68 free MCQs on Nuclei with worked answers and explanations. Radioactivity, nuclear reactions, fission, fusion, and binding energy.
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Binding energy per nucleon rises sharply for light nuclei, peaks around iron-56 (the most stable nucleus), then slowly declines for heavier nuclei - which is exactly why fusing light nuclei or splitting heavy nuclei both release energy: each moves the products toward this stability peak.
Q1.
The nucleus of an atom consists of:
Answer: C. Protons and neutrons
Why: The nucleus contains protons (positive) and neutrons (neutral), collectively called nucleons.
Q2.
Atomic number Z of an element is:
Answer: B. Number of protons
Why: Atomic number Z = number of protons in the nucleus. It uniquely identifies an element.
Q3.
Alpha radiation consists of:
Answer: B. Helium-4 nuclei (2 protons + 2 neutrons)
Why: Alpha particle = helium-4 nucleus (2 protons + 2 neutrons). Symbol: alpha or He-4.
Q4.
Beta-minus decay involves:
Answer: B. Emission of an electron from nucleus (neutron to proton)
Why: Beta-minus: neutron converts to proton + electron + antineutrino inside nucleus. Atomic number increases by 1.
Q5.
Gamma rays are:
Answer: C. High energy electromagnetic radiation
Why: Gamma rays are high-energy electromagnetic radiation (photons) emitted by excited nuclei during gamma decay.
Q6.
Half-life of a radioactive element is the time for:
Answer: B. Half the sample to decay
Why: Half-life T(1/2): time for half the radioactive atoms in a sample to decay. After n half-lives: N = N<sub>0</sub>/2<sup>n.</sup>
Q7.
Which radiation has the greatest penetrating power?
Answer: C. Gamma
Why: Gamma radiation is most penetrating (needs thick lead or concrete to stop). Alpha is least penetrating (stopped by paper).
Q8.
Which radiation has the greatest ionizing power?
Answer: A. Alpha
Why: Alpha particles are most ionizing (large charge +2, slow speed: they cause intense ionization but are least penetrating).
Q9.
Nuclear fission is:
Answer: B. Splitting of heavy nucleus
Why: Nuclear fission: a heavy nucleus (like U-235) splits into two medium-mass nuclei + neutrons + large energy release.
Q10.
Nuclear fusion is:
Answer: B. Joining of light nuclei releasing energy
Why: Nuclear fusion: light nuclei combine to form heavier nucleus + large energy release. Powers the Sun.
Q11.
1 atomic mass unit (1 amu) in energy equivalent (Einstein mass-energy):
Answer: B. 931.5 MeV
Why: 1 amu = 1.66 x 10<sup>-27</sup> kg. E = mc<sup>2</sup> = 931.5 MeV. This is important for nuclear energy calculations.
Q12.
Binding energy per nucleon is maximum for:
Answer: B. Iron-56
Why: Iron-56 has the highest binding energy per nucleon (~8.8 MeV/nucleon). Elements near iron are most stable.
Q13.
Mass defect in a nucleus is:
Answer: A. Difference between mass of nucleus and sum of its nucleons
Why: Mass defect delta_m = (Z mp + N mn) - M<sub>nucleus</sub>. This mass is converted to binding energy (E = delta_m x c<sup>2</sup>).
Q14.
Isotopes have the same:
Answer: C. Number of protons (atomic number)
Why: Isotopes of an element have the same atomic number Z (same protons) but different mass numbers (different neutrons).
Q15.
Carbon-14 dating is used to determine:
Answer: B. Age of ancient organic materials
Why: C-14 has T(1/2) = 5730 years. Living organisms absorb C-14; after death it decays. Ratio of C-14/C-12 gives age.
Q16.
Radioactive decay constant lambda is related to half-life by:
Answer: B. lambda = ln2 / T(1/2)
Why: lambda = 0.693/T(1/2). Activity A = lambda x N = A<sub>0</sub> x e<sup>-lambda t</sup>.
Q17.
A nuclear chain reaction in fission occurs when:
Answer: A. Average number of neutrons causing further fission > 1
Why: Chain reaction: each fission releases 2-3 neutrons; if at least 1 causes further fission, the reaction is self-sustaining.
Q18.
Moderator in a nuclear reactor is used to:
Answer: A. Slow down neutrons (for thermal fission)
Why: Moderator (heavy water, graphite) slows fast neutrons to thermal speeds. Slow neutrons are better captured by U-235 for fission.
Q19.
Which particle is emitted in beta-plus decay?
Answer: B. Positron
Why: Beta-plus decay: proton converts to neutron + positron + neutrino. Positron = antiparticle of electron with +e charge.
Q20.
