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

Correct Answer: 27

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:

\[ x = 27 \]