Q142 / 200 · NEET 2008 (Screening) · Physics
Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be
- A$1: 3$
- B$3: 1$
- C$(3)^{1 / 3}: 1$
- Correct answerD$1: 1$
Solution
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.
Hence, the correct answer is option: 'D'.