Nuclear & Radioactivity — Set 2

Correct Answer: A. Alpha radiation

• **Alpha radiation** = Alpha particles have the highest ionising power because they carry a +2 charge and are relatively heavy (mass ≈4 u), creating dense ionisation tracks — about 10,000 ion pairs per mm of air. • **~10,000 ion pairs per mm** — This intense ionisation means alpha particles lose energy quickly and travel only a few centimetres in air; high ionisation = low penetration. • 💡 Wrong-option analysis: Gamma radiation: gamma rays ionise very sparsely because they are uncharged photons, which is why they penetrate so deeply; Beta radiation: beta particles create about 100 ion pairs per mm in air — far less than alpha; Radio waves: radio waves are non-ionising electromagnetic radiation and do not create ion pairs at ordinary intensities.

Correct Answer: D. Gamma radiation

• **Gamma radiation** = Gamma rays carry no electric charge, so they experience no force in electric or magnetic fields and travel in straight lines unaffected. • **Charge = 0, mass = 0** — Alpha particles (+2e) deflect toward the negative plate; beta-minus (−1e) deflect toward the positive plate; gamma photons pass straight through any field. • 💡 Wrong-option analysis: Positive ions: positive ions carry charge and are deflected toward the negative electrode in an electric field; Alpha radiation: alpha particles carry +2e charge and are deflected by both electric and magnetic fields; Beta radiation: beta particles carry −1e charge and are deflected in the opposite direction to alpha in electric fields.

Correct Answer: C. Half of the nuclei decay

• **Half of the nuclei decay** = The half-life (T₁/₂) is the time after which exactly half of the original undecayed nuclei in a large sample have undergone radioactive decay. • **N(t) = N₀ (1/2)^(t/T₁/₂)** — After n half-lives, the fraction remaining is (1/2)ⁿ; the half-life is constant and independent of temperature, pressure, or chemical state. • 💡 Wrong-option analysis: All nuclei decay: the time for all nuclei to decay is theoretically infinite for exponential decay — never a finite half-life; Temperature becomes half: temperature has no role in radioactive decay rate; Mass becomes double: mass cannot spontaneously double — this is thermodynamically impossible.

Correct Answer: A. T1/2 = 0.693/lambda

• **T₁/₂ = 0.693/λ** = The half-life is derived from the exponential decay law; setting N = N₀/2 gives T₁/₂ = ln2/λ, and ln2 ≈ 0.693. • **λ in s⁻¹** — A large decay constant λ means rapid decay and a short half-life; a small λ means slow decay and a long half-life; they are inversely proportional. • 💡 Wrong-option analysis: T₁/₂ = λ/0.693: this inverts the correct relation — it would give T₁/₂ that increases with λ, which contradicts physical reality; T₁/₂ = 1 + λ: adding 1 to λ has no physical meaning in decay theory; T₁/₂ = λ²: squaring the decay constant has no basis in exponential decay mathematics.

Correct Answer: D. A = lambda N

• **A = λN** = Activity equals the product of the decay constant and the number of undecayed nuclei; as N decreases over time, activity decreases proportionally. • **A in Bq (s⁻¹)** — Because N(t) = N₀ e^(−λt), the activity A(t) = λN₀ e^(−λt) also decays exponentially with the same half-life as N. • 💡 Wrong-option analysis: A = N²: squaring N has no physical basis in nuclear decay — activity is linearly proportional to N; A = N/λ: dividing by λ gives units of N·s, not disintegrations per second; A = N + λ: adding dimensionally incompatible quantities (count and s⁻¹) is physically meaningless.

Correct Answer: A. 1/8

• **1/8** = 30 days = 3 half-lives of 10 days each; after each half-life the remaining fraction halves: 1 → 1/2 → 1/4 → 1/8. • **(1/2)³ = 1/8** — Using N/N₀ = (1/2)^n where n = t/T₁/₂ = 30/10 = 3; so fraction remaining = (1/2)³ = 0.125 = 1/8. • 💡 Wrong-option analysis: 1/6: 1/6 does not correspond to any integer number of half-lives — n would need to be log₂6 ≈ 2.58; 1/4: 1/4 = (1/2)² corresponds to exactly 2 half-lives (20 days), not 3; 1/2: 1/2 corresponds to only 1 half-life (10 days), not 30 days.

Correct Answer: C. Once-living organic materials

• **Once-living organic materials** = Carbon-14 dating works because living organisms continuously exchange carbon with the atmosphere, maintaining a fixed ¹⁴C/¹²C ratio; after death the ¹⁴C decays without replenishment. • **T₁/₂ (C-14) ≈ 5730 years** — This half-life makes the method reliable for materials up to about 50,000 years old; the ratio of ¹⁴C remaining to original ¹⁴C gives the age. • 💡 Wrong-option analysis: Plastic materials only: most plastics are synthetic polymers from petroleum, which is ancient and contains no measurable ¹⁴C; Metals in machines: metals do not incorporate carbon in the same biological cycle as living organisms; Igneous rocks only: igneous rocks are dated using potassium-argon or uranium-lead methods because their formation involves no biological carbon exchange.

Correct Answer: B. 5730 years

• **5730 years** = The accepted half-life of carbon-14 is approximately 5730 years (the original 'Libby half-life' was 5568 years, but the corrected value is 5730 years). • **Dating range ~500–50,000 years** — With T₁/₂ = 5730 yr, about 10 half-lives (57,300 yr) is the practical upper limit; below ~500 years the method is less precise due to industrial ¹⁴C dilution effects. • 💡 Wrong-option analysis: 5.73 years: this is 1000 times too small — it would limit dating to only a few decades; 57,300 years: this is the practical upper detection limit of the method, not the half-life itself; 573 years: this is 10 times too small and would limit the method's range to only a few thousand years.

Correct Answer: C. A heavy nucleus splits into smaller nuclei with energy release

• **A heavy nucleus splits into smaller nuclei with energy release** = In nuclear fission, a heavy nucleus (such as U-235 or Pu-239) splits into two medium-mass daughter nuclei plus 2–3 neutrons, releasing ~200 MeV per event. • **~200 MeV per fission** — This energy arises from the mass defect; the daughter nuclei have higher binding energy per nucleon than the original heavy nucleus, so mass is converted to energy via E = mc². • 💡 Wrong-option analysis: Light nuclei combine to form a heavier nucleus: that is nuclear fusion, the opposite of fission; A nucleus absorbs light and disappears: nuclei do not disappear on absorbing light — photodisintegration is different and does not make the nucleus vanish; Electrons are removed from atoms: removing electrons is ionisation, a chemical/atomic process, not a nuclear one.

Correct Answer: C. Combining light nuclei to form a heavier nucleus

• **Combining light nuclei to form a heavier nucleus** = In nuclear fusion, two light nuclei (such as deuterium and tritium) overcome the Coulomb barrier at extremely high temperatures and merge, releasing large amounts of energy. • **~17.6 MeV per D-T fusion** — The energy released per unit mass of fuel is several times greater than fission; the Sun generates energy primarily through the proton–proton fusion chain. • 💡 Wrong-option analysis: Splitting of heavy nuclei: splitting heavy nuclei describes nuclear fission, the opposite reaction; Decay of radioactive nuclei: radioactive decay is a spontaneous process of an unstable nucleus, not a combining reaction; Ionization of gases: ionisation is the removal of electrons from atoms — an atomic process entirely unrelated to nuclear fusion.