Chapter 13: Nuclei Application Questions | physics Class 12 CBSE

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

Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 1

Applied Concept

A nuclear power plant uses the fission of uranium-235 to generate electricity. With reference to the binding energy per nucleon concept, explain why fission of U-235 releases energy and estimate the approximate energy per fission event.

U-235 (A ≈ 240) has a binding energy per nucleon of ~7.6 MeV; its fission products (A ≈ 120) have Ebn ≈ 8.5 MeV. The products are more tightly bound, and the excess binding energy is released.
The gain in binding energy per nucleon is ~0.9 MeV; over 240 nucleons, the total energy released is approximately 240 × 0.9 ≈ 216 MeV per fission event, which is of the order of 200 MeV.
This energy first appears as kinetic energy of fragments and neutrons, then converts to heat, which generates steam to drive turbines — the working principle of a nuclear power plant.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 2

Applied Concept

A student claims that nuclear density should vary with the size of the nucleus, increasing for heavier nuclei. Using the empirical formula for nuclear radius, show that this claim is incorrect.

The nuclear radius follows R = R₀A^(1/3), so nuclear volume V = (4/3)πR₀³A, which is proportional to A. The mass M ≈ A × mₙ is also proportional to A.
Density ρ = M/V = (Amₙ)/((4/3)πR₀³A) = mₙ/((4/3)πR₀³). Since A cancels out completely, ρ is a universal constant for all nuclei.
Numerically, ρ ≈ 2.3 × 10¹⁷ kg/m³ for all nuclei regardless of A. The student's claim is incorrect — nuclear density is constant and independent of the size or mass number of the nucleus.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 3

Applied Concept

During World War II, the first atomic bomb used uncontrolled fission. In contrast, nuclear reactors use controlled fission. With reference to the chain reaction process, explain the key difference between the two and the role of control rods.

In an atomic bomb, the fission chain reaction is uncontrolled — each fission releases ~3 neutrons that trigger more fissions in a rapidly multiplying (supercritical) chain, releasing enormous energy almost instantaneously.
In a nuclear reactor, control rods (made of neutron-absorbing material like boron or cadmium) are inserted to absorb excess neutrons so that on average exactly one neutron per fission event causes a new fission — maintaining a critical, steady chain reaction.
The controlled energy release in a reactor generates heat at a manageable rate, which is used to produce steam and generate electricity; uncontrolled release produces an explosive blast — the fundamental operational difference between a reactor and an atomic bomb.

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Application Question

Hard difficulty • Concept in a practical situation

Hard

Question 4

Applied Concept

A scientist proposes splitting an iron-56 nucleus into two aluminium-28 nuclei to generate energy. With reference to the binding energy per nucleon curve, evaluate whether this proposal is feasible.

Iron-56 lies near the peak of the Ebn vs A curve, with Ebn ≈ 8.75 MeV/nucleon — the highest binding energy per nucleon of all nuclei, making it the most stable nucleus.
Aluminium-28 (A = 28) lies on the lighter side of the curve with a lower Ebn. Splitting Fe-56 into two Al-28 fragments would move away from the peak to lower Ebn, meaning the products are less tightly bound.
Since the products have lower Ebn than the reactant, the process would require energy input rather than releasing it — the Q-value would be negative (endothermic). The proposal is not feasible as an energy source.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 5

Applied Concept

A carbon-14 nucleus is radioactive but carbon-12 is stable. Using the concept of neutron-to-proton ratio, explain this difference in stability.

Carbon-12 (Z = 6, N = 6) has a neutron-to-proton ratio of 1:1, which is within the stability range for light nuclei — hence it is stable.
Carbon-14 (Z = 6, N = 8) has a neutron-to-proton ratio of 8:6 = 4:3, which deviates from the 1:1 stability ratio for light nuclei. The excess neutrons make the nucleus unstable.
To achieve stability, C-14 undergoes beta-minus decay (a neutron converts to a proton), which decreases N and increases Z, moving the nucleus toward the N/Z ≈ 1 stability line. This radioactive property of C-14 is used in carbon dating.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 6

Applied Concept

In a hospital, radioactive isotopes are used for both diagnosis and therapy. Explain the basis of radioactivity and state the three types of emissions, relating each to their nature and penetrating power.

Radioactivity is the spontaneous disintegration of an unstable nucleus. It occurs because certain nuclei have neutron-to-proton ratios that deviate from the stability curve, causing them to emit radiation to reach a more stable configuration.
Alpha particles (⁴₂He nuclei) are the least penetrating — stopped by a sheet of paper or a few cm of air; beta particles (electrons/positrons) are more penetrating — stopped by a few mm of aluminium; gamma rays (high-energy photons) are the most penetrating — require several cm of lead or metres of concrete for shielding.
In medicine, gamma emitters (e.g., Tc-99m) are used for imaging because gamma rays penetrate tissue and can be detected outside the body; beta and gamma emitters are used in radiotherapy to destroy tumour cells by depositing radiation energy locally.

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Application Question

Hard difficulty • Concept in a practical situation

Hard

Question 7

Applied Concept

Two deuterium nuclei need to come very close for fusion to occur. Calculate and interpret the significance of the Coulomb barrier height for this head-on collision, given that the radius of a deuteron is 2.0 fm.

