A radioactive nucleus n₂ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n₁. If initial number of both nuclei are the same, what is the ratio of number of nuclei of n₂ to the number of nuclei of n₁, after one half-life of n₁? (a) 1/4 (b) 1/8 (c) 4 (d) 8

Answer: (a). λ₂ = 3λ₁, so T₂ = T₁/3. In time T₁: n₁ goes through 1 half-life, n₂ through 3 half-lives. (N₂)/(N₁) = (N₀/8)/(N₀/2) = 1/4. So the answer is (a) 1/4.

A radioactive nucleus n₂ has 3 times the decay constant as compared… | JEE Main 2025 (23 Jan, Shift 1)

Q19JEE Main 2025 · 23 JAN · SHIFT 1Medium

Law of Radioactive Decay

A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$ , after one half-life of $n_1$ ?

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Answer: (a)

$\lambda_2 = 3\lambda_1$ , so $T_2 = T_1/3$ .
In time $T_1$ : $n_1$ goes through 1 half-life, $n_2$ through 3 half-lives.
$\frac{N_2}{N_1} = \frac{N_0/8}{N_0/2} = \frac{1}{4}$ .
So the answer is (a) 1/4.

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