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

Options

A. 138.6 hr
B. 1386 hr
C. 13860 hr
D. 138600 hr

Answer

C

Explanation

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