1 Mole of an `alpha`-emitting nuclide with `t_(1//2)=10`hous, is placed in a sealed container. The time in which `4.52xx10^(23)` molecules of He will accumulate is

Options

A. 4.52 hr
B. 9.40 hr
C. 10.10 hr
D. 20.00 hr

Answer

D

Explanation

`t_(1//2)=10` hr
`lambda=(28)/(0.0231)=1212`
`=0.0693 hr^(-1)`
He molecules formed `=4.52xx10^(23)`
`=(4.52xx10^(23))/(6.02xx10^(23))=0.75` mol
`therefore` Nuclide decayed=0.75 mol
Nuclide left undecayed =1-0.75 = 0.25 mol
`t=(2.303)/(lambda)"log"(1)/(0.25)`
`=(2.303)/(0.0693)"log"([N]_(0))/([N])`
`=(2.303)/(0.0693)"log"(1)/(0.25)`
=33.20 log 4
`=33.20 xx 0.6021`
`~~20` hr