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Question

The mean lives of a radioactive substance are 1620yr and 405yr for α-emission and β-emission, respectively. Find out the time during which three-fourth of a sample will decay, if it is decaying both by α-emission and β-emission simultaneously.

A
643yr
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B
449yr
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C
528yr
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D
279yr
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Solution

The correct option is D 449yrλ=λα+λβ=1Tα+1Tβ [∵λ=1T]=11620+1405 [given, Tα=1620yr and Tβ=405yr]=51620yr−134th sample will decay, i.e., remaining 1/4th,N=No(12)nNo4=No(12)n⇒n=2∴t=2T1/2=nIn2λ=2×0.6935/1620=449yr.

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