Question

The fraction of the original number of a radioactive atom having a mean life of 10 days, that decays during the $5^{th}$ day is :

• A. 0.15
• B. 0.3
• C. 0.045
• D. 0.064

Answer 1

Answer: (D)

0.064

$T_{av}=10days=\frac{1}{\lambda }$

Number of decays during $5^{th}$ day $=N_0{e}^{-\lambda 4}-N_0{e}^{-\lambda 5}$

Fraction decayed during $5^{th}$ day $=e^{-4\lambda }-e^{-5\lambda }$

$=e^{-4/10}-e^{-1/2}=0.0637\approx 0.064$