Following statements related to radioactivity are given below: (A)… | JEE Main 2022 (28 Jun, Shift 2)

Q41JEE Main 2022 · 28 JUN · SHIFT 2Easy

Law of Radioactive Decay

Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ( $\tau$ ).

(D) Product of decay constant ( $\lambda$ ) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below:

Show answer and solution

Answer: (c)

(A) False: radioactivity is random and spontaneous but independent of physical and chemical conditions.
(B) True: $N = N_0 e^{-\lambda t}$ , an exponential decay.
(C) True: $\ln N = \ln N_0 - \lambda t$ , slope magnitude $\lambda = \frac{1}{\tau}$ .
(D) False: $\lambda T_{1/2} = \ln 2$ , a constant.
So the answer is (c) (B) and (C) only.

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