The strong nuclear force:
Answer: C. Is strongest at short range inside nucleus
Why: Strong nuclear force: very short range (~1-3 fm), strongest known force, attractive: binds protons and neutrons in nucleus.
Q21.
In a nuclear reaction, which of these is NOT conserved?
Answer: C. Kinetic energy
Why: Kinetic energy alone is not conserved in nuclear reactions (some converts to binding energy). Mass-energy (total) is conserved.
Q22.
The Q-value of a nuclear reaction is:
Answer: B. Energy released (or absorbed): Q = (mass_reactants - mass_products) × c²
Why: Q-value: Q = (M<sub>reactants</sub> - M<sub>products</sub>)c². Positive Q = exothermic (energy released). Negative Q = endothermic.
Q23.
Binding energy per nucleon is maximum for:
Answer: B. Iron (Fe-56)
Why: Iron-56 has maximum binding energy per nucleon (~8.8 MeV/nucleon). Elements lighter or heavier than iron release energy by fusion or fission respectively.
Q24.
Carbon-14 dating uses the decay: ¹⁴C → ¹⁴N + ?
Answer: C. Beta minus particle (electron)
Why: C-14 decay: ¹⁴₆C → ¹⁴₇N + β⁻ + antineutrino. Used for dating organic matter (half-life 5730 years).
Q25.
Radioactive decay law: N(t) = N₀ e<sup>-lambda t</sup>. Activity A = dN/dt in magnitude is:
Answer: A. lambda N(t)
Why: Activity A = |dN/dt| = lambda × N(t). Activity is proportional to number of undecayed nuclei.
Q26.
After 3 half-lives, the fraction remaining is:
Answer: A. 1/8
Why: After n half-lives: N/N₀ = (1/2)<sup>n.</sup> After 3: (1/2)³ = 1/8.
Q27.
Nuclear fission of U-235 releases energy by:
Answer: B. Converting mass to energy via E=mc² (mass defect)
Why: Fission: heavy nucleus splits into fragments. Product masses total less than reactant masses. Difference (mass defect) appears as energy: E = delta_m × c².
Q28.
The moderator in a nuclear reactor:
Answer: B. Slows down (moderates) fast neutrons to thermal energies
Why: Moderator (heavy water, graphite): slows fast neutrons to thermal energies (~0.025 eV) where U-235 fission cross-section is highest.
Q29.
Critical mass in nuclear weapons/reactors refers to:
Answer: A. Minimum mass for sustained chain reaction
Why: Critical mass: minimum amount of fissile material for self-sustaining chain reaction (each fission on average causes exactly one more fission).
Q30.
Gamma radiation is best shielded by:
Answer: C. Lead or concrete (dense material)
Why: Gamma rays are high-energy photons. Dense materials (lead, concrete) are effective shields. Alpha stopped by paper, beta by Al.
Q31.
Stable nuclei have mass number A such that:
Answer: B. Z is approximately A/2 for light nuclei, Z < A/2 for heavy nuclei
Why: Light stable nuclei: Z ≈ N ≈ A/2. Heavy nuclei need more neutrons for stability (neutron-proton ratio > 1).
Q32.
The decay constant lambda and half-life T<sub>1</sub>/2 are related by:
Answer: B. lambda = ln 2 / T<sub>1</sub>/2
Why: N = N₀ e<sup>-lambda t</sup>. At t = T<sub>1</sub>/2: 1/2 = e^(-lambda T<sub>1</sub>/2). lambda × T<sub>1</sub>/2 = ln 2. lambda = ln 2 / T<sub>1</sub>/2 = 0.693/T<sub>1</sub>/2.
Q33.
Neutrinos are emitted in:
Answer: C. Beta decay (along with electron/positron)
Why: Beta decay: nucleus emits electron + antineutrino (beta-minus) or positron + neutrino (beta-plus). Neutrino carries away some energy.
Q34.
The reaction: ²H + ²H → ³He + n is:
Answer: B. Fusion
Why: Deuterium-deuterium fusion: two light nuclei combine to form heavier nucleus. Releases energy. Basis of hydrogen bomb and future fusion reactors.
Q35.
Specific activity refers to:
Answer: B. Activity per unit mass
Why: Specific activity = activity per unit mass (Bq/kg or Ci/g). Useful for comparing radioactivity of different materials.
Q36.
What is the product when ²³⁸U emits an alpha particle?
Answer: A. ²³⁴Th
Why: Alpha emission: Z decreases by 2, A decreases by 4. U-238 (Z=92) → Th-234 (Z=90, A=234).
Q37.
In a chain reaction, the multiplication factor k represents:
Answer: B. Ratio of neutrons in successive generations
Why: Multiplication factor k = neutrons in next generation / neutrons in previous generation. k=1: critical, k>1: supercritical, k<1: subcritical.
