Q.

Nuclei of a radio active element are produced at the rate of α=200 s−1. Initial number of active nuclei of the sample is 4000. It after one half life, rate of disintegration is equal to rate of production, then half life of the radio active element is

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a

7 sec

b

120 sec

c

200 sec

d

15 sec

answer is A.

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Detailed Solution

After time t, number of active nuclei is given by N=N0/2tTNow rate of disintegration =λN∴ λN=α⇒ln2TN02TT=α⇒T=N0ln22α=4000×0.6932×200sec⇒T=6.93 sec≃7 sec
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