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

Answer: (B)

1 : 1

Answer 2

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.