JEE Physics Nuclei MCQs Set 10

Answer: (b) 98.32%

Explanation:
1. Momentum conservation gives KE ∝ 1/mass
2. Fraction carried by α = m_U/(m_U + m_α) = 235/239 = 98.3%.

Teacher's Note:
1. The heavy daughter nucleus recoils with only a small share of energy.
2. Fraction for α = (A − 4)/A.

Answer: (a) 1600 years

Explanation:
1. Number of atoms in 1 g = 6.02 × 10²³/226 = 2.66 × 10²¹
2. λ = A/N = 3.7 × 10¹⁰/2.66 × 10²¹ = 1.39 × 10⁻¹¹ s⁻¹
3. T½ = 0.693/λ = 4.98 × 10¹⁰ s ≈ 1580 years ≈ 1600 years.

Teacher's Note:
1. Use A = λN to find λ.
2. Convert seconds to years by dividing by 3.15 × 10⁷.

Answer: (a) 27.72 years

Explanation:
1. 75% decayed leaves 25%: e^(−0.05t) = 1/4
2. t = ln4/0.05 = 1.386/0.05 = 27.7 years.

Teacher's Note:
1. 75% decay is two half-lives, and T½ = 0.693/0.05 = 13.86 years.
2. 2 × 13.86 = 27.7 years.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Neutrons are electrically neutral, so they are not repelled by nuclei or slowed by electric forces, and penetrate matter easily: A is true
2. It is also true that a neutron is slightly more massive than a proton, but this is not the cause of the penetration
3. So both are true, but R does not explain A.

Teacher's Note:
1. The reason for high penetration is the absence of charge.
2. Mass difference is only about 0.14%.

Answer: (d) A is false, but R is true.

Explanation:
1. Actual values: He-4 about 7.07 MeV, Be-9 about 6.46 MeV, Li-7 about 5.6 MeV, so the stated order is wrong and A is false
2. Binding energy per nucleon does not vary linearly with (N − Z); R is also false.

Teacher's Note:
1. Helium-4 is exceptionally stable because it is doubly magic.
2. Binding energy per nucleon first increases with A, then falls.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Fission fragments are more tightly bound than the heavy parent
2. The gain in total binding energy appears as released energy, so R correctly explains A.

Teacher's Note:
1. Energy released = B.E.(fragments) − B.E.(parent).
2. Fragments lie closer to the peak of the binding energy curve.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Ordinary hydrogen captures neutrons to form deuterium, wasting them
2. Deuterium absorbs neutrons far less, so heavy water slows neutrons without losing them: R explains A.

Teacher's Note:
1. This is why natural uranium can be used with heavy water.
2. Ordinary water needs enriched uranium.

Answer: (c) A is true, but R is false.

Explanation:
1. Fusion fuel must be light nuclei: Cl-35 has a high binding energy per nucleon (about 8.5 MeV) and lies near the peak, so fusing it would not release energy; A is true
2. The binding energy of Cl-35 is large, not small, so R is false.

Teacher's Note:
1. Fusion releases energy only for nuclei lighter than iron.
2. Cl-35 total binding energy is about 298 MeV.

Answer: (c) A is true, but R is false.

Explanation:
1. Beyond the peak near A = 56 the curve falls slowly, so A is true
2. The real reason is the growing Coulomb repulsion between protons, which is long-range, while nuclear force is short range and saturated; saying nuclear forces are weak is incorrect.

Teacher's Note:
1. Nuclear forces are strong at every nucleus; the Coulomb repulsion grows as Z².
2. The curve is the result of competition between the two.

Answer: (c) A is true, but R is false.

Explanation:
1. Deuterium is light and has a small absorption probability, so A is true
2. The collision between a neutron and a moderator nucleus is elastic, not inelastic, so R is false.

Teacher's Note:
1. Elastic collisions with light nuclei transfer the most energy.
2. An inelastic collision would excite the nucleus rather than slow the neutron.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Beryllium is a light element with a low neutron absorption, so it can serve as a moderator: A is true
2. A fast neutron colliding elastically with a light nucleus loses a large part of its energy, which is exactly why light nuclei are used as moderators: R explains A.

Teacher's Note:
1. A good moderator has a low mass number and low absorption.
2. Heavy nuclei would reflect neutrons without slowing them much.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A coolant carries away heat, and Q = mcΔT: a high specific heat means a large amount of heat is absorbed for a small rise in temperature
2. So A is true and R explains it.

Teacher's Note:
1. Water has one of the highest specific heats of common liquids (4200 J/kg·K).
2. Cheap and easy to circulate.

