The activity of radioactive sample is measured as N₀ counts per minute at time t = 0, and N₀/e counts per minute at time t = 3 minute, The activity reduces to half its value in time (in minute) (a) 1/3log e 2 (b) 3log e 2 (c) 3log ₁₀ 2 (d) 3log ₁₀ 2

Answer: (b). N₀/e = N₀e-3λ ⇒ λ = 1/3 min⁻¹. T = (log e2)/(λ) = 3log e2 min. So the answer is (b) 3log e2.

The activity of radioactive sample is measured as N₀ counts per… | MHT CET 2025 (23 Apr, Shift 1)

Q17MHT CET 2025 · 23 APR · SHIFT 1Medium

Law of Radioactive Decay

The activity of radioactive sample is measured as $\text{N}_0$ counts per minute at time $\text{t} = 0$ , and $\frac{\text{N}_0}{\text{e}}$ counts per minute at time $\text{t} = 3$ minute, The activity reduces to half its value in time (in minute)

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Answer: (b)

$\frac{N_0}{e} = N_0e^{-3\lambda} \Rightarrow \lambda = \frac{1}{3}\text{ min}^{-1}$ .
$T = \frac{\log_e2}{\lambda} = 3\log_e2$ min.
So the answer is (b) $3\log_e2$ .

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