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13.Nuclei
medium
Two nuclei have their mass numbers in the ratio of $1 : 3.$ The ratio of their nuclear densities would be
A
${\left( 3 \right)^{\frac{1}{3}}}:1$
B
$1:1$
C
$1:3$
D
$3:1$
(AIPMT-2008)
Solution
$A_{1}: A_{2}=1: 3$
Their radii will be in the ratio
$R_{0} A_{1}^{1 / 3}: R_{0} A_{2}^{1 / 3}=1: 3^{1 / 3}$
Density $=\frac{A}{\frac{4}{3} \pi R^{3}}$
$\therefore \quad \rho_{A_{1}}: \rho_{A_{2}}=\frac{1}{\frac{4}{3} \pi R_{0}^{3} \cdot 1^{3}}$ $=\frac{3}{\frac{4}{3} \pi R_{0}^{3}\left(3^{1 / 3}\right)^{3}}$
Their nuclear densities will be the same.
Standard 12
Physics
