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 $
• E. $ 0.6\,{{\log }_{e}}2 $

Answer 1

Answer: (B)

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 $