Question

During nuclear explosion, one of the products is ⁹⁰Sr with half life of 28.1 years. If 1 µg of ⁷⁰Sr was absorbed in bones of a newly born baby instead of calcium, how much of it will remain after 10 year, and 60 years. If it is not lost metabolically?

Answer 1

Decay constant (k) = \(\frac { 0.693 }{ t_{ 1/2 } } =\frac { 0.693 }{ 28.1 } \)
0.025 = 25 x 10^-2 year^-1
After 10 years, the left amount will be
[A]₀ = 1 µg,
[A] = ?
t = 10 years
k = 2.5 x 10^-2 year^-1

log [A] = –0.1086
[A] = Antilog (-0.1086)
[A] = 0.78 µg
Hence after 10 years only 0.78 µg will remain.
Calculation of amount left after 60 years.
t = 60 years
[A]₀ = 1 µg
k= 2.5 x 10^-2 year^-1
[A] = ?

–log [A] = 65.13 x 10^-2
–log [A] = 0.6513
[A] = Antilog (-0.6513)
[A] = 0.2232 µg.
After 60 years only 0.2235 µg will remain.