The radius of a nucleus with mass number 27 i | vedclass

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(C) The radius of a nucleus is given by the relation $R = R_0 A^{1/3}$, where $A$ is the mass number.Given $R_1 = R$ for $A_1 = 27$ and $R_2 = 2R$ for

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It is likely to undergo fission reaction

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(C) The radius of a nucleus is given by the relation $R = R_0 A^{1/3}$, where $A$ is the mass number.Given $R_1 = R$ for $A_1 = 27$ and $R_2 = 2R$ for $A_2$.Taking the ratio: $\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}ight)^{1/3}$.Substituting the values: $\frac{R}{2R} = \left(\frac{27}{A_2}ight)^{1/3}$.$\frac{1}{2} = \left(\frac{27}{A_2}ight)^{1/3}$.Cubing both sides: $\frac{1}{8} = \frac{27}{A_2}$.$A_2 = 27 	imes 8 = 216$.Nuclei with very high mass numbers (like $A=216$) are generally unstable and tend to undergo radioactive decay or fission to reach a more stable state.

The radius of a nucleus with mass number $27$ is $R$. Which of the following is true about a nucleus whose radius is $2R$?

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