A) \[\frac{hc}{{{m}_{0}}}\]
B) \[\frac{h}{{{m}_{0}}c}\]
C) \[\frac{h}{{{m}_{0}}{{c}^{2}}}\]
D) \[\frac{{{m}_{0}}c}{h}\]
Correct Answer: B
Solution :
From conservation of momentum, two identical photons must travel in opposite directions with equal magnitude of momentum and energy \[\frac{hc}{\lambda }\]. From conservation of energy, \[\frac{hc}{\lambda }+\frac{hc}{\lambda }={{m}_{0}}{{c}^{2}}+{{m}_{0}}{{c}^{2}}\] or \[\lambda =\frac{h}{{{m}_{0}}c}\] Alternative: The dimensions of wavelength is [L]. In the four option only option [b] can give the dimensions of [L], i. e, \[\frac{h}{{{m}_{0}}c}=\frac{J-s}{kg-m/s}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}]\,\,[T]}{[M]\,\,[L{{T}^{-1}}]}\] = [L]
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