Modern & Nuclear Physics: 25 MCQs with Explanations

After n half-lives, fraction remaining = (1/2)^n. After 30 days = 3 half-lives, fraction = (1/2)³ = 1/8.

E = hc/λ = (1240 eV·nm)/600 nm ≈ 2.07 eV (using hc ≈ 1240 eV·nm).

(1/2)^n = 1/8 ⇒ n = 3 half-lives in 24 hours. So half-life = 24/3 = 8 hours.

λ = h/√(2meV) ≈ 1.227/√V nm = 1.227/10 = 0.1227 nm ≈ 0.123 nm.

Energy released E = Δmc², where Δm is mass defect. This equals increase in binding energy.

Activity measured in Becquerel (Bq = 1 decay/s) or Curie (Ci = 3.7 × 10¹⁰ Bq).

Energy released E = Δmc² due to mass defect (conversion of mass to energy).

Number of half-lives n = 30/10 = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8.

(1/2)ⁿ = 1/8 → n = 3 half-lives in 24 hours. Half-life = 24/3 = 8 hours.

de Broglie wavelength λ = h/√(2meV) = 1.227/√V nm = 1.227/10 = 0.1227 nm ≈ 0.123 nm. Wait, √100 = 10, so λ = 1.227/10 = 0.1227 nm. But option A is 0.123 nm. Let me recalculate formula: λ (in Å) = √(150/V). For V=100, λ = √1.5 = 1.225 Å = 0.1225 nm ≈ 0.123 nm. So answer is A.

E = hc/λ = (1240 eV·nm)/400 nm = 3.1 eV (using hc ≈ 1240 eV·nm).

(1/2)^n = 1/16 ⇒ n = 4 half-lives in 32 hours. Half-life = 32/4 = 8 hours.

Activity measured in Becquerel (Bq = 1 decay/s) or Curie (Ci = 3.7 × 10¹⁰ Bq). Gray measures absorbed dose.

Typical fission (e.g., ²³⁵U + n) produces two medium-mass fragments with mass ratio ~3:2, plus neutrons and energy.

Half-life is intrinsic nuclear property, unaffected by external physical or chemical conditions.

N = N₀e^(-λt). At t = T_{1/2}, N = N₀/2 ⇒ 1/2 = e^(-λT_{1/2}) ⇒ λT_{1/2} = ln2 ⇒ λ = ln2 / T_{1/2}.

Stopping potential V₀ stops even the most energetic photoelectrons: eV₀ = K_max = hν - φ.

Q = (initial mass - final mass)c². Q > 0 for exothermic reaction (energy released); Q < 0 for endothermic (energy absorbed).

Rutherford (1919) performed first artificial transmutation by bombarding nitrogen with alpha particles.

Beta-minus (β⁻) = electron; beta-plus (β⁺) = positron emitted from nucleus during radioactive decay.

K_max = hν - φ, where φ = work function. In terms of stopping potential: eV₀ = hν - φ.

λ = h/p = h/mv for non-relativistic particle. For relativistic: λ = h/(γmv).

Radioactivity involves changes within the nucleus of an unstable atom, leading to the emission of particles and energy. It is a nuclear phenomenon, independent of chemical or external conditions.

Half-life is the time for half the nuclei to decay. After 1 half-life (10 days), 1/2 remains. After 2 half-lives (20 days), (1/2) × (1/2) = 1/4 of the original sample remains.

Beta decay involves the conversion of a neutron into a proton (or vice versa). This changes the atomic number (Z) of the nucleus by ±1 while the mass number (A) remains the same. The number of beta particles emitted is related to the net change in Z.