In an accelerator experiment on high energy collision of electrons with positrons, a certain events is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two `gamma`-rays of equal energy. What is the wavelength associated with each `gamma`-rays? `(1BeV=10^(9)eV)`

Explanation

Total energy of two `gamma` rays = Total energy of electron positron pair before annihilation = 10.2 BeV
Energy of each `gamma` - rays photon
`E=(10.2)/2` BeV
`=5.1 BeV = 5.1 xx10^(9) eV`
`=5.1xx10^(9) xx1.602xx10^(-19)J`
Also , energy of `gamma` - ray (photon) is given by
`E=(hc)/lamda`
where `lamda` is the wavelength of `gamma` - ray
`lamda=(hc)/E`
`=(6.625xx10^(-34)xx3xx10^(8))/(5.1xx10^9xx1.602xx10^(-19))`
`=2.44 xx10^(-16)m `