Answer: (c) A is true, but R is false.

Explanation:
1. Fission occurs because the binding energy per nucleon is less for heavy nuclei: A is true
2. A heavy nucleus has more protons, so the total Coulomb repulsion is greater, not smaller; R is false.

Teacher's Note:
1. Coulomb repulsion grows roughly as Z²; the nuclear force grows only as A.
2. This is why very heavy nuclei become unstable.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. α-particles from a given nuclide are emitted with definite energy and hence a definite speed, a characteristic of the nucleus
2. R states that the speed depends on the nucleus, which is exactly why it is characteristic.

Teacher's Note:
1. Different α-emitters give different energies (4 to 9 MeV).
2. In contrast, β-particles have a spread of speeds.

Answer: (c) A is true, but R is false.

Explanation:
1. A nucleus can emit electrons in β⁻ decay: A is true
2. The nucleus contains only protons and neutrons, with no electrons or negative charge; the electron is created at the time of decay. So R is false.

Teacher's Note:
1. The uncertainty principle rules out electrons inside the nucleus.
2. β⁻ comes from n → p + e⁻ + ν̄.

Answer: (d) A is false, but R is true.

Explanation:
1. β⁺ emission reduces Z by 1, so Na-22 (Z = 11) gives Ne-22 (Z = 10), not Mg (Z = 12): A is false
2. In β⁺ emission a proton is transformed into a neutron, so R is also false.

Teacher's Note:
1. β⁺ decay: p → n + e⁺ + ν.
2. It occurs in proton-rich nuclei such as Na-22.

Answer: (c) A is true, but R is false.

Explanation:
1. Radioactive nuclei with a neutron excess do emit β⁻ particles: A is true
2. But electrons do not exist inside the nucleus; they are produced when a neutron decays. R is false.

Teacher's Note:
1. A neutron changes into a proton and an electron at the moment of decay.
2. Compare with photon emission by an atom: the photon is created, not stored.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Cobalt-60 emits penetrating γ-rays, which destroy rapidly dividing cancer cells
2. So R is true and explains A.

Teacher's Note:
1. Cobalt-60 therapy units are common in hospitals.
2. Half-life 5.3 years.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A proton is lighter than a neutron, so a free proton cannot change into a neutron, positron and neutrino without a violation of energy conservation
2. So A is true, and R gives the reason.

Teacher's Note:
1. A free neutron can decay because it is heavier than the proton.
2. Inside nuclei a proton can convert through binding-energy changes.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The β energy spectrum is continuous because the energy is shared between the β-particle and a neutrino, so A is true
2. β decay is indeed a spontaneous statistical process, but this does not explain the continuous spectrum. Both are true and R is not the reason.

Teacher's Note:
1. The continuous spectrum was the clue that led to the neutrino.
2. Statistical nature explains the exponential law, not the spectrum.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Heavy nuclei have large Coulomb repulsion and tend to decay: A is true
2. They do have more neutrons than protons, but this alone does not make them unstable (the neutron excess actually helps binding). So R does not explain A.

Teacher's Note:
1. The real cause is the long-range Coulomb force of many protons.
2. The valley of stability bends toward neutron-rich nuclei at high A.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The nuclear force acts only over about 2–3 fm, while gravity and the electric force extend to large distances: A is true
2. It is also true that the nuclear force does not obey the inverse square law, but this is a separate property that does not by itself explain the range. Both true, R not the explanation.

Teacher's Note:
1. The short range comes from the exchange of massive mesons.
2. Gravity and Coulomb force follow 1/r².

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. U-238 does decay by α-emission, with half-life 4.5 × 10⁹ years: A is true
2. U-238 has 146 neutrons and 92 protons: R is also true, but α-decay occurs because of large Coulomb repulsion, not the neutron excess. R is not the explanation.

Teacher's Note:
1. α-emission is typical of heavy nuclei with Z > 82.
2. It reduces both the Coulomb repulsion and the size.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Nucleons are held together by the strong force, and the potential energy associated with this interaction is the stored nuclear energy
2. So R explains A.

Teacher's Note:
1. Binding energy is the work needed to separate the nucleons.
2. Nuclear reactions release part of this stored energy.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Reactor fuel is enriched only to about 3–5% U-235, while a bomb needs about 90% or more, so a bomb-like chain reaction cannot take place
2. Hence R explains A.

Teacher's Note:
1. Reactor fuel can overheat (meltdown) but cannot detonate like a bomb.
2. Natural uranium has only 0.7% U-235.