Atoms & Nuclei

JEE Main level, single correct, medium

157 of 239

Question 157 of 239

A nucleus has mass number α\alpha and radius RαR_{\alpha}. Another nucleus has mass number β\beta and radius RβR_{\beta}. If β=8α\beta=8 \alpha then Rα/RβR_{\alpha} / R_{\beta} is:

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Answer: (B) 0.5

Nuclear radius follows R=R0A1/3R = R_0 A^{1/3} where AA is mass number.
Given β=8α\beta = 8\alpha, we have Rα=R0α1/3R_\alpha = R_0 \alpha^{1/3} and Rβ=R0(8α)1/3=R0⋅2α1/3=2RαR_\beta = R_0 (8\alpha)^{1/3} = R_0 \cdot 2 \alpha^{1/3} = 2R_\alpha.
Thus Rα/Rβ=1/2=0.5R_\alpha/R_\beta = 1/2 = 0.5.

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