 31:
The correct order of increasing energy of orbitals is:
🔴 ① 3p < 4s < 3d < 4p
🟢 ② 3p < 3d < 4s < 4p
🟡 ③ 3p < 4s < 4p < 3d
🔵 ④ 4s < 3p < 4p < 3d
🟢 Answer: ① 3p < 4s < 3d < 4p
📘 Exam: JEE Advanced
📅 Year: 2014 | Paper: 1 | Conducted by: IIT Kanpur

🔵 Question 32:
If n=4, the total number of possible orbitals is:
🔴 ① 4
🟢 ② 8
🟡 ③ 16
🔵 ④ 32
🟢 Answer: ③ 16
📘 Exam: JEE Advanced
📅 Year: 2015 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 33:
The energy of electron in nth orbit of hydrogen atom is given by:
🔴 ① –13.6/n² eV
🟢 ② –13.6 × n² eV
🟡 ③ –n/13.6 eV
🔵 ④ 13.6/n eV
🟢 Answer: ① –13.6/n² eV
📘 Exam: JEE Advanced
📅 Year: 2007 | Paper: 1 | Conducted by: IIT Bombay

🔵 Question 34:
The total number of nodes for 3p orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ③ 2
📘 Exam: JEE Advanced
📅 Year: 2018 | Paper: 1 | Conducted by: IIT Kanpur

PRACTICE SETS FROM THIS LESSON

🔵 Question 1:
Who proposed the “plum pudding model” of the atom?
🔴 ① Rutherford
🟢 ② J.J. Thomson
🟡 ③ Niels Bohr
🔵 ④ James Chadwick
🟢 Answer: ② J.J. Thomson
🎯 Difficulty: NEET

🔵 Question 2:
Which subatomic particle was discovered by Goldstein?
🔴 ① Proton
🟢 ② Neutron
🟡 ③ Electron
🔵 ④ Positron
🟢 Answer: ① Proton
🎯 Difficulty: NEET

🔵 Question 3:
The charge of an electron was determined by which experiment?
🔴 ① Rutherford’s scattering experiment
🟢 ② Millikan’s oil drop experiment
🟡 ③ Cathode ray experiment
🔵 ④ Canal ray experiment
🟢 Answer: ② Millikan’s oil drop experiment
🎯 Difficulty: NEET

🔵 Question 4:
The discovery of neutron was made by:
🔴 ① Goldstein
🟢 ② Chadwick
🟡 ③ Rutherford
🔵 ④ Bohr
🟢 Answer: ② Chadwick
🎯 Difficulty: NEET

🔵 Question 5:
Which of the following has a mass nearly equal to that of a proton?
🔴 ① Electron
🟢 ② Neutron
🟡 ③ Positron
🔵 ④ Alpha particle
🟢 Answer: ② Neutron
🎯 Difficulty: NEET

🔵 Question 6:
The radius of the nucleus is of the order of:
🔴 ① 10⁻¹⁰ m
🟢 ② 10⁻¹⁴ m
🟡 ③ 10⁻¹² m
🔵 ④ 10⁻⁸ m
🟢 Answer: ② 10⁻¹⁴ m
🎯 Difficulty: NEET

🔵 Question 7:
Which model of the atom first introduced the concept of quantized energy levels?
🔴 ① Bohr’s model
🟢 ② Rutherford’s model
🟡 ③ Thomson’s model
🔵 ④ Quantum mechanical model
🟢 Answer: ① Bohr’s model
🎯 Difficulty: NEET

🔵 Question 8:
An electron revolves around the nucleus due to:
🔴 ① Nuclear force
🟢 ② Electrostatic attraction
🟡 ③ Gravitational force
🔵 ④ Weak force
🟢 Answer: ② Electrostatic attraction
🎯 Difficulty: NEET

🔵 Question 9:
The angular momentum of an electron in Bohr’s orbit is quantized in integral multiples of:
🔴 ① h
🟢 ② h/2π
🟡 ③ hν
🔵 ④ hc
🟢 Answer: ② h/2π
🎯 Difficulty: NEET

🔵 Question 10:
The spectral line series observed in the visible region of hydrogen spectrum is:
🔴 ① Lyman
🟢 ② Balmer
🟡 ③ Paschen
🔵 ④ Brackett
🟢 Answer: ② Balmer
🎯 Difficulty: NEET

🔵 Question 11:
Which quantum number describes the orientation of an orbital?
🔴 ① Principal (n)
🟢 ② Azimuthal (l)
🟡 ③ Magnetic (mₗ)
🔵 ④ Spin (s)
🟢 Answer: ③ Magnetic (mₗ)
🎯 Difficulty: NEET

