Question

Compare the radio of two nuclei with mass numbers A1 and A2 respectively

Answer 1

The answer to the question is $\frac{R_{1}} {R_{2}}\ =\ (\frac{A_{1}} {A_{2}}) {1/3}$

EXPLANATION:

The radius of a nucleus is directly proportional to the cube root of atomic mass number.

Mathematically it can be written as $R\ \alpha\ A^{1/3}$

                                                           $R\ =\ R_{0}A^{1/3}$

Here, R is the radius of the nucleus having mass number A.

$R_{0}$  is a constant whose value is 1.2 fermi.

We are given two atoms having mass numbers $A_{1}\ and\ A_{2}\ respectively$

We are asked to compare the radii of the two nuclei.

Let the radius of the two atoms are $R_{1}\ and\ R_{2}\ respectively$

From above we know that $R_{1}\ =\ R_{0}A_{1}^ {1/3}$   [1]

                                            $R_{2}\ =\ R_{0}A_{2}^ {1/3}$    [2]

Dividing 1 by 2 we get-

                        $\frac{R_{1}} {R_{2}}\ =\ (\frac{A_{1}} {A_{2}}) {1/3}$ [ans]