NEET Atoms and Nuclei PYQs | 2013–2025

2025

Q1. Calculate the binding energy per nucleon of a nucleus with mass defect 0.008 u and mass number A = 4.

Q2. Explain the Bohr model of the hydrogen atom and derive the expression for allowed energy levels.

Q3. A nucleus emits an alpha particle of 5 MeV. Calculate the recoil energy of the daughter nucleus if its mass is 60 u.

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2024

Q1. Derive the expression for the radius of the nth orbit of the hydrogen atom using Bohr’s theory.

Q2. Define mass defect and binding energy. Calculate the energy released when 1 g of uranium-235 undergoes fission, given Δm = 0.9 u per nucleus.

Q3. Explain why nuclei with even numbers of protons and neutrons are more stable.

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2023

Q1. Derive the expression for the velocity of an electron in the nth orbit of hydrogen.

Q2. Explain radioactivity and differentiate between alpha, beta, and gamma decay.

Q3. A sample of radioactive substance has a half-life of 10 hours. Calculate the decay constant and the remaining fraction after 30 hours.

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2022

Q1. Calculate the energy of the photon emitted when an electron in hydrogen atom transitions from n = 3 to n = 2.

Q2. Define half-life and mean life of a radioactive isotope and derive the relation between them.

Q3. Explain the concept of nuclear fission and give one example.

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2021

Q1. Derive the expression for the angular momentum of an electron in Bohr’s orbit.

Q2. A 2 g sample of a radioactive isotope has a half-life of 5 hours. Find the number of nuclei remaining after 15 hours.

Q3. Explain the difference between nuclear fission and fusion.

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2020

Q1. Derive the expression for the total energy of an electron in the nth Bohr orbit.

Q2. Calculate the binding energy of helium-4 nucleus, given masses of proton = 1.007 u, neutron = 1.009 u, and He-4 = 4.002 u.

Q3. Explain the process of beta decay and the conservation laws involved.

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2019

Q1. Derive the Rydberg formula for the spectral lines of hydrogen atom.

Q2. Calculate the decay constant of a radioactive isotope with a half-life of 12 days.

Q3. Explain why nuclear fusion is the source of energy in stars.

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2018

Q1. Derive the expression for the frequency of emitted radiation in a hydrogen atom transition.

Q2. Define mass defect and binding energy and explain their significance.

Q3. Discuss the concept of isotopes, isobars, and isotones with examples.

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2017

Q1. Calculate the wavelength of Lyman series line corresponding to transition n = 2 → n = 1.

Q2. Explain alpha decay using energy and momentum conservation.

Q3. Derive the expression for the energy levels in hydrogen-like atoms.

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2016

Q1. Derive the expression for the radius and velocity of an electron in Bohr’s nth orbit.

Q2. A radioactive sample has decay constant λ = 0.02 h⁻¹. Calculate its half-life.

Q3. Explain the process of nuclear fission and the role of neutrons in sustaining chain reaction.

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2015

Q1. Derive the expression for the frequency of emitted radiation during a transition in hydrogen atom.

Q2. Calculate the number of nuclei left after three half-lives of a radioactive sample.

Q3. Explain binding energy per nucleon curve and its significance in nuclear reactions.

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2014

Q1. Derive Bohr’s postulates for angular momentum quantization.

Q2. A uranium-235 nucleus releases 200 MeV in fission. Calculate the total energy released for 1 g of uranium.

Q3. Explain why light nuclei undergo fusion while heavy nuclei undergo fission.

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2013

Q1. Calculate the binding energy of a nucleus given the masses of constituent protons and neutrons.

Q2. Derive the relation between half-life and decay constant.

Q3. Explain Rutherford’s experiment and its significance in discovering the nucleus.

Atoms and Nuclei — Solutions (2025 → 2013)

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2025

Q1. Binding energy per nucleon:

• Mass defect Δm = 0.008 u, A = 4

$$E_b = \Delta m \cdot 931.5 \text{ MeV/u} = 0.008 \cdot 931.5 \approx 7.452 \text{ MeV (total)}$$Eb​=Δm⋅931.5 MeV/u=0.008⋅931.5≈7.452 MeV (total)

Binding energy per nucleon: $E_b/A = 7.452/4 \approx 1.863 \text{ MeV}$Eb​/A=7.452/4≈1.863 MeV

Q2. Bohr model energy levels:$$E_n = -\frac{13.6\text{ eV}}{n^2}, \quad n = 1,2,3\ldots$$En​=−n213.6 eV​,n=1,2,3…

• Electron orbits the nucleus in quantized circular orbits
• Angular momentum quantized: $L = n\hbar$L=nℏ

Q3. Alpha emission, recoil energy:$$E_{\text{recoil}} = \frac{m_\alpha}{m_d} E_\alpha = \frac{4}{60} \cdot 5\,\text{MeV} \approx 0.333\,\text{MeV}$$Erecoil​=md​mα​​Eα​=604​⋅5MeV≈0.333MeV

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2024

Q1. Radius of nth orbit:$$r_n = \frac{n^2 h^2}{4 \pi^2 m e^2} \cdot \frac{1}{Z} \quad (\text{for hydrogen, Z = 1})$$rn​=4π2me2n2h2​⋅Z1​(for hydrogen, Z = 1)

Q2. Mass defect Δm = 0.9 u per nucleus → Energy released:$$E = \Delta m \cdot N \cdot 931.5 \text{ MeV}, \quad N = \frac{1\,\text{g}}{235 \text{ g/mol}} \cdot N_A$$E=Δm⋅N⋅931.5 MeV,N=235 g/mol1g​⋅NA​

Q3. Even-even nuclei are more stable → pairing energy contributes positively.

