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  • In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy.

Q: 11.24 In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy  10.2\hspace{1mm}BeV into two \gamma-rays of equal energy. What is the wavelength associated with each \gamma-ray?  (1\hspace{1mm}BeV=10^9\hspace{1mm}eV) 

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The total energy of 2 \gamma rays=10.2 BeV

The average energy of 1 \gamma ray, E=5.1 BeV

The wavelength of the gamma-ray is given by

\\\lambda =\frac{c}{\nu }\\\lambda =\frac{hc}{h\nu }\\ \lambda =\frac{hc}{E}\\ \lambda =\frac{6.62\times 10^{-34}\times 3\times 10^{8}}{5.1\times 10^{9}\times 1.6\times 10^{-19}}\\ \lambda =2.436\times 10^{-16}m

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