A) \[t=\frac{1}{\lambda }\,\ln \,\left\{ \frac{D}{p} \right\}\]
B) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 1+\frac{p}{D} \right\}\]
C) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 2+\frac{p}{D} \right\}\]
D) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 1+\frac{D}{p} \right\}\]
E) \[t=\frac{1}{\lambda }\,\ln \,\left\{ 2+\frac{D}{p} \right\}\]
Correct Answer: B
Solution :
Age of specimen\[(t)\]is related to the daughter/parent ratio of number of atoms (D/P) by equation \[D=P(1-{{e}^{\lambda t}})\] where\[\lambda =\]decay constant \[\frac{D}{P}=1-{{e}^{\lambda t}}\] \[1+\frac{D}{P}={{e}^{\lambda t}}\] \[t=\frac{1}{\lambda }\,\ln \,\left( 1+\frac{D}{p} \right)\]
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