Question

A radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5\, min$, the rate becomes $1250$ disintegration per minute. Then, its decay constant (per minute) is

• A. $0.8\,{{\log }_{e}}2$
• B. $0.4\,{{\log }_{e}}2$
• C. $0.2\,{{\log }_{e}}2$
• D. $0.1\,{{\log }_{e}}2$

Answer 1

Answer: (B)

$0.4\,{{\log }_{e}}2$

Answer 2

Given R = 1250,
${{R}_{0}}=5000$ and t = 5 min
Hence $R={{R}_{0}}{{e}^{-\lambda t}}$
$1250=5000{{e}^{-\lambda \times 5}}$
$\lambda =0.4\,{{\log }_{e}}2$