` 1 mg` of `Th` emits 22 `alpha`-particles per unit solid angle per minute. Calculate `t_(1//2)` or `Th (Th = 232)`.

Explanation

Number of `alpha`-particles per minute in all directions emitted
`= 22 xx 4 pi = (22 xx 4pi)/(60) s^(-1)`
Number of atoms in `1 mg` of `th = (10^(-3) g xx 6.02 xx 10^(23))/(232)`
decay per second `= (22)/(15) pi`
`:. (22)/(15) pi = (K xx 10^(-3) xx 6.02 xx 10^(23))/(232)`
`:. K = 1.77 xx 10^(-18)`
and `t_(1//2) = (0.693)/(K) = 1.28 xx 10^(10)` years