🔵 Question 12:
The maximum number of electrons that can be accommodated in an orbital is:
🔴 ① 1
🟢 ② 2
🟡 ③ 3
🔵 ④ 4
🟢 Answer: ② 2
🎯 Difficulty: NEET

🔵 Question 13:
The energy of an electron in the first Bohr orbit of hydrogen atom is:
🔴 ① –13.6 eV
🟢 ② –3.4 eV
🟡 ③ –1.51 eV
🔵 ④ –0.85 eV
🟢 Answer: ① –13.6 eV
🎯 Difficulty: NEET

🔵 Question 14:
Which rule states that orbitals are filled in increasing order of (n + l) value?
🔴 ① Hund’s rule
🟢 ② Pauli’s principle
🟡 ③ Aufbau principle
🔵 ④ Heisenberg’s principle
🟢 Answer: ③ Aufbau principle
🎯 Difficulty: NEET

🔵 Question 15:
Which scientist proposed the uncertainty principle?
🔴 ① Schrodinger
🟢 ② Heisenberg
🟡 ③ Bohr
🔵 ④ Planck
🟢 Answer: ② Heisenberg
🎯 Difficulty: NEET

🔵 Question 16:
The value of Planck’s constant (h) is approximately:
🔴 ① 6.63 × 10⁻²⁷ erg·s
🟢 ② 6.63 × 10⁻³⁴ J·s
🟡 ③ 3 × 10⁸ m/s
🔵 ④ 9.1 × 10⁻³¹ kg
🟢 Answer: ② 6.63 × 10⁻³⁴ J·s
🎯 Difficulty: NEET

🔵 Question 17:
The energy of a photon is given by:
🔴 ① hv
🟢 ② hc/λ
🟡 ③ Both (①) and (②)
🔵 ④ mv²/2
🟢 Answer: ③ Both (①) and (②)
🎯 Difficulty: NEET

🔵 Question 18:
Which principle explains that no two electrons can have the same set of four quantum numbers?
🔴 ① Hund’s rule
🟢 ② Pauli exclusion principle
🟡 ③ Aufbau principle
🔵 ④ Bohr’s theory
🟢 Answer: ② Pauli exclusion principle
🎯 Difficulty: NEET

🔵 Question 19:
The number of orbitals present in the third shell (n = 3) is:
🔴 ① 3
🟢 ② 9
🟡 ③ 16
🔵 ④ 4
🟢 Answer: ② 9
🎯 Difficulty: NEET

🔵 Question 20:
The maximum number of electrons in a subshell with l = 2 is:
🔴 ① 2
🟢 ② 6
🟡 ③ 10
🔵 ④ 14
🟢 Answer: ③ 10
🎯 Difficulty: NEET

🔵 Question 21:
What is the wavelength of a particle of mass m moving with velocity v, according to de Broglie?
🔴 ① λ = h/mv
🟢 ② λ = mv/h
🟡 ③ λ = hc/E
🔵 ④ λ = hν
🟢 Answer: ① λ = h/mv
🎯 Difficulty: NEET

🔵 Question 22:
Which orbital has the shape of a dumbbell?
🔴 ① s orbital
🟢 ② p orbital
🟡 ③ d orbital
🔵 ④ f orbital
🟢 Answer: ② p orbital
🎯 Difficulty: NEET

🔵 Question 23:
The number of radial nodes in an orbital is given by:
🔴 ① n – l – 1
🟢 ② l – 1
🟡 ③ n + l
🔵 ④ 2l + 1
🟢 Answer: ① n – l – 1
🎯 Difficulty: NEET

🔵 Question 24:
In which region of electromagnetic spectrum does Lyman series lie?
🔴 ① Visible
🟢 ② Ultraviolet
🟡 ③ Infrared
🔵 ④ Microwave
🟢 Answer: ② Ultraviolet
🎯 Difficulty: NEET

🔵 Question 25:
Which spectral line corresponds to transition from n = 3 to n = 2 in hydrogen atom?
🔴 ① Hα line
🟢 ② Hβ line
🟡 ③ Lyman-α line
🔵 ④ Paschen-α line
🟢 Answer: ① Hα line
🎯 Difficulty: NEET

🔵 Question 26:
If the wavelength of a photon is doubled, its energy becomes:
🔴 ① Doubled
🟢 ② Halved
🟡 ③ Remains the same
🔵 ④ Becomes one-fourth
🟢 Answer: ② Halved
🎯 Difficulty: JEE Main

