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  • The radioactivity of a sample is  at a time and at a time <img alt="t_2" sr

The radioactivity of a sample is X at a time t_1 and Y at a time t_2. If the mean life time of the specimen is \tau, the number of atoms that have disintegrated in the time interval \left(t_1-t_2\right) is:

Option: 1

\mathrm{Xt}_1-\mathrm{Yt}_2


Option: 2

\mathrm{X}-\mathrm{Y}


Option: 3

\frac{\mathrm{X}-\mathrm{Y}}{\tau}


Option: 4

\quad(X-Y) \tau


Answers (1)

best_answer

Activity at time t_1 \text {, }

\mathrm{X}=\lambda \mathrm{N}_1=\frac{1}{\tau} \mathrm{N}_1 \quad \text { or } \quad \mathrm{N}_1=\tau \mathrm{X} \quad\left(\because \tau=\frac{1}{\lambda}\right)

Activity at time \mathrm{t}_2, \mathrm{Y}=\lambda \mathrm{N}_2=\frac{1}{\tau} \mathrm{N}_2                 \text { or } \quad \mathrm{N}_2=\tau \mathrm{Y}  

Therefore, the number of nuclei decayed during time interva \left(t_1-t_2\right) is

\mathrm{N}_1-\mathrm{N}_2=\tau \mathrm{X}-\tau \mathrm{Y}=(\mathrm{X}-\mathrm{Y}) \tau

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