During nuclear explosion, one of the products is $^{90} S r$ with half life of $28.1 y r$ . If $1 μ g$ of $^{90} S r$ was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after $10$ year and $60$ year if it is not lost metabolically.

Question

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Answer 1

$k = \frac{0 . 6 9 3}{t _{1 / 2}}$

$k = \frac{0 . 6 9 3}{2 8 . 1} = 0.0247 / y e a r$

(i) After 10 years, let $x μ$ be the concentration of $^{90} S r$ .
$k = \frac{2 . 3 0 3}{t} l o g \frac{[ A ] _{0}}{[ A ]}$

$0.0247 = \frac{2 . 3 0 3}{1 0 y e a r s} l o g (\frac{1}{x})$

$x = 0.782 μ g$

(ii) After 60 years, let $y μ$ be the concentration of $^{90} S r$ .
$k = \frac{2 . 3 0 3}{t} l o g \frac{[ A ] _{0}}{[ A ]}$

$0.0247 = \frac{2 . 3 0 3}{6 0 y e a r s} l o g (\frac{1}{y})$

$y = 0.228 μ g$

Answer 2

k = \frac{0 . 6 9 3}{t _{1 / 2}}

k = \frac{0 . 6 9 3}{2 8 . 1} = 0.0247 / y e a r

(i) After 10 years, let

x μ

be the concentration of

^{90} S r

.

k = \frac{2 . 3 0 3}{t} l o g \frac{[ A ] _{0}}{[ A ]}

0.0247 = \frac{2 . 3 0 3}{1 0 y e a r s} l o g (\frac{1}{x})

x = 0.782 μ g

(ii) After 60 years, let

y μ

be the concentration of

^{90} S r

.

k = \frac{2 . 3 0 3}{t} l o g \frac{[ A ] _{0}}{[ A ]}

0.0247 = \frac{2 . 3 0 3}{6 0 y e a r s} l o g (\frac{1}{y})

y = 0.228 μ g