The mass number of a nucleus having a radius | vedclass

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Question

(A) The radius $R$ of a nucleus with mass number $A$ is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant.Let the mass number of the fi

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(A) The radius $R$ of a nucleus with mass number $A$ is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant.Let the mass number of the first nucleus be $A_1$ and its radius be $R_1$.Let the mass number of the second nucleus be $A_2 = 192$ and its radius be $R_2$.According to the problem,$R_1 = \frac{R_2}{2}$.Substituting the formula for radius: $R_0 (A_1)^{1/3} = \frac{1}{2} R_0 (A_2)^{1/3}$.Dividing both sides by $R_0$: $(A_1)^{1/3} = \frac{1}{2} (A_2)^{1/3}$.Cubing both sides: $A_1 = \frac{1}{8} A_2$.Given $A_2 = 192$,we have $A_1 = \frac{192}{8} = 24$.Therefore,the mass number of the nucleus is $24$.

The mass number of a nucleus having a radius equal to half of the radius of a nucleus with mass number $192$ is:

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