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

Solution

All radioactive decay are first order process.

∴

decay constant.

λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{28.1} = 0.0247 {year}^{- 1}

(i) where t = 10 years,

λ = \frac{2.303}{t} \log \frac{N_{0}}{N} t = 10 years N_{0} = 1 microgram = 1 \times 10^{- 6} g, N = ? 10 = \frac{2.303}{0.0247} \log \frac{1 \times 10^{- 6}}{N}

\log \frac{1 \times 10^{- 6}}{N} = \frac{10 \times 0.0247}{2.303} = 0.1072 \frac{1 \times 10^{- 6}}{N} = Antilog 0.1072 = 1.1280 N = \frac{1 \times 10^{- 6}}{1.1280} = 0.7842 \log

(ii)

t = 60 years 60 = \frac{2.303}{0.0247} \log \frac{1 \times 10^{- 6}}{N} \log \frac{1 \times 10^{- 6}}{N} = \frac{60 \times 0.0247}{2.303} = 0.6435 \frac{1 \times 10^{- 6}}{N} = \frac{60 \times 0.0247}{2.303} = 0.6435 \frac{1 \times 10^{- 6}}{N} = Antilog 0.6453 = 4.400 N = \frac{1 \times 10^{- 6}}{4.400} = 0.227 μg

Thus, after 10 years and 60 years, 0.7842 log and 0.227 log of ⁹⁰Sr will be left as undecayed.

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