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10 g atoms of an alpha-active radioactiv...

10 g atoms of an `alpha`-active radioactive isotope are disintegrating in a sealed container. In one hour, helium gas collected at STP is 11.2 `"cm"^3`. The half-life of the radioactive isotope is

A

138.6 hr

B

1386 hr

C

13860 hr

D

138600 hr

Text Solution

Verified by Experts

The correct Answer is:
C
Gram atoms of helium gas formed in 1 hour `=11.2/22400=5xx10^(-4)`
i.e., Gram atoms of radioactive isotope disintegrated in one hour =`5xx10^(-4)`
Rate of disintegration = `lambdaN`
`5xx10^(-4) = lambda xx 10` or `lambda=5xx10^(-5)hr^(-1)`
`t_(1//2) = 0.693/lambda=0.693/(5xx10^(-5))` hr = 13860 hr
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Knowledge Check

  • The half-life of a radioactive isotope is 3 hours. Value of its disintegration constant is

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