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  • The activity of radioactive sample is measured as 8750 counts per minute at and 875 counts per minute at <img alt="\mathrm{t=

The activity of radioactive sample is measured as 8750 counts per minute at \mathrm{t= 0} and 875 counts per minute at \mathrm{t=5 \, \mathrm{min}}.The decay constant approximately is:

Option: 1

0.46


Option: 2

0.36


Option: 3

 0.26


Option: 4

0.56


Answers (1)

best_answer

\mathrm{A(t)=A_0 e^{-\lambda t} \Rightarrow 875=8750 e^{-5 \lambda} \text {. }}

\mathrm{\Rightarrow \frac{1}{10}=e^{-5 \lambda} \Rightarrow \ln 10=5 \lambda }
\mathrm{\Rightarrow \lambda=\frac{1}{5} \ln 10=\frac{1}{5} \times 2.30 \times 1=0.46 \text { count } / \mathrm{min} . }

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himanshu.meshram

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