When two deuterons just touch, the separation between their centres is d = 2r = 2 × 2.0 fm = 4.0 × 10⁻¹⁵ m. Each deuteron has charge e = 1.6 × 10⁻¹⁹ C.
Coulomb barrier height U = (1/4πε₀)(e²/d) = (9 × 10⁹ × (1.6 × 10⁻¹⁹)²) / (4.0 × 10⁻¹⁵) = (9 × 10⁹ × 2.56 × 10⁻³⁸) / (4.0 × 10⁻¹⁵) ≈ 5.76 × 10⁻¹⁴ J ≈ 360 keV.
This barrier of ~360 keV means deuterons need kinetic energies of this magnitude to fuse. Thermal energy (3/2)kT = 360 keV gives T ≈ 2.8 × 10⁹ K — explaining why thermonuclear fusion requires extremely high temperatures.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 8

Applied Concept

An engineer proposes using 1 gram of matter as fuel, converting it entirely to energy by E = mc². Calculate the energy that would be released and compare it with the energy from burning 1 kg of coal (10⁷ J).

Using E = mc²: E = 10⁻³ kg × (3 × 10⁸)² = 10⁻³ × 9 × 10¹⁶ = 9 × 10¹³ J from complete conversion of just 1 gram of mass.
Burning 1 kg of coal gives 10⁷ J. To compare: 9 × 10¹³ / 10⁷ = 9 × 10⁶, meaning 1 g of matter (if fully converted) yields about 9 million times the energy of burning 1 kg of coal.
In practice, nuclear processes only convert a tiny fraction (~0.1%) of mass to energy; complete mass-energy conversion is not achievable with current technology. Even so, nuclear fuels release roughly 10⁷ times more energy per kg than chemical fuels like coal.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 9

Applied Concept

With reference to the structure of the sun, describe how nuclear fusion sustains solar energy. What would happen to the sun after its hydrogen fuel is exhausted?

The sun's core temperature (~1.5 × 10⁷ K) provides protons with sufficient kinetic energy to overcome Coulomb repulsion and undergo fusion via the proton-proton cycle, releasing ~26.7 MeV per cycle as four hydrogen nuclei convert to helium-4.
The sun has enough hydrogen in its core to sustain this process for approximately another 5 billion years; the rate of energy output matches its current luminosity.
Once hydrogen is exhausted, the sun's core cools and contracts under gravity, raising temperatures sufficiently (~10⁸ K) for helium fusion to begin (producing carbon); the outer layers expand, turning the sun into a red giant. Eventually heavier elements up to those near the Ebn peak can be synthesised before the star's life ends.

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Application Question

Medium difficulty • Concept in a practical situation

Medium

Question 10

Applied Concept

A gold coin of known mass can be used to calculate the nuclear energy needed to separate all its nucleons. With reference to the formula for nuclear binding energy, explain the steps involved in such a calculation.

To find the nuclear energy required to separate all nucleons in the coin, first find the number of atoms in the coin using n = (mass / molar mass) × Nₐ, where Nₐ = 6.023 × 10²³.
For each nucleus, calculate the mass defect ΔM = [Zmp + Nmn – M(atom) + Zme]. Then compute binding energy per nucleus: Eb = ΔM × 931.5 MeV (using 1 u = 931.5 MeV/c²).
Total nuclear energy required = Eb per nucleus × total number of nuclei. This immense total energy illustrates how tightly nucleons are bound and why nuclear reactions release vastly more energy than chemical reactions.

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Chapter 13: Nuclei | Application Questions

A nuclear power plant uses the fission of uranium-235 to generate electricity. With reference to the binding energy per nucleon concept, explain why fission of U-235 releases energy and estimate the approximate energy per fission event.

A student claims that nuclear density should vary with the size of the nucleus, increasing for heavier nuclei. Using the empirical formula for nuclear radius, show that this claim is incorrect.

During World War II, the first atomic bomb used uncontrolled fission. In contrast, nuclear reactors use controlled fission. With reference to the chain reaction process, explain the key difference between the two and the role of control rods.

A scientist proposes splitting an iron-56 nucleus into two aluminium-28 nuclei to generate energy. With reference to the binding energy per nucleon curve, evaluate whether this proposal is feasible.

A carbon-14 nucleus is radioactive but carbon-12 is stable. Using the concept of neutron-to-proton ratio, explain this difference in stability.

In a hospital, radioactive isotopes are used for both diagnosis and therapy. Explain the basis of radioactivity and state the three types of emissions, relating each to their nature and penetrating power.

Two deuterium nuclei need to come very close for fusion to occur. Calculate and interpret the significance of the Coulomb barrier height for this head-on collision, given that the radius of a deuteron is 2.0 fm.

An engineer proposes using 1 gram of matter as fuel, converting it entirely to energy by E = mc². Calculate the energy that would be released and compare it with the energy from burning 1 kg of coal (10⁷ J).

With reference to the structure of the sun, describe how nuclear fusion sustains solar energy. What would happen to the sun after its hydrogen fuel is exhausted?

A gold coin of known mass can be used to calculate the nuclear energy needed to separate all its nucleons. With reference to the formula for nuclear binding energy, explain the steps involved in such a calculation.

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