During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1µg of 90Sr 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.

Question 4.17: During nuclear explosion, one of the products is ⁹⁰Sr with half-life of 28.1 years. If 1µg of ⁹⁰Sr 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.
Answer
Given that
All nuclear reaction are first order reaction

Half life t1/2 = 28.1 years
Initial quantity [R]o = 1 µg
Time, t = 1o years
Use the formula of rate constant for the first order reaction

k = 0.02466 y ^-1
Use formula of first order reaction
For the First part t = 10 year

Use formula log 1/[R] = - log [R], we get

log [R] = -0.1071
take antilog both side, we get
[R] = antilog [-0.1071]
We can not take antilog of negative value so convert it in positive values by adding and subtracting 1
[R] = antilog [-0.1071 + 1 -1 ]
We can write -1 as 1 bar
We get

Now take antilog we get
[R] = 0.7814 µg
For the second part t = 60 year

Use formula log 1/[R] = - log [R], we get

log [R] = -0.6425
take antilog both side, we get
[R] = antilog [-0.6425]
We can not take antilog of negative value so convert it in positive values by adding and subtracting 1
[R] = antilog [-0.6425 + 1 -1 ]
We can write -1 as 1 bar
We get

Now take antilog we get
[R] = 0.2278 µg
Answer
After 1o years amount = 0.7814 µg
After 60 years amount = 0.2278 µg