Search any question & find its solution
Question:
Answered & Verified by Expert
Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be
Options:
Solution:
2723 Upvotes
Verified Answer
The correct answer is:
$1: 1$
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
$$
\begin{aligned}
R_{0} A_{1}^{1 / 3}: R_{0} A_{2}^{1 / 3}=1: 3^{1 / 3} \\
\text { Density }=\frac{A}{\frac{4}{3} \pi R^{3}} \\
\therefore \rho_{A_{1}}: \rho_{A_{2}}=\frac{1}{\frac{4}{3} \pi R_{0}^{3} \cdot 1^{3}}=\frac{3}{\frac{4}{3} \pi R_{0}^{3}\left(3^{1 / 3}\right)^{3}}
\end{aligned}
$$
Their nuclear densities will be the same.
Alternative
$$
A_{1}: A_{2}=1: 3
$$
Their radii will be in the ratio
$$
\begin{aligned}
R_{0} A_{1}^{1 / 3}: R_{0} A_{2}^{1 / 3}=1: 3^{1 / 3} \\
\text { Density }=\frac{A}{\frac{4}{3} \pi R^{3}} \\
\therefore \rho_{A_{1}}: \rho_{A_{2}}=\frac{1}{\frac{4}{3} \pi R_{0}^{3} \cdot 1^{3}}=\frac{3}{\frac{4}{3} \pi R_{0}^{3}\left(3^{1 / 3}\right)^{3}}
\end{aligned}
$$
Their nuclear densities will be the same.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.