A) \[{{\left( \frac{53}{13} \right)}^{\frac{1}{3}}}{{R}_{\text{Al}}}\]
B) \[\frac{5}{3}{{\text{R}}_{\text{Al}}}\]
C) \[\frac{3}{5}{{\text{R}}_{\text{Al}}}\]
D) \[{{\left( \frac{13}{53} \right)}^{\frac{1}{3}}}{{\text{R}}_{\text{Al}}}\]
Correct Answer: B
Solution :
Radius of the nucleus is given by \[R={{R}_{0}}{{A}^{1/3}}\Rightarrow R\propto {{A}^{1/3}}\] \[\frac{{{R}_{\text{Al}}}}{{{R}_{Te}}}={{\left( \frac{{{A}_{\text{Al}}}}{{{A}_{Te}}} \right)}^{1/3}}={{\left( \frac{27}{125} \right)}^{1/3}}=\frac{3}{5}\] \[{{R}_{Te}}=\frac{5}{3}{{R}_{\text{Al}}}\]
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