Question

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$ , where x is _____.

Answer 1

Given:

$R = R_0 A^{1/3}$

We know that:

$R^3 \propto A$

For the first nucleus:

$\frac{4.8^3}{A} = \frac{4^3}{64}$

Rearranging and simplifying:

$\frac{64}{A} = \left(\frac{4}{4.8}\right)^3$

Calculating:

$\frac{64}{A} = (1.2)^3$

$\frac{64}{A} = 1.44 \times 1.2$

Next, equating for the second nucleus:

$\frac{1000}{x} = 64 \times 1.44 \times 12$

Calculating:

$x = 27$