🔵 Question 27:
Which of the following sets of quantum numbers is not possible?
🔴 ① n = 3, l = 0, mₗ = 0, s = +½
🟢 ② n = 2, l = 2, mₗ = 1, s = –½
🟡 ③ n = 4, l = 1, mₗ = 0, s = +½
🔵 ④ n = 1, l = 0, mₗ = 0, s = –½
🟢 Answer: ② n = 2, l = 2, mₗ = 1, s = –½
🎯 Difficulty: JEE Main

🔵 Question 28:
The ratio of the velocity of an electron in the first orbit of hydrogen to that in the second orbit is:
🔴 ① 1:4
🟢 ② 2:1
🟡 ③ 4:1
🔵 ④ 1:2
🟢 Answer: ② 2:1
🎯 Difficulty: JEE Main

🔵 Question 29:
The ionization energy of hydrogen atom in the ground state is 13.6 eV. The energy required to excite it from n = 1 to n = 3 is:
🔴 ① 12.09 eV
🟢 ② 10.2 eV
🟡 ③ 1.51 eV
🔵 ④ 3.4 eV
🟢 Answer: ① 12.09 eV
🎯 Difficulty: JEE Main

🔵 Question 30:
For hydrogen-like species, the radius of the nth orbit is proportional to:
🔴 ① n²/Z
🟢 ② Z/n²
🟡 ③ n/Z²
🔵 ④ n²Z
🟢 Answer: ① n²/Z
🎯 Difficulty: JEE Main

🔵 Question 31:
The frequency of radiation emitted when electron falls from n = 4 to n = 2 in hydrogen atom is (R = Rydberg constant):
🔴 ① (3Rhc/16)
🟢 ② (Rhc/4)
🟡 ③ (3Rhc/4)
🔵 ④ (5Rhc/16)
🟢 Answer: ① (3Rhc/16)
🎯 Difficulty: JEE Main

🔵 Question 32:
Number of orbitals with n = 4 and l = 2 is:
🔴 ① 3
🟢 ② 5
🟡 ③ 7
🔵 ④ 9
🟢 Answer: ② 5
🎯 Difficulty: JEE Main

🔵 Question 33:
The degeneracy of the third energy level (n = 3) is:
🔴 ① 9
🟢 ② 18
🟡 ③ 16
🔵 ④ 36
🟢 Answer: ① 9
🎯 Difficulty: JEE Main

🔵 Question 34:
Which orbital will have maximum penetration power?
🔴 ① 2s
🟢 ② 2p
🟡 ③ 3s
🔵 ④ 3p
🟢 Answer: ① 2s
🎯 Difficulty: JEE Main

🔵 Question 35:
The number of radial nodes in 4p orbital is:
🔴 ① 0
🟢 ② 1
🟡 ③ 2
🔵 ④ 3
🟢 Answer: ② 1
🎯 Difficulty: JEE Main

🔵 Question 36:
Which transition in the hydrogen atom will emit radiation of the shortest wavelength?
🔴 ① n = 3 → n = 2
🟢 ② n = 2 → n = 1
🟡 ③ n = 4 → n = 2
🔵 ④ n = 5 → n = 4
🟢 Answer: ② n = 2 → n = 1
🎯 Difficulty: JEE Main

🔵 Question 37:
The uncertainty in position of an electron is 1 Å. The minimum uncertainty in its momentum will be (h = 6.6 × 10⁻³⁴ Js):
🔴 ① 5.3 × 10⁻²⁴ kg·m/s
🟢 ② 5.3 × 10⁻²⁵ kg·m/s
🟡 ③ 1.1 × 10⁻²⁴ kg·m/s
🔵 ④ 6.6 × 10⁻²⁵ kg·m/s
🟢 Answer: ① 5.3 × 10⁻²⁴ kg·m/s
🎯 Difficulty: JEE Main

🔵 Question 38:
Which orbital among the following is spherical in shape?
🔴 ① 3s
🟢 ② 2p
🟡 ③ 3d
🔵 ④ 4f
🟢 Answer: ① 3s
🎯 Difficulty: JEE Main

🔵 Question 39:
How many radial and angular nodes are present in 3d orbital?
🔴 ① Radial = 0, Angular = 2
🟢 ② Radial = 1, Angular = 2
🟡 ③ Radial = 2, Angular = 1
🔵 ④ Radial = 1, Angular = 1
🟢 Answer: ① Radial = 0, Angular = 2
🎯 Difficulty: JEE Main

