KVPY Sample Paper KVPY Stream-SX Model Paper-8

The counting rate observed from a radioactive Source at \[t=0\] second was \[1600\] counts per second and at \[t=8\] seconds it was \[100\]counts per second. The counting rate observed, as Counts per second at \[t=6\] seconds, will be

A) 400

B) 300

C) 200

D) 150

Correct Answer: C

Solution :

\[N={{N}_{0}}{{e}^{-\lambda t}}\]

Or \[100\,\,\,\,=1600{{e}^{-\lambda \times 8}}..\left( i \right)\]

and \[N\,\,\,\,\,=1600{{e}^{-\lambda \times 6}}..\left( \operatorname{ii} \right)\]

(ii)/(i), we have

\[\frac{N}{100}\,\,\,\,=\,\,\,\,\,{{e}^{\left( -6\lambda +9\lambda \right)}}\]

\[\,=\,\,\,\,{{e}^{+2\lambda }}\,\,..\left( \operatorname{iii} \right)\]

Now from equation (i) and (iii), we get \[\frac{N}{100}\,\,\,\,=\,\,\,\,2\]

\[N\,\,\,\,\,=\,\,\,\,200.\]