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13.Nuclei
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The ratio of radii of nuclei $_{13}A{l^{27}}$ and $_{52}{X^A}$ is $3 : 5$. The number of neutrons in the nuclei of $X$ will be
A
$52$
B
$73$
C
$125$
D
$13$
Solution
(b) $r \propto {A^{1/3}}$ ==> $\frac{{{r_1}}}{{{r_2}}} = {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^{1/3}}$
==> $\frac{3}{5} = {\left( {\frac{{27}}{A}} \right)^{1/3}}$
==> $\frac{{27}}{{125}} = \frac{{27}}{A}$
==> $A = 125$
Number of nuclei in atom $X = A – 52 = 125 – 52 = 73.$
Standard 12
Physics
