Physics Class 12 Modern Physics Atom Nuclei Questions for AGNIVEER NAVY

Bohr Model of Atom

Bohr proposed that electrons orbit the nucleus in fixed energy levels (shells) without radiating energy. Each orbit has a specific radius and energy. Electrons jump between orbits by absorbing or emitting photons. This model works perfectly for hydrogen but fails for multi-electron atoms. Think of it like planets orbiting the sun at fixed distances — stable, predictable, no spiraling inward.

• Electrons exist in discrete energy levels (n = 1, 2, 3...)
• Lowest energy level (n=1) is ground state; higher levels are excited states
• Energy difference between levels determines photon frequency emitted/absorbed
• Radius of nth orbit: r_n = 0.53 × n² Angstroms (for hydrogen)
• Model explains hydrogen spectrum but fails for helium and beyond
• Angular momentum is quantized: L = n × h/2π

Nuclear Structure and Stability

The nucleus contains protons (positive charge) and neutrons (neutral). Protons determine atomic number Z; total nucleons (protons + neutrons) give mass number A. Nuclei are held together by the strong nuclear force, which is short-range but very powerful. Stability depends on the neutron-to-proton ratio. Light nuclei are stable near N=Z; heavy nuclei need more neutrons (N > Z) to overcome proton repulsion.

• Atomic number Z = number of protons
• Mass number A = protons + neutrons
• Neutron number N = A - Z
• Stable nuclei follow the valley of beta stability (N/Z ratio ~1 for light, ~1.5 for heavy)
• Nuclei with Z > 83 (bismuth) are inherently unstable and radioactive
• Magic numbers (2, 8, 20, 50, 82, 126) indicate extra stability — like closed electron shells

Radioactivity and Decay Modes

Unstable nuclei spontaneously emit radiation to reach stability. Three main types: alpha decay (He-4 nucleus), beta decay (electron or positron), and gamma decay (photon). Each changes the nucleus composition. Alpha decay reduces A by 4 and Z by 2. Beta-minus decay increases Z by 1 (neutron becomes proton). Gamma decay releases energy without changing A or Z. Think of it as the nucleus 'shedding weight' or 'rebalancing' to find stability.

• Alpha decay: Heavy nucleus ejects He-4 (2 protons, 2 neutrons); A decreases by 4, Z by 2
• Beta-minus decay: Neutron converts to proton + electron; Z increases by 1, A unchanged
• Beta-plus decay: Proton converts to neutron + positron; Z decreases by 1, A unchanged
• Gamma decay: Nucleus releases high-energy photon; A and Z unchanged
• Decay is random and spontaneous; rate follows exponential decay law
• Half-life is the time for half the sample to decay — independent of initial amount

Binding Energy and Mass Defect

When nucleons bind together, the nucleus mass is slightly less than the sum of individual proton and neutron masses. This 'missing mass' is the mass defect, converted to binding energy via E=mc². Binding energy per nucleon indicates nuclear stability — higher value means more stable. Iron-56 has the highest binding energy per nucleon, making it the most stable nucleus. This is why fusion of light nuclei and fission of heavy nuclei both release energy.

• Mass defect: Δm = (Z × m_p + N × m_n) - m_nucleus
• Binding energy: BE = Δm × c² (in joules or MeV)
• Binding energy per nucleon: BE/A indicates stability
• Higher BE/A = more stable nucleus
• Iron-56 is the peak of stability (BE/A ≈ 8.8 MeV)
• Fusion (light nuclei) and fission (heavy nuclei) both increase average BE/A, releasing energy

Nuclear Reactions and Conservation Laws

In nuclear reactions, mass number A and atomic number Z are conserved. When a nucleus is bombarded by a particle (alpha, neutron, proton), it may absorb and emit particles, or split. Common notation: Target(projectile, ejectile)Product. For example, N-14(n,p)C-14 means nitrogen-14 absorbs a neutron and emits a proton, becoming carbon-14. Energy is released or absorbed based on the Q-value (difference in binding energies).

• Conservation of mass number: A_initial = A_final
• Conservation of atomic number: Z_initial = Z_final
• Reaction notation: Target(projectile, ejectile)Product
• Q-value = (initial mass - final mass) × c² (positive = exothermic, negative = endothermic)
• Threshold energy needed for endothermic reactions to occur
• Common reactions: (n,p), (n,α), (p,n), (α,p), fission, fusion

• Confusing mass number A with atomic number Z. Remember: A = protons + neutrons; Z = protons only. Isotopes have same Z but different A.
• Forgetting that in alpha decay, both A and Z decrease. Students often only decrease one. Alpha is He-4: loses 2 protons and 2 neutrons.
• Misapplying the half-life formula. After n half-lives, remaining fraction is (1/2)^n, not 1 - n/2. After 3 half-lives, 1/8 remains, not 1/2.
• Mixing up binding energy with mass defect. Mass defect is the missing mass (in u or kg); binding energy is that mass converted to energy (in joules or MeV).
• Ignoring conservation laws in nuclear reactions. Always check that A and Z balance on both sides. A common trap is forgetting to account for the emitted particle.

• ABZN: A = mass number, B = binding energy, Z = atomic number, N = neutron count. Use this to organize nuclear data.
• Bohr's Orbits: Like a parking lot — cars (electrons) park at fixed spots (n=1,2,3...), not in between. Jump to a closer spot, emit light; jump to farther spot, absorb light.
• Decay Modes: Alpha = Heavy loss (He-4 nucleus), Beta = Charge change (electron out), Gamma = Energy only (photon). Think A-B-G.
• Half-life Halving: After each half-life, divide by 2. After 1 half-life: 50%. After 2: 25%. After 3: 12.5%. It's exponential, not linear.
• BE/A Peak: Iron-56 is the 'sweet spot' of nuclear stability. Light nuclei fuse toward Fe-56; heavy nuclei fission toward Fe-56. Both release energy.

• Agniveer Navy papers often include 1-2 half-life calculation problems. Practice converting between half-life, decay constant, and remaining nuclei. Time pressure is real — memorize the formula and practice substitution.
• Bohr model questions usually ask for energy transitions or ionization energy. Know E_n = -13.6/n² eV for hydrogen. Expect 1-2 MCQs on this per paper.
• Nuclear reaction balancing is a frequent trap. Always write out the reaction and check A and Z on both sides. Examiners love asking what particle is emitted or what nucleus is produced.
• Binding energy per nucleon comparisons appear in conceptual questions. Memorize that Fe-56 has the highest BE/A (~8.8 MeV). Use this to explain why fusion and fission release energy.
• Recent Agniveer papers (2022-2024) show increased focus on numerical problems over pure theory. Expect 60% calculations, 40% concepts. Bring a calculator and practice unit conversions (u to MeV, hours to years for half-life).