A) 1s
B) \[\frac{1}{ln\left( 2 \right)}s\]
C) \[ln\,(2)\,s\]
D) 2 s
Correct Answer: C
Solution :
| Let N be the number of nuclei at any time t. Then \[\frac{dN}{dt}=200-\lambda N;\] |
| \[\therefore \,\,\,\,\,\int\limits_{0}^{N}{\frac{dN}{200-\lambda N}=\int\limits_{0}^{t}{dt}}\] or \[N=\frac{200}{\lambda }\left( 1-{{e}^{-\lambda t}} \right)\] |
| Given that \[N=100\,\,\,\] and \[\lambda =1{{s}^{-1}}\] |
| \[\therefore \,\,\,\,100=200\left( 1-{{e}^{-t}} \right)\]or \[{{e}^{-t}}=\left( \frac{1}{2} \right)\] |
| \[\therefore \,\,\,\,t=1n\left( 2 \right)\sec \] |
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