The rate of disintegration was observed to be `1017` disintegrations per sec when its half life period is `1445` years. The original number of particles are.

Options

A. `8.9 xx 10^27`
B. `6.6 xx 10^27`
C. `1.4 xx 10^16`
D. `1.2 xx 10^17`

Answer

B

Explanation

(b) Rate of disintegration `(dN)/(dt) = 10^17 s^-1`
Half life `T_(1//2) = 1445 year`
=`1445 xx 365 xx 24 xx 60 xx 60 = 4.55 xx 10^10 sec`
Now decay constant
`lamda = (0.693)/(T_(1//2)) = (0.93)/(4.55 xx 10^10) = 1.5 xx 10^-11 per sec`
The rate of disintegration
`(dN)/(dt) = lamda xx N_0 rArr 10^17 = 1.5 xx 10^-11 xx N_0`
`rArr N_0 = 6.6 xx 10^27`.