Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

Question

Aicharya · Accepted Answer

Density of nuclear matter is independent of mass number, so the required ratio is $1: 1$.
Alternative :
$A_1: A_2=1: 3$
Their radii will be in the ratio
$\begin{gathered}
R_0 A_1^{1 / 3}: R_0 A_2^{1 / 3}=1: 3^{1 / 3} \\
\text { Density }=\frac{A}{\frac{4}{3} \pi R^3} \\
\therefore \rho_{A_1}: \rho_{A_2}=\frac{1}{\frac{4}{3} \pi R_0^3 \cdot 1^3}: \frac{3}{\frac{4}{3} \pi R_0^3\left(3^{1 / 3}\right)^3}
\end{gathered}$
Their nuclear densities will be the same.

Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

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