🔵 Question 40:
The azimuthal quantum number (l) for an orbital with magnetic quantum numbers mₗ = –2, –1, 0, +1, +2 is:
🔴 ① 1
🟢 ② 2
🟡 ③ 3
🔵 ④ 4
🟢 Answer: ② 2
🎯 Difficulty: JEE Main

🚀 Advanced-level (Q41–Q50):

🔵 Question 41:
If the ratio of de Broglie wavelengths of an electron to a proton is 1836:1, both having same kinetic energy, then the ratio of their momenta is:
🔴 ① 1:1836
🟢 ② 1836:1
🟡 ③ 1:1
🔵 ④ Cannot be determined
🟢 Answer: ② 1836:1
🎯 Difficulty: JEE Advanced

🔵 Question 42:
For hydrogen-like ion He⁺, the energy required to remove an electron from n = 2 is:
🔴 ① 54.4 eV
🟢 ② 13.6 eV
🟡 ③ 3.4 eV
🔵 ④ 6.8 eV
🟢 Answer: ④ 6.8 eV
🎯 Difficulty: JEE Advanced

🔵 Question 43:
Which of the following orbitals has zero radial node?
🔴 ① 1s
🟢 ② 2p
🟡 ③ 2s
🔵 ④ 3p
🟢 Answer: ① 1s
🎯 Difficulty: JEE Advanced

🔵 Question 44:
Calculate the wavelength (in nm) of photon emitted when electron in hydrogen jumps from n = 3 to n = 2. (R = 1.097 × 10⁷ m⁻¹)
🔴 ① 656 nm
🟢 ② 486 nm
🟡 ③ 434 nm
🔵 ④ 410 nm
🟢 Answer: ① 656 nm
🎯 Difficulty: JEE Advanced

🔵 Question 45:
For n = 4 shell, the number of possible orbitals is:
🔴 ① 16
🟢 ② 32
🟡 ③ 8
🔵 ④ 9
🟢 Answer: ① 16
🎯 Difficulty: JEE Advanced

🔵 Question 46:
The probability of finding an electron at the nucleus is maximum for:
🔴 ① 1s orbital
🟢 ② 2p orbital
🟡 ③ 3d orbital
🔵 ④ 4f orbital
🟢 Answer: ① 1s orbital
🎯 Difficulty: JEE Advanced

🔵 Question 47:
The energy of electron in the nth orbit of hydrogen atom is proportional to:
🔴 ① –1/n²
🟢 ② 1/n
🟡 ③ –n²
🔵 ④ 1/n²
🟢 Answer: ① –1/n²
🎯 Difficulty: JEE Advanced

🔵 Question 48:
If uncertainty in position of an electron is 5.3 × 10⁻¹¹ m, the uncertainty in its velocity will be approximately:
(mass of electron = 9.1 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ Js)
🔴 ① 3.5 × 10³ m/s
🟢 ② 1.2 × 10⁴ m/s
🟡 ③ 2.1 × 10³ m/s
🔵 ④ 5.0 × 10⁴ m/s
🟢 Answer: ② 1.2 × 10⁴ m/s
🎯 Difficulty: JEE Advanced

🔵 Question 49:
Which one among the following is NOT consistent with Bohr’s theory?
🔴 ① Energy levels are quantized
🟢 ② Electron revolves in definite orbits
🟡 ③ Electrons radiate energy in stationary orbits
🔵 ④ Angular momentum is quantized
🟢 Answer: ③ Electrons radiate energy in stationary orbits
🎯 Difficulty: JEE Advanced

🔵 Question 50:
For hydrogen atom, the ratio of energies of electron in n = 1 and n = 2 is:
🔴 ① 1:2
🟢 ② 4:1
🟡 ③ 2:1
🔵 ④ 1:4
🟢 Answer: ② 4:1
🎯 Difficulty: JEE Advanced

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Class 11 : Chemistry (In English) – Chapter 2: Structure of Atom Chapter

EXPLANATION & SUMMARY

QUESTIONS FROM TEXTBOOK

OTHER IMPORTANT QUESTIONS FOR EXAMS

NEET QUESTIONS FROM THIS LESSON

JEE MAINS QUESTIONS FROM THIS LESSON

JEE ADVANCED QUESTIONS FROM THIS LESSON

PRACTICE SETS FROM THIS LESSON

MISCONCEPTIONS “ALERTS”

KNOWLEDGE WITH FUN

MNEMONICS

ONE PAGE REVISION SHEET

MIND MAPS

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