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  •  The half life period of a radioactive element is same as the mean life time of another radioactive element <img alt="\mathrm{Y}"

 The half life period of a radioactive element \mathrm{X} is same as the mean life time of another radioactive element \mathrm{Y}. Initially both of them have same number of atoms. Then

Option: 1

\mathrm{X} and \mathrm{Y} have the same decay rate initially.


Option: 2

\mathrm{X} and \mathrm{Y} decays at the same rate always.


Option: 3

\mathrm{Y} will decay at a faster rate than \mathrm{Y}.


Option: 4

\mathrm{X} will decay at a faster rate than \mathrm{Y}


Answers (1)

best_answer

\mathrm{\left(T_{1 / 2}\right)_X=T_Y}

\mathrm{\Rightarrow \frac{0.693}{\lambda_X}=\frac{1}{\lambda_Y} \Rightarrow \lambda_Y=\frac{\lambda_X}{0.693}>\lambda_X}

\mathrm{Since \left(-\frac{d N}{d t}\right)_X=\lambda_X N\, and \: \left(-\frac{d N}{d t}\right)_Y=\lambda_Y N}.

\mathrm{\Rightarrow\left(-\frac{d N}{d t}\right)_Y>\left(-\frac{d N}{d t}\right)_X}.

Decay rate of \mathrm{Y> } Decay rate of \mathrm{X }.
Correct option is (C).

Posted by

Ajit Kumar Dubey

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