Indian Navy Pilot Atoms and Nuclei — practice questions

Explore 2 free Atoms and Nuclei questions in Indian Navy Pilot Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Half-life of radioactive sample is T₁/₂. Decay constant λ:Read the answer and worked solution →Activity of N nuclei with decay constant λ:Read the answer and worked solution →

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Half-life of radioactive sample is T₁/₂. Decay constant λ:

λ = 2 T₁/₂
λ = T₁/₂
λ = ln 2 / T₁/₂ ≈ 0.693/T₁/₂
λ = 1/T₁/₂

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Correct answer: C. λ = ln 2 / T₁/₂ ≈ 0.693/T₁/₂

N(t) = N₀ e^(-λt). After T₁/₂, N = N₀/2 We have → e^(-λ T₁/₂) = 1/2 → λ T₁/₂. That is → e^(-λ T₁/₂) = ln 2 → λ. So → e^(-λ T₁/₂) = 0.693/T₁/₂.

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Activity of N nuclei with decay constant λ:

A = e^N
A = 1/N
A = λ N (rate of decay = number remaining × decay constant)
A = N/λ

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Correct answer: C. A = λ N (rate of decay = number remaining × decay constant)

Activity A = -dN/dt = λN. **Units:** becquerel (Bq = 1 decay/sec) or curie (1 Ci = 3.7 × 10¹⁰ Bq). Decreases exponentially with same half-life as N.