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. `3.6 xx 10^10`
B. `3.6 xx 10^12`
C. `3.1 xx 10^15`
D. `31.1 xx 10^15`

Answer

A

Explanation

(a) According to Avogadro's hypothesis,
`N_0 = (6.02 xx 10^23)/(226) = 2.66 xx 10^21`
Half-life = `T = (0.693)/(lamda) = 1620 years`
`:. lamda = (0.6931)/(1620 xx 3.16 xx 10^7)`
`=1.35 xx 10^-11 sec^-1`
Because half-life is very much large as compared to its time interval, hence
Now `(dN)/(dt) lamda N ~~ lamda N_0`
or `dN = lamda N_0 dt`
`=(1.35 xx 10^-11) (2.66 xx 10^21) xx 1`
`=3.61 xx 10^10`.