Q38.
Nuclear radius R = R₀ × A<sup>1/3</sup>. R₀ ≈
Answer: A. 1.2 fm (femtometers)
Why: R = R₀ A<sup>1/3</sup> where R₀ ≈ 1.2-1.3 femtometers = 1.2 × 10⁻¹⁵ m. Nuclear density is roughly constant.
Q39.
The mass defect of a nucleus is:
Answer: A. Mass of nucleus - sum of component nucleon masses
Why: Mass defect: delta_m = Z m<sub>p</sub> + N m<sub>n</sub> - M<sub>nucleus</sub>. This is positive for stable nuclei. Binding energy = delta_m × c².
Q40.
Radioactive dating works because:
Answer: B. The initial amount of radioactive isotope is assumed known and decay is predictable
Why: Dating: knowing initial ratio (from atmospheric C-14/C-12 for carbon dating), measuring current ratio, and knowing half-life allows calculation of elapsed time.
Q41.
The binding energy of Fe-56 is approximately 492 MeV. Binding energy per nucleon:
Answer: A. 8.79 MeV/nucleon
Why: BE/A = 492/56 ≈ 8.79 MeV/nucleon. This is the maximum for any stable nucleus, explaining why iron is the endpoint of stellar fusion.
Q42.
The semi-empirical mass formula (Bethe-Weizsacker) has terms for:
Answer: A. Volume, surface, Coulomb, asymmetry, and pairing
Why: Semi-empirical formula: E<sub>B</sub> = a<sub>V</sub> A - a<sub>S</sub> A<sup>2/3</sup> - a<sub>C</sub> Z(Z-1)/A<sup>1/3</sup> - a<sub>A</sub> (A-2Z)²/A ± delta (pairing). Five terms capture nuclear physics.
Q43.
Tunneling in alpha decay: the alpha particle tunnels through:
Answer: B. The Coulomb barrier surrounding the nucleus
Why: Alpha decay: alpha particle trapped inside but quantum tunnels through the Coulomb potential barrier. Gamow theory explains the wide range of half-lives.
Q44.
Geiger-Nuttall law for alpha decay relates log(decay constant) to:
Answer: B. 1/sqrt(Q) (inverse square root of Q-value)
Why: Geiger-Nuttall law: log(lambda) = A + B/sqrt(E<sub>alpha</sub>) where E<sub>alpha</sub> is alpha energy. Explains dramatic variation of half-lives with energy.
Q45.
The strong nuclear force acts:
Answer: C. At short range (< 2-3 fm), between any nucleons
Why: Strong force (residual from QCD): short range (~1-3 fm), attractive at ~1-3 fm, repulsive below ~0.7 fm. Holds nucleus together against Coulomb repulsion.
Q46.
Beta-minus decay: n → p + e⁻ + antineutrino. The antineutrino is needed for:
Answer: C. Energy and momentum conservation (and lepton number)
Why: Antineutrino is needed to conserve energy (continuous electron spectrum), momentum, angular momentum, and lepton number in beta decay. Pauli proposed it 1930.
Q47.
In nuclear reactions using liquid drop model, fission occurs when:
Answer: B. Electrostatic energy exceeds surface energy (fissility parameter x > 1 approx)
Why: Liquid drop: fission favorable when deformation energy cost (surface) < energy gain (Coulomb reduction). Fissility x = E<sub>C</sub>/(2E<sub>S</sub>) > 1 means spontaneous fission possible.
Q48.
Magic numbers (2, 8, 20, 28, 50, 82, 126) in nuclear physics indicate:
Answer: B. Nuclei with closed shell structure (extra stability)
Why: Magic numbers: closed shells in nuclear shell model (analogous to noble gas electronic structure). Nuclei with magic Z or N are exceptionally stable.
Q49.
The pion (pi meson) is the particle primarily responsible for:
Answer: B. Mediating the nuclear force (residual strong force)
Why: Yukawa (1935): nuclear force mediated by pion exchange. Heavier mediator (compared to photon) gives short range. Pion mass ~ 140 MeV.
Q50.
Nuclear fission vs fusion: which releases more energy per unit mass?
Answer: B. Fusion
Why: Fusion releases more energy per unit mass. D-T fusion yields ~14.1 MeV per event with ~5 amu total, ~ 3 MeV/amu. Fission: U-235 yields ~200 MeV with 236 amu, ~ 0.85 MeV/amu.
Q51.
Radioactive equilibrium (secular) occurs when:
Answer: B. Daughter activity equals parent activity (after many daughter half-lives)
Why: Secular equilibrium: when parent half-life much longer than daughter. Eventually daughter decays as fast as it is produced. A<sub>daughter</sub> = A<sub>parent</sub>.
