JEE Main 2020 · Physics · Atoms, Nuclei and Dual Nature of Radiation · easy

Two radioactive samples A and B contain equal numbers of atoms at t = 0. Their half-lives are 1 h and 2 h respectively. The activities of the two…

Single correct option

Two radioactive samples A and B contain equal numbers of atoms at

t = 0

. Their half-lives are

1\ \mathrm{h}

and

2\ \mathrm{h}

respectively. The activities of the two samples will be equal at time

Show answer and solution

Answer: (B) $2\ \mathrm{h}$

Activity

A = \lambda N_0 e^{-\lambda t}

with

\lambda_A = 2\lambda_B \equiv 2\lambda

. Equating activities:

2\lambda N_0e^{-2\lambda t} = \lambda N_0e^{-\lambda t}

, so

e^{\lambda t} = 2

and

t = \dfrac{\ln 2}{\lambda} = T_{1/2}(B) = 2\ \mathrm{h}

. Check: at

2\ \mathrm{h}

N_A = N_0/4

and

N_B = N_0/2

, so

A_A = 2\lambda\cdot N_0/4 = \lambda N_0/2 = A_B

. The initial activities are in ratio

2:1

, so they cross once.

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