Question

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

• A. $(3)^{1/3} : 1$
• B. 1 : 1
• C. 1 : 3
• D. 3 : 1

Answer 1

The Correct Option is B

Given :
A₁ : A₂ = 1 : 3
Their radii will be in the ratio
\(R_0A_1^{1/3}:R_0A_2^{1/3}=1:3^{1/3}\)
Now, Density = \(\frac{A}{\frac{4}{3}\pi R_3}\)
\(\therefore \rho_{A_1}:\rho_{A_2}=\frac{1}{\frac{4}{3}\pi R_0^{3}.1^3}\)
\(=\frac{3}{\frac{4}{3}\pi R_0^3(3^{1/3})^3}\)
Hence, their nucleus densities will be the same.
Therefore, the correct option is (B) : 1 : 1.