A radioactive sample is `alpha-`emitter with half life `138.6` days is observed by a student to have `2000` disintegration/sec. The number of radioactive nuclei for given activity are.

Options

A. `3.45 xx 10^10`
B. `1 xx 10^10`
C. `3.45 xx 10^15`
D. `2.75 xx 10^11`

Answer

A

Explanation

(a) Activity of substance that has `2000` disintegration/sec
`=(2000)/(3.7 xx 10^10) = 0.054 xx 10^-6 ci = 0.054 mu ci`
The number of radioactive nuclei having activity `A`
`N = (A)/(lamda) = (2000 xx T_(1//2))/(log_e 2)`
=`(2000 xx 138.6 xx 24 xx 3600)/(0.693) = 3.45 xx 10^10`.