#### Question

During nuclear explosion, one of the products is ^{90}Sr with half-life of 28.1 years. If 1μg of ^{90}Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

#### Solution

Here, k = `0.693/t_"1/2" = 0.693/28.1 y^(-1)`

It is known that,

`t = 2.303/k log ([R]_0)/([R])`

`=> 10 = 2.303/(0.693/28.1) log 1/[R]`

`=>10 = 2.303/(0693/28.1)(-log [R])`

`=> log [R] = -(10xx0.693)/(2.303xx28.1)`

=>[R] = antilog (-0.1071)

= antilog(`(bar"1".8929`)

= 0.7814 `mug`

Therefore, 0.7814 μg of ^{90}Sr will remain after 10 years.

Again,

` t= 2.303/k log ([R]_0)/([R])`

`=> 60 = 2.303/(0.693/28.1) log 1/[R]`

`=>log[R] = -(60xx0.693)/(2.303xx28.1)`

=>[R] = antilog (-0.6425)

=antilog(`bar"1"`.3575)

= 0.2278 `mug`

Therefore, 0.2278 μg of ^{90}Sr will remain after 60 years