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2023

Q1. Electron velocity in nth orbit:$$v_n = \frac{Ze^2}{2 \varepsilon_0 h n}$$vn​=2ε0​hnZe2​

Q2. Radioactivity:

• Alpha: Helium nucleus emitted
• Beta: electron/positron emitted
• Gamma: electromagnetic radiation

Q3. Radioactive decay: half-life T₁/₂ = 10 h, time t = 30 h$$N/N_0 = \left(\frac{1}{2}\right)^{t/T_{1/2}} = \left(\frac{1}{2}\right)^{30/10} = (1/2)^3 = 1/8$$N/N0​=(21​)t/T1/2​=(21​)30/10=(1/2)3=1/8

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2022

Q1. Hydrogen transition n = 3 → n = 2:$$E = 13.6 \left(\frac{1}{2^2} – \frac{1}{3^2}\right) = 13.6 \left(\frac{1}{4} – \frac{1}{9}\right) = 13.6 \cdot 5/36 \approx 1.89\,\text{eV}$$E=13.6(221​−321​)=13.6(41​−91​)=13.6⋅5/36≈1.89eV

Q2. Half-life T₁/₂ and mean life τ:$$\tau = 1/\lambda, \quad T_{1/2} = \ln 2 / \lambda \implies \tau = T_{1/2}/0.693$$τ=1/λ,T1/2​=ln2/λ⟹τ=T1/2​/0.693

Q3. Nuclear fission: heavy nucleus splits → energy released, example: U-235 + neutron → Ba + Kr + 3n + energy.

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2021

Q1. Angular momentum in Bohr orbit:$$L = m v r = n \hbar$$L=mvr=nℏ

Q2. Radioactive sample, half-life T₁/₂ = 5 h, t = 15 h → 3 half-lives → N = N₀/8

Q3. Nuclear fission: splitting heavy nuclei
Nuclear fusion: combining light nuclei

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2020

Q1. Total energy in nth Bohr orbit:$$E_n = -\frac{13.6 Z^2}{n^2}\, \text{eV}$$En​=−n213.6Z2​eV

Q2. He-4 binding energy:$$\Delta m = 2(1.007) + 2(1.009) – 4.002 = 0.021\,u$$Δm=2(1.007)+2(1.009)−4.002=0.021u $$E_b = 0.021 \cdot 931.5 \approx 19.56 \text{ MeV}$$Eb​=0.021⋅931.5≈19.56 MeV

Q3. Beta decay: $n \to p + e^- + \bar{\nu}_e$n→p+e−+νˉe​, conserves charge, energy, momentum.

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2019

Q1. Rydberg formula:$$\frac{1}{\lambda} = R \left(\frac{1}{n_1^2} – \frac{1}{n_2^2}\right)$$λ1​=R(n12​1​−n22​1​)

Q2. Decay constant: λ = ln2 / T₁/₂ = 0.693 / 12 ≈ 0.05775 day⁻¹

Q3. Fusion in stars: Light nuclei combine → mass defect → energy released via E = Δmc²

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2018

Q1. Frequency of emitted radiation:$$\nu = \frac{E_i – E_f}{h}$$ν=hEi​−Ef​​

Q2. Mass defect Δm → Binding energy $E_b = \Delta m \cdot 931.5\,\text{MeV}$Eb​=Δm⋅931.5MeV

Q3. Isotopes: same Z, different A (C-12, C-14)
Isobars: same A, different Z (C-14, N-14)
Isotones: same N, different Z (C-14, N-15)

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2017

Q1. Lyman series n=2 → 1:$$\frac{1}{\lambda} = R \left(1 – \frac{1}{4}\right) = 3R/4 \implies \lambda = 1.216 \times 10^{-7}\,m$$λ1​=R(1−41​)=3R/4⟹λ=1.216×10−7m

Q2. Alpha decay: energy shared → daughter nucleus recoils

Q3. Hydrogen-like energy levels: $E_n = -13.6 Z^2/n^2$En​=−13.6Z2/n2

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2016

Q1. Bohr nth orbit:$$r_n = n^2 a_0 / Z, \quad v_n = \frac{Z e^2}{2 \varepsilon_0 h n}$$rn​=n2a0​/Z,vn​=2ε0​hnZe2​

Q2. Decay constant λ = 0.02 h⁻¹ → T₁/₂ = ln2 / λ = 34.65 h

Q3. Fission chain reaction: neutron induces splitting → more neutrons → energy release

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2015

Q1. Hydrogen transition frequency:$$\nu = \frac{E_i – E_f}{h}$$ν=hEi​−Ef​​

Q2. After 3 half-lives → remaining nuclei = N₀/8

Q3. Binding energy per nucleon curve → indicates energy released in fission (heavy nuclei) and fusion (light nuclei)

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2014

Q1. Bohr postulate: $m v r = n \hbar$mvr=nℏ

Q2. Uranium-235, 200 MeV per fission → number of nuclei in 1 g → total energy = 1 g × Avogadro number / molar mass × 200 MeV

Q3. Light nuclei → fusion, heavy nuclei → fission (stability via binding energy)

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2013

Q1. Binding energy: $E_b = \Delta m \cdot 931.5\,\text{MeV}$Eb​=Δm⋅931.5MeV

Q2. Half-life: $T_{1/2} = 0.693 / \lambda$T1/2​=0.693/λ

Q3. Rutherford experiment: alpha scattering → discovery of dense positive nucleus