How many disintegrations per second will Occur in one gram of `._(92)^(238)U`, if its half-life against `alpha`- decay is `1.42xx10^(-17)s` ?

Explanation

Given Half-life period (T)
`= (0.693)/(lamda) =1.42 xx 10 ^(17) s`
` lamda = (0.693)/(1.42 xx 10 ^(17)) = 4.88 xx 10 ^(-18)`
Avagadro number `(N) = 6.023 xx 10 ^(23)` atoms
n= Numbers of atoms present in 1 g of `"" _(92) ^(238) U = (N)/(A)= (6. 023 xx 10 ^(23))/(238) = 25.30 xx 10 ^(20)`
Number of disintegrations `= (dN)/(dt) = lamda n`
` 4. 88 x 10 ^(-18) x 25.30 x 10 ^(20)`
` = 1.2346 x 10 ^(4)` disintegrates/sec