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13.Nuclei
medium
The radius of germanium $(Ge)$ nuclide is measured to be twice the radius of ${}_4^9Be$ . The number of nucleons in $Ge$ are
A
$72$
B
$73$
C
$74$
D
$75$
(AIPMT-2006)
Solution
Nuclear radii $R=R_{0}(A)^{1 / 3}$
where $R_{0} \approx 1.2 \mathrm{Fm}$
or $R \propto(A)^{1 / 3}$
$\therefore \,\,\frac{{{R_{{\text{Bc}}}}}}{{{R_{{\text{Ge}}}}}} = \frac{{{{(9)}^{1/3}}}}{{{{(A)}^{1/3}}}}{\text{ }}$ or $\frac{{{R_{{\text{Be}}}}}}{{2{R_{{\text{Be}}}}}} = \frac{{{{(9)}^{1/3}}}}{{{{(A)}^{1/3}}}}$
( $\because $ given ${R_{Ge}}\, = \,2{R_{Be}}$)
or, $(A)^{1 / 3}=2 \times(9)^{1 / 3}$ or, $A=2^{3} \times 9=8 \times 9=72$
$\therefore$ The number of nucleons in $Ge$ is $72$
Standard 12
Physics
