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JEE Main 2024 (1 Feb, Shift 1) · Nucleus: Composition, Size & Nuclear Force

Nucleus: Composition, Size & Nuclear Force question from JEE Main 2024 (1 Feb, Shift 1)

Q10JEE Main 2024 · 1 FEB · SHIFT 1Easy

Nucleus: Composition, Size & Nuclear Force

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 _______.

Numerical answer type. Work it out, then open the answer.

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Answer: 27

$A \propto R^3$ , so $\frac{A}{64} = \left(\frac{4}{4.8}\right)^3 = \left(\frac{5}{6}\right)^3 = \frac{125}{216}$ .
$A = \frac{125 \times 64}{216} = \frac{8000}{216} = \frac{1000}{27}$
So $x = 27$ .

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