A `U^(238)` preparation of mass 1 g emits `1.24 xx 10^(4) alpha` -particles per second. Find the half life of this nuclide and the activity of the preparation in becquerels:

Options

A. `4.5 xx 10^(9) yrs, 1.24 xx 10^(4) Bq`
B. `1.5 xx 10^(10) yrs, 1.01 xx 10^(5) Bq`
C. `6.2 xx 10^(10) yrs,3.24 xx 10^(5) Bq`
D. `2.6 xx 10^(8) yrs, 1.4 xx 10^(4) Bq`

Answer

A

Explanation

`N=N_(0) e^(-lambdat)," activity "=-(d N)/(dt)= lambda N`
N=No. of atoms in 1 g
`=(6.023 xx 10^(23))/(238) =2.53 xx 10^(21)`
`(d N)/(dt)=lambda N`
`1.24 xx 10^(4) =lambda xx 2.53 xx 10^(21)`
`or lambda=4.9 xx 10^(-18)`
Now `T=(0.6931)/(lambda) =(0.693)/(4.9 xx 10^(-18)) =1.4 xx 10^(17)`
`=4.5 xx 10^(9)"yrs"`
Acitivity of preparation `=1.24 xx 10^(4) Bq`.