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Question

The mean lives of a radioactive substance are 1620 and 405 years 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

449 years

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B

440 years

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C

520 years

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D

549 years

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Solution

The correct option is A

449 years


When a substance decays by α and β emission simultaneously, the average rate of disintegration λav is given by
λav=λα+λβ when λα = disintegration constant for α-emission only λβ = disintegration constant for β-emission only
Mean life is given by Tm=1λ,λav=λα+λβ1Tm=1Tα+1Tβ=11620+1405=1324
λav×t=2.303logN0Nt,1324t=2.303log10025t=2.303×324log4=449 years


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