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13.Nuclei
hard
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______.
A
$27$
B
$28$
C
$29$
D
$30$
(JEE MAIN-2024)
Solution
$\mathrm{R}=\mathrm{R}_0 \mathrm{~A}^{1 / 3}$
$\mathrm{R}^3 \propto \mathrm{A}$
$\left(\frac{4.8}{4}\right)^3=\frac{64}{\mathrm{~A}}$
$=\frac{64}{\mathrm{~A}}=(1.2)^3$
$\frac{64}{\mathrm{~A}}=1.44 \times 1.2$
$\mathrm{~A}=\frac{64}{1.44 \times 1.2}=\frac{1000}{\mathrm{x}}$
$\mathrm{x}=\frac{144 \times 12}{64}=27$
Standard 12
Physics
