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 y-rays:
`E = 10.2 Bev`
`= 10.2xx10^(9) eV`
`= 10.2xx10^(9)xx1.6xx10^(-10) J`
Hence, the energy of each `gamma`-rays:
`E' = (E)/(2)`
`=(10.2xx1.6xx10^(-10))/(2)=8.16xx10^(-10)J`
Planck's constant, `h = 6.626xx10^(-34) Js`
Speed of light, `C = 3xx10^(8)m//s`
Energy is related to wavelength as :
`E' = (hc)/(lambda)`
`:. lambda = (hc)/(E')`
`= (6.626xx10^(-34)xx3xx10^(8))/(8.16xx10^(-10))=2.436xx10^(-16)m`
Therefore, the wavelength associated with each `gamma`-ray is `2.436xx10^(-16)m`