Chapter 13: Nuclei Long Questions | physics Class 12 CBSE

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Chapter 13: Nuclei Long Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Explain the concept of binding energy per nucleon. Describe the main features of the Ebn versus mass number curve and discuss the conclusions drawn from it regarding nuclear stability, fission, and fusion.

Binding energy per nucleon Ebn = Eb/A is the average energy needed per nucleon to disintegrate the nucleus; a higher Ebn means a more stable nucleus.
The curve is nearly flat at ~8 MeV for 30 < A < 170, peaks near A = 56 (Fe) at ~8.75 MeV, and drops for both very light (A < 30) and very heavy (A > 170) nuclei.
Heavy nuclei (A > 170) have lower Ebn, so when they undergo fission into intermediate fragments they move to higher Ebn, releasing energy (~200 MeV for uranium fission).
Light nuclei (A ≤ 10) have lower Ebn, so when they fuse into a heavier nucleus the Ebn increases, releasing energy (e.g., ~26.7 MeV in the proton-proton cycle).
The constancy of Ebn in the middle range reflects the saturation property of nuclear force; peaks at ⁴He and ¹⁶O suggest shell structure inside the nucleus.

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Question 2

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Describe the properties of nuclear force. How does it differ from Coulomb force and gravitational force in terms of strength, range, and charge dependence?

Nuclear force is the strongest of the three forces: it is far stronger than the Coulomb force (which it must overcome) and enormously stronger than gravitational force.
Unlike Coulomb and gravitational forces which are long-range (proportional to 1/r²), the nuclear force is extremely short-ranged — it drops rapidly to zero beyond a few femtometres.
Nuclear force is charge-independent: the neutron-neutron, proton-neutron, and proton-proton nuclear interactions are approximately equal; Coulomb force only acts between charges.
The nuclear force is attractive for separations greater than ~0.8 fm and becomes strongly repulsive below ~0.8 fm, preventing nucleons from collapsing into each other.
There is no simple mathematical expression for the nuclear force, unlike the well-defined inverse square laws of Coulomb and gravitational forces.

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Question 3

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Describe the three types of radioactive decay. State the emission in each, and explain the conditions under which a nucleus is stable or unstable.

In alpha decay, a helium nucleus (⁴₂He) is emitted; the daughter nucleus has Z decreased by 2 and A decreased by 4 compared to the parent.
In beta decay, an electron (β⁻) or positron (β⁺) is emitted along with an antineutrino or neutrino; Z changes by ±1 while A remains the same.
In gamma decay, a nucleus in an excited state emits high-energy photons (gamma rays) to reach the ground state; neither Z nor A changes.
Nuclear stability depends on the neutron-to-proton (N/Z) ratio: for light nuclei this should be ~1:1, while for heavy nuclei it increases to ~3:2 to compensate for greater proton repulsion.
Only about 10% of known isotopes are stable; nuclei with N/Z deviating from the stability curve are radioactive and undergo decay to approach stability.

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Question 4

Long Form

Explain nuclear fission with a suitable example. How is the energy released estimated using the binding energy per nucleon concept? Mention two practical applications.

Nuclear fission is the splitting of a heavy nucleus (e.g., ²³⁵₉₂U) upon neutron capture into two intermediate-mass radioactive fragments, 2–4 neutrons, and large energy release.
Example: ²³⁵₉₂U + n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3n. The released neutrons can trigger further fissions, leading to a chain reaction.
A nucleus of A = 240 has Ebn ≈ 7.6 MeV; the two A = 120 fragments each have Ebn ≈ 8.5 MeV. The gain of ~0.9 MeV/nucleon over 240 nucleons gives ~216 MeV per fission.
In a nuclear reactor, controlled fission of uranium releases heat to generate steam and electricity — a peaceful application of fission energy.
In an atomic bomb, uncontrolled fission produces an explosive release of energy; fission of 1 kg of uranium generates about 10¹⁴ J, compared to 10⁷ J from burning 1 kg of coal.

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Question 5

Long Form

Describe nuclear fusion as the source of stellar energy. Outline the proton-proton cycle in the sun and calculate the net energy released per cycle.

Nuclear fusion is the combination of two light nuclei to form a heavier, more tightly bound nucleus, releasing energy because the product's Ebn is higher than the reactants'.
In the sun, the proton-proton (p-p) cycle fuses four hydrogen nuclei into one ⁴He nucleus in a multi-step process at the solar core temperature of ~1.5 × 10⁷ K.
Steps: (i) p + p → ²H + e⁺ + ν (0.42 MeV), (ii) e⁺ + e⁻ → 2γ (1.02 MeV), (iii) ²H + p → ³He + γ (5.49 MeV), (iv) ³He + ³He → ⁴He + 2p (12.86 MeV).
The net reaction is: 4¹H → ⁴He + 2e⁺ + 2ν + 6γ with net energy release of ~26.7 MeV per cycle (combining 2(i) + 2(ii) + 2(iii) + (iv)).
The sun has enough hydrogen to sustain this process for another ~5 billion years; after hydrogen is depleted, helium fusion begins, eventually producing heavier elements up to those near the peak of the binding energy curve.

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Question 6

Long Form

Derive an expression for nuclear density and show that it is independent of mass number A. Compare it with the density of ordinary matter and comment on its significance.

Nuclear radius: R = R₀A^(1/3), so volume V = (4/3)πR³ = (4/3)πR₀³A. The volume is directly proportional to A.
Mass of nucleus M ≈ A × mₙ (each nucleon mass ≈ 1.67 × 10⁻²⁷ kg), so mass is also proportional to A.
Nuclear density ρ = M/V = (Amₙ) / ((4/3)πR₀³A) = mₙ / ((4/3)πR₀³), which is independent of A.
Substituting values: ρ ≈ 2.3 × 10¹⁷ kg/m³, which is about 10¹⁴ times the density of water (10³ kg/m³).
This enormous and constant nuclear density implies that all nuclei are like drops of incompressible nuclear fluid; matter in neutron stars is compressed to densities comparable to nuclear density.

