The radius of a nucleus of mass number 64 is | vedclass

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Question

(A) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.This implies $R^3 \propto A

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(A) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.This implies $R^3 \propto A$,or $\frac{R_1^3}{R_2^3} = \frac{A_1}{A_2}$.Given $R_1 = 4.8 	ext{ fermi}$,$A_1 = 64$,and $R_2 = 4 	ext{ fermi}$.Substituting the values: $\left(\frac{4.8}{4}ight)^3 = \frac{64}{A_2}$.$(1.2)^3 = \frac{64}{A_2}$.$1.728 = \frac{64}{A_2}$.$A_2 = \frac{64}{1.728} = \frac{64000}{1728}$.Simplifying the fraction: $A_2 = \frac{1000}{27}$.Comparing this with $\frac{1000}{x}$,we get $x = 27$.

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

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