Question

Mass numbers of two nuclei are in the ratio of $4 : 3$. Their nuclear densities will be in the ratio of

• A. $4 : 3$
• B. $\bigg(\frac{3}{4}\bigg)^{\frac{1}{3}}$
• C. $1:1$
• D. $\bigg(\frac{4}{3}\bigg)^{\frac{1}{3}}$

Answer 1

Answer: (C)

$1:1$

Answer 2

$R = R_0A^{\frac{1}{3}}$

$⇒ \frac{R_1}{R_2} = \bigg(\frac{A_1}{A_2}\bigg)^\frac{1}{3}$

$= \bigg(\frac{4}{3}\bigg)^{\frac{1}{3}}$

Ratio of density between two nuclei: $\frac{ρ_1}{ρ_2} = \frac{\frac{A_1}{V_1}}{\frac{A_2}{V_2}}$

= $\bigg(\frac{A_1}{A_2}\bigg) \times \bigg(\frac{R_2}{R_1}\bigg)^3$

= $1 : 1$