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Home » 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 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
Physics | Physics
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}

Solution: The correct answer is 0.5 \log _{e}^{2}

{{N}_{0}}\lambda =10000

N\lambda =2500

also\,we\,have:\,\,N={{N}_{0}}{{e}^{-\lambda t}}

Multiplying\,by\,\lambda \,on\,both\,sides,

N\lambda ={{N}_{0}}{{e}^{-\lambda t}}

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

\lambda =0.5\,\log _{e}^{2}

 

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