$(a)\;\large\frac{h}{m_{0} C}\qquad(b)\;\large\frac{2h}{m_{0} C}\qquad(c)\;\large\frac{h}{2m_{0}C}\qquad(d)\;None$

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Answer : (a) $\;\large\frac{h}{m_{0} C}$

Explanation :

Where $m_{0}=\;$ rest mass of an electron (or positron)

C=speed of light

Considering the momenta of system just before and after event (anhiliation) we see that two identical photons will be resulted and travel in opposited directions with equal magnitude of momenta and energy $\;\large\frac{hc}{\lambda}\;$ where

$\lambda$= wavelength of radiation

Conservation of energy yields

$\large\frac{hC}{\lambda}+\large\frac{hC}{\lambda}=m_{0}C^2+m_{0}C^2$

$\large\frac{hC}{\lambda}=m_{0}C^2$

$\lambda=\large\frac{h}{m_{0}C}\;.$

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