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Question

In a radioactive sample 4019K nuclei either decay into stable 4020Ca nuclei with decay constant 4.5×1010 per year or into stable 4018Ar nuclei with decay constant 0.5×1010 per year. Given that in this sample all the stable 4020Ca and 4018Ar nuclei are produced by the 4019K nuclei only. In time t×109 years, if the ratio of the sum of stable 4020Ca and 4018Ar nuclei to the radioactive 4019K nuclei is 99, the value of t will be? [Given: In 10=2.303]

A
1.15
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B
9.2
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C
2.3
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D
4.6
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Solution

The correct option is B 9.2
λ=λ1+λ2=4.5×1010+0.5×1010
λ=5×1010 per year
N=N0eλt .... (i)


In time "t" 99% of K decayed, so the undecayed part of the sample
N=N0(99N0100)=N0/100,
and now putting the value of N in equation (i)

N0100=N0eλt

eλt=100
t=(2.303)×2λ
t=4.6λ=4.65×1010 years
4.65×1010=t ×109
t=465=9.2

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