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Question 7

Long Form

Explain mass defect and nuclear binding energy with the worked example of the oxygen-16 nucleus. How does Einstein's mass-energy relation connect the two concepts?

The mass defect ΔM of a nucleus is the difference between the sum of masses of all constituent nucleons and the actual nuclear mass: ΔM = [Zmp + (A–Z)mn] – M.
For ¹⁶₈O: sum of masses = 8×1.00866 + 8×1.00727 + 8×0.00055 = 16.12744 u; experimental atomic mass = 15.99493 u; after subtracting 8 electron masses, nuclear mass = 15.99053 u.
Mass defect ΔM = 16.12744 – 15.99053 = 0.13691 u. Since 1 u = 931.5 MeV/c², the binding energy Eb = 0.13691 × 931.5 ≈ 127.5 MeV.
By Einstein's relation E = mc², this mass defect is the energy equivalent that must be supplied to completely disassemble the nucleus into its 16 free nucleons.
Conversely, 127.5 MeV of energy is released when 8 protons and 8 neutrons combine to form the oxygen-16 nucleus; this is the nuclear binding energy, Eb = ΔMc².

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Question 8

Long Form

Discuss the discovery of the neutron by Chadwick. Why was the existence of electrons in the nucleus ruled out? What is the composition of the nucleus according to modern understanding?

Chadwick (1932) bombarded beryllium with alpha particles and found neutral radiation that could eject protons from light nuclei; he showed this could not be photons because energy-momentum conservation would require impossibly high photon energies.
He concluded the radiation was a new neutral particle — the neutron — with mass nearly equal to that of a proton (1.00866 u); he won the Nobel Prize in 1935 for this discovery.
Earlier, it was thought the nucleus might contain electrons; this was ruled out by quantum theory (confinement of an electron in nuclear dimensions would require energies far exceeding observed beta-decay energies).
The modern nucleus consists of Z protons and N = (A–Z) neutrons, where A is the mass number. Protons and neutrons are collectively called nucleons.
A free neutron is unstable (mean life ~1000 s, decays to proton + electron + antineutrino) but is stable when bound inside a nucleus due to the nuclear force.

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Question 9

Long Form

Analyse why mass-energy interconversion occurs in chemical reactions as well as nuclear reactions, yet the two are considered fundamentally different in terms of energy scale.

In both chemical and nuclear reactions, the total rest mass of products differs slightly from that of reactants; this mass difference (mass defect) is converted into or from energy via E = mc².
In nuclear reactions, the binding energy change is due to nuclear forces; in chemical reactions, it is due to changes in chemical (electronic) binding energies between atoms and molecules.
The mass defects in chemical reactions are nearly a million times smaller than those in nuclear reactions, leading to energy releases of electron-volts (chemical) vs. mega-electron-volts (nuclear).
Therefore, the general impression that mass-energy interconversion does not occur in chemistry is technically incorrect — it occurs in both, just at vastly different scales.
Nuclear processes are about 10⁶ times more energetic than chemical processes per unit mass, which explains why nuclear fuels are so vastly superior to chemical fuels for energy production.

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Question 10

Long Form

Explain the concept of isotopes, isobars, and isotones. How does isotope existence relate to the structure of the nucleus? Why do isotopes of an element have identical chemical properties?

Isotopes have the same Z (proton number) but different A (mass number) due to varying neutron count: e.g., ¹H, ²H, ³H are isotopes of hydrogen with 0, 1, and 2 neutrons respectively.
Isobars have the same A but different Z: e.g., ³₁H and ³₂He both have A = 3 but differ in their proton-neutron composition.
Isotones share the same neutron number N but different Z: e.g., ¹⁹⁸₈₀Hg and ¹⁹⁷₇₉Au both have N = 118.
Isotope existence demonstrates that protons and neutrons are independent nuclear components; adding neutrons changes nuclear mass and stability without changing the element's identity.
Chemical properties depend entirely on the number of electrons, which equals Z; since isotopes have identical Z, they have the same electron configuration and thus identical chemical behaviour, though they occupy the same position in the periodic table.

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Chapter 13: Nuclei | Long Questions

Explain the concept of binding energy per nucleon. Describe the main features of the Ebn versus mass number curve and discuss the conclusions drawn from it regarding nuclear stability, fission, and fusion.

Describe the properties of nuclear force. How does it differ from Coulomb force and gravitational force in terms of strength, range, and charge dependence?

Describe the three types of radioactive decay. State the emission in each, and explain the conditions under which a nucleus is stable or unstable.

Explain nuclear fission with a suitable example. How is the energy released estimated using the binding energy per nucleon concept? Mention two practical applications.

Describe nuclear fusion as the source of stellar energy. Outline the proton-proton cycle in the sun and calculate the net energy released per cycle.

Derive an expression for nuclear density and show that it is independent of mass number A. Compare it with the density of ordinary matter and comment on its significance.

Explain mass defect and nuclear binding energy with the worked example of the oxygen-16 nucleus. How does Einstein's mass-energy relation connect the two concepts?

Discuss the discovery of the neutron by Chadwick. Why was the existence of electrons in the nucleus ruled out? What is the composition of the nucleus according to modern understanding?

Analyse why mass-energy interconversion occurs in chemical reactions as well as nuclear reactions, yet the two are considered fundamentally different in terms of energy scale.

Explain the concept of isotopes, isobars, and isotones. How does isotope existence relate to the structure of the nucleus? Why do isotopes of an element have identical chemical properties?

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