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 log_e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ( $τ$ ).
(D) Product of decay constant ( $λ$ ) and half-life time (T_1/2) is not constant.
Choose the most appropriate answer from the options given below:

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(B) and (C) only

(A) and (B) only

(B) and (D) only

answer is C.

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Detailed Solution

Radioactivity is not a random but it is a spontaneous process.

Number of un-decayed nuclei in the radioactive sample can be calculated as

$N = N_{o} e^{- λt}, where, λ is the decay constant .$

$\Rightarrow \ln (N) = \ln (N_{o}) - λt \Rightarrow \ln (N) = \ln (N_{o}) - (\frac{1}{τ}) t [∵ λ = \frac{1}{τ}]$

Also,

$λ = \frac{\ln 2}{T_{\frac{1}{2}}} \Rightarrow λ \times T_{\frac{1}{2}} = \ln 2 = constant$

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