A) \[\frac{3}{23}\]
B) \[\frac{5}{27}\]
C) \[\frac{7}{29}\]
D) \[\frac{9}{31}\]
Correct Answer: B
Solution :
The distance of closest approach is given by \[\frac{1}{{{\lambda }_{L}}}=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{1}^{2}}} \right)=R.\frac{3}{4}\] and \[\frac{1}{{{\lambda }_{B}}}=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)=R.\frac{5}{36}\] \[\therefore \]\[\frac{{{\lambda }_{B}}}{{{\lambda }_{L}}}=\frac{3}{4}\times \frac{36}{5}=\frac{27}{5}\]or \[{{\lambda }_{L}}:{{\lambda }_{B}}=5:27.\] Hence, the correction option is [b].
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