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  • 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) Th

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  \mathrm{\log _{e}} (no. of undecayed nuclei) Vs. time represents the reciprocal of the mean lifetime \mathrm{(\tau) .}

(D) Product of decay constant \mathrm{(\lambda)} and half-life time \mathrm{\left(\mathrm{T}_{1 / 2}\right)} is not constant.

Choose the most appropriate answer from the options given below :

Option: 1

\mathrm{\text { (A) and (B) only }}


Option: 2

\mathrm{\text { (B) and (D) only }}


Option: 3

\mathrm{\text { (B) and (C) only }}


Option: 4

\mathrm{\text { (C) and (D) only }}


Answers (1)

best_answer

A) Statement A is False 

Radioactivity is a random and spontaneous process and is dependent on physical conditions like temperature, the presence of fast-moving particles etc.

Radioactivity is a nuclear process, it is not concerned in any manner with the extranuclear part of the atom. It is independent of any chemical property of the element for example it does not effect the electronic configuration of the element.

B) Statement B is True

As \mathrm{N=Noe^{-\lambda t}}

where N=The number of un-decayed nuclei in the radioactive sample

(C) Statement C is True

\mathrm{N=Noe^{-\lambda t}}

\mathrm{\ln (N)=-\lambda t+\ln N_{0} }

so slope=-\lambda

(D) Statement D is False
\mathrm{t_{\frac{1}{2}}=\frac{ln2}{\lambda }}
so, t_{\frac{1}{2}} \times \lambda=\ln 2=\text { constant }

Hence option C is correct.

Posted by

SANGALDEEP SINGH

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