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Q.

The mean lives of a radioactive substance are 1620 and 405 years for α-emission and β-emission respectively Find out the time (in years) after which three fourth of a sample will decay if it is decaying both by α-emission and β-emission simultaneously. (Take In 2 = 0.693)

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answer is 449.

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Detailed Solution

For a simultaneous decay process, we have 1T=1Tα+1Tβ⇒ T=TαTβTα+Tβ=324 years Since NN0=12n, where n=tT12According to problem, we have NN0=14⇒tT12=2⇒t=2T12⇒t=2(0.693T)≈449 yr

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