A) \[{{2}^{1/3}}:1\]
B) \[1:{{3}^{1/2}}\]
C) \[{{3}^{1/3}}:1\]
D) \[1:{{2}^{1/3}}\]
Correct Answer: D
Solution :
Let the mass number of the two nuclear parts be \[{{A}_{1}}\] and\[{{A}_{2}}\]. The by conservation of linear momentum, we have \[m{{A}_{1}}\times 2m{{A}_{2}}\times 1\] \[{{A}_{1}}/{{A}_{2}}=1/2\] The ratio of their nuclear size is \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{R}_{0}}}{{{R}_{0}}}\frac{A_{1}^{1/3}}{A_{2}^{1/3}}={{\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)}^{1/3}}=\frac{1}{{{2}^{1/3}}}\]
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