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A radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant, per minute, is

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Solution

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Therefore, ATQ, initially disintegration rate,

R=N∘λ=5000→(1)

Also, in 2nd case, disintegration rate after 5 min is,

$1250=N\lambda\rightarrow (2)$

Dividing equation (1) by (2), we get

N∘λNλ=60001250N∘N=4

And as we know, the number of decay, N is given by,

N=N∘e−λt(t=5min)14=e−5λ−ln(4)=−5λλ=0.4ln2

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