The half-life of radium is `1620 years` and its atomic weight is `226`. The number of atoms that will decay from its `1 g` sample per second will be .

Options

A. `3.61 xx 10^10`
B. `3.6 xx 10^12`
C. `3.11 xx 10^15`
D. `31.1 xx 10^15`

Answer

A

Explanation

(a) `(dN)/(dt) = lamda N , lamda = (0.6931)/(t_12) = (0.6931)/(1630 xx 365 xx 24 xx 60 xx 60)`,
`N = (6.023 xx 10^23)/(226)`
`:. (dN)/(dt) = (0.6931 xx 6.023 xx 10^23)/(1620 xx 365 xx 24 xx 60 xx 60 xx 226)`
`=3.61 xx 10^10`
(Avogadro's number `N = 6.02 xx 10^26` atom/kilomol).