Q52.
The electron capture process is:
Answer: B. Atomic electron absorbed by nucleus (p + e⁻ → n + neutrino)
Why: Electron capture: inner atomic electron captured by nucleus. Proton + electron → neutron + electron neutrino. Competes with positron emission.
Q53.
In a nuclear reactor, the four-factor formula k∞ =
Answer: A. eta × epsilon × p × f
Why: Four-factor formula (infinite medium): k∞ = eta × epsilon × p × f where eta = reproduction factor, epsilon = fast fission factor, p = resonance escape probability, f = thermal utilization.
Q54.
The thermonuclear reaction in stars: Proton-proton chain. Net reaction:
Answer: A. 4H → He-4 + energy
Why: PP chain net result: 4 ¹H → ⁴He + 2 e⁺ + 2 neutrinos + 2 gamma + 26.7 MeV energy. Powers the Sun.
Q55.
Spent nuclear fuel is primarily radioactive due to:
Answer: B. Fission products (including long-lived isotopes) and actinides
Why: Spent fuel: highly radioactive fission products (Sr-90, Cs-137, etc.) and minor actinides (Pu, Am, etc.) from neutron capture.
Q56.
The cross-section sigma in nuclear reactions measures:
Answer: B. Effective target area for reaction probability (in barns = 10⁻²⁴ cm²)
Why: Cross-section sigma: effective area for nuclear reaction. 1 barn = 10⁻²⁴ cm² = 10⁻²⁸ m². Reaction rate R = n × phi × sigma × N<sub>target</sub>.
Q57.
Isomers in nuclear physics are nuclei with:
Answer: B. Same A and Z but different energy states (metastable excited states)
Why: Nuclear isomers: same nucleus (same Z, same A) but in different long-lived excited states. Decay by gamma emission. Example: Tc-99m.
Q58.
Pair production (photon → e⁺ + e⁻) requires photon energy greater than:
Answer: B. 1.022 MeV
Why: Minimum energy for pair production = 2 × m<sub>e</sub> c² = 2 × 0.511 MeV = 1.022 MeV. Excess energy becomes kinetic energy of pair.
Q59.
Annihilation radiation: when e⁺ and e⁻ annihilate, they produce:
Answer: B. Two gammas, each 0.511 MeV emitted in opposite directions
Why: Pair annihilation: e⁺ + e⁻ → 2 gamma. Two 511 keV photons emitted back-to-back (momentum conservation). Basis of PET scans.
Q60.
The Breit-Wigner resonance formula describes nuclear cross-section as a function of energy near:
Answer: B. A resonance energy (sharp peak in cross-section)
Why: Breit-Wigner formula: sigma(E) = sigma_max × Gamma²/4 / [(E-E<sub>R</sub>)² + Gamma²/4] near resonance energy E<sub>R</sub>. Gamma is the width.
Q61.
The radius of a nucleus is proportional to A<sup>1/3</sup>. If the mass number increases eightfold, the nuclear radius becomes:
Answer: A. 2×
Why: R ∝ A<sup>1/3</sup>, so 8<sup>1/3</sup> = 2; the radius doubles.
Q62.
A nuclear reaction has a mass defect of 0.1 u (1 u = 931.5 MeV). The energy released is:
Answer: B. 93.15 MeV
Why: E = Δm·931.5 = 0.1·931.5 = 93.15 MeV.
Q63.
After 3 half-lives, the fraction of a radioactive sample remaining undecayed is:
Answer: C. 1/8
Why: Fraction remaining = (1/2)³ = 1/8.
Q64.
In beta-minus decay, the atomic number of the nucleus:
Answer: A. increases by 1
Why: A neutron converts to a proton, so Z increases by 1 while the mass number stays the same.
Q65.
When a nucleus undergoes alpha decay, its mass number and atomic number change by:
Answer: A. A − 4 and Z − 2
Why: An alpha particle carries away 4 nucleons and 2 protons, so A decreases by 4 and Z by 2.
Q66.
The binding energy per nucleon is maximum for nuclei near:
Answer: C. iron (A ≈ 56)
Why: The binding energy per nucleon curve peaks near iron (A ≈ 56), the most stable region.
Q67.
A radioactive sample of 800 atoms has a half-life of 5 years. The number of atoms remaining after 15 years is:
Answer: B. 100
Why: 15 years = 3 half-lives, so 800·(1/2)³ = 800/8 = 100 atoms.
Q68.
The density of nuclear matter is:
Answer: A. approximately independent of mass number
Why: Since mass ∝ A and volume ∝ R³ ∝ A, the nuclear density is nearly constant for all nuclei.