A) less than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
B) \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
C) \[v{{\left( \frac{3}{4} \right)}^{1/2}}\]
D) greater than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
Correct Answer: D
Solution :
[d]: From Einsteins?s photoelectric equation, we get\[\frac{hc}{\lambda }=\frac{1}{2}m{{v}^{2}}+h{{\upsilon }_{0}}\] ?(i) and\[\frac{hc}{3\lambda /4}=\frac{1}{2}mv{{'}^{2}}+h{{\upsilon }_{0}}\] or\[\frac{1}{2}mv{{'}^{2}}=\frac{4}{3}\left( \frac{hc}{\lambda } \right)-h{{\upsilon }_{0}}=\frac{4}{3}\left( h{{\upsilon }_{0}}+\frac{1}{2}m{{v}^{2}} \right)-h{{\upsilon }_{0}}\] (Using (i))\[=\frac{1}{3}h{{v}_{0}}+\frac{4}{3}\left( \frac{1}{2}m{{v}^{2}} \right)\] or\[\frac{1}{2}mv{{'}^{2}}>\frac{4}{3}\left( \frac{1}{2}m{{v}^{2}} \right)or\,v{{'}^{2}}>\frac{4}{3}{{v}^{2}}\]or\[v'>v{{\left( \frac{4}{3} \right)}^{1/2}}\]
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