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 where x is

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Solution

Q.
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 ______ . [2024]

Ans.
(27) $R = R_{0} A^{1 / 3}$

   $4.8 = R_{0} {(64)}^{1 / 3}$

   $4.8 = R_{0} 4$ ...(i)

   $4 = R_{0} {(A)}^{1 / 3}$ ...(ii)

   $(i) divided by (i i), 1.2 = \frac{4}{{(A)}^{1 / 3}}$

$A = \frac{64}{1.728} = \frac{1000}{x}$

$x = \frac{1728}{64} = 27$

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