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Question

The mean lives of a radioactive substance for α and β emissions are 1620 years and 405 years respectively. After how much time will the activity be reduced to one fourth

A
405 year
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B
1620 year
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C
449 year
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D
None of these
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Solution

The correct option is C 449 year
λα=11620 per year and λβ=1405 per year and it is given that the fraction of the remained activity
AA0=14
Total decay constant λ=λα+λβ=11620+1405=1324 per year
We know that A=A0eλtt=1λlogeA0At=1λloge4=2λloge2=324×2×0.693=449 years.

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