Question

A radioactive element has rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is

• A. $0.2{\log }_e^2$
• B. $0.5{\log }_e^2$
• C. $0.6{\log }_e^2$
• D. $0.8{\log }_e^2$

Answer 1

The correct option is B $0.5{\log }_e^2$

$N_o\lambda =10000$, $N\lambda =2500$

also $N=N_o{e}^{-\lambda t}$, multiplying by $\lambda$ on both side

$N\lambda =N_o\lambda e^{-\lambda t}$

$e^{-4\lambda }=\frac{1}{4}$

$\lambda =0.5ln2$