Q.

The mean lives of a radioactive sample are 30 years and 60 years for α-emission and β- emission respectively. If the sample decays both by α-emission and  β-emissionsimultaneously, the time after which, only one-fourth of the sample remain is

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a

32.45 years

b

20 years

c

27.72 years

d

45 years

answer is C.

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Detailed Solution

λe=130+160=120 Now N=N0e-λet =N04=N0e-t20        ⇒t=27.72 yrs
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The mean lives of a radioactive sample are 30 years and 60 years for α-emission and β- emission respectively. If the sample decays both by α-emission and  β-emissionsimultaneously, the time after which, only one-fourth of the sample remain is