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Question
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?
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Solution
k = `0.693/t_(1//2)`
= `0.693/28.1`
= 2.466 × 10−2 y−1
[A]0 = 1 µg
After 10 years,
k = `2.303/t log_10 ([A]_0]/([A])`
⇒ 2.466 × 10−2 = `2.303/10 log_10 1/([A])`
`1/([A]) = "antilog"_10 [(2.466 xx 10^-2 xx 10)/2.303]`
`1/([A]) = "antilog"_10 [0.2466/2.303]`
`1/([A])` = antilog10 (0.10707)
`1/([A])` = 1.2796
∴ [A] = `[1/1.2796]`
[A] = 0.7815 µg
After 60 years,
`1/([A]) = "antilog"_10 [(2.466 xx 10^-2 xx 60)/2.303]`
`1/([A]) = "antilog"_10 [1.4796/2.303]`
`1/([A])` = antilog10 [0.6424]
`1/([A])` = 4.39
[A] = `1/4.39`
[A] = 0.227 µg
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