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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+λβ⇒1Tm=1Tα+1Tβ=11620+1405=1324 λav×t=2.303logN0Nt,1324t=2.303log10025⇒t=2.303×324log4=449 years

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