Nuclear Physics Test 3, Past Papers of MDCAT ECAT Physics

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Q21: A radioactive nucleus undergoes decay A →(α) A₁ →(β) A₂ →(α) A₃ →(γ) A₄. If mass number & atomic number of A = 180, 72, then A₄ is:

A) 172, 69

B) 176, 69

C) 174, 70

D) 176, 70

Explanation: ¹⁸⁰₇₂A → α → ¹⁷⁶₇₀ → β → ¹⁷⁶₇₁ → α → ¹⁷²₆₉ → γ → ¹⁷²₆₉.

Q22: Neutron decay in free space: n → p⁺ + e⁻ + [ ]. The bracket represents:

A) Photon

B) Neutrino

C) Graviton

D) Antineutrino

Explanation: Neutron decay: ¹n → ¹H + e⁻ + ν̄ (antineutrino).

Q23: The ratio of decay rate of parent to number of nuclei present is:

A) Half-life

B) Mean life

C) Decay constant

D) Activity

Explanation: λ = (ΔN/Δt)/N.

Q24: Two radioactive substances have equal mass, half-lives 1 yr & 2 yr. Ratio of activities after 6 yr:

A) 1:4

B) 4:1

C) 1:8

D) 8:1

Explanation: A₁/A₂ = 2³/2⁶ = 1/8.

Q25: Mean life = T. 75% nuclei decay in time:

A) 2T

B) 4T

C) (1/2)(ln2)T

D) 2(ln2)T

Explanation: 25% remains → t = 2T½ = 2(ln2)T.

Q26: Fraction of nuclei remaining after half of a half-life:

A) 1/4

B) 1/√2

C) 1/(2√2)

D) √2−1

Explanation: Fraction = (1/2)^(1/2) = 1/√2.

Q27: If decay constant is smaller:

A) More atoms decay

B) Infinite atoms decay

C) Fewer atoms decay

D) Both A and C

Explanation: Smaller λ → larger half-life → fewer decays in given time.

Q28: 3/4 nuclei decay in 3/4 s. Half-life is:

A) 3/4 s

B) 3/8 s

C) 1 s

D) 1/2 s

Explanation: n=2 → T½ = t/n = (3/4)/2 = 3/8 s.

Q29: Radium decay constant λ=4.28×10⁻⁴ yr⁻¹. Half-life?

A) 1240 yr

B) 1620 yr

C) 2000 yr

D) 63 yr

Explanation: T½ = 0.693/λ ≈ 1620 yr.

Q30: Which graph shows activity A vs time t?

A) Exponential decay

B) Linear

C) Parabolic

D) Step

Explanation: Activity decreases exponentially with time.

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