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

Given, energy of 2 `gamma`- rays 2E = 10.2 BeV `[because overset(0)underset(-1)e+overset(0)underset(+1)e rarr2gamma -" rays "]`
`rArr 2(hc)/(lambda)=10.2BeV[becauseE=(hc)/(lambