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13.Nuclei
medium
પ્રાણી હાડકામાં ${}^{14}C:{}^{12}C$ નો ગુણોતર $\left( {\frac{1}{{16}}} \right)$ છે. ${}^{14}C$ નું અર્ધઆયુ $5730$ વર્ષ છે. હાડકાની ઉમર ........ વર્ષ
A
$11460$
B
$17190$
C
$22920$
D
$45840$
(AIIMS-2006)
Solution
$\frac{{^{14}{\text{C}}}}{{^{12}{\text{C}}}} = \frac{1}{{16}} = \frac{{\text{N}}}{{{{\text{N}}_0}}}$
$\because \frac{\mathrm{N}}{\mathrm{N}_{0}}=\left(\frac{1}{2}\right)^{\mathrm{n}}$
$\Rightarrow \quad \frac{1}{16}=\left(\frac{1}{2}\right)^{n} \Rightarrow\left(\frac{1}{2}\right)^{4}=\left(\frac{1}{2}\right)^{n}$
or, $\quad \mathrm{n}=4$
or $\quad \frac{t}{\mathrm{T}}=4$
or $\quad \mathrm{t}=4 \times \mathrm{T}=4 \times 5730=22920$ $years$
Standard 12
Physics
