Question

The mass numbers of nuclei A and B are respectively 135 and 5. The ratio of their radii is

• A. 1 : 3
• B. 3 : 1
• C. $\sqrt{27}:1$
• D. $1:\sqrt{27}$

Answer 1

Answer: (B)

We know that $m=\frac{4}{3}\pi r^{3}d$ $\therefore$ $m\propto r^3$ $r\propto {(m)}^{1/3}$ Here $\frac{r_A}{r_B}={\left(\frac{m_A}{m_B}\right)}^{1/3}$ $\frac{r_A}{r_B}={\left(\frac{135}{5}\right)}^{1/3}$ $\frac{r_A}{r_B}={\left(27\right)}^{1/3}$ $\frac{r_A}{r_B}=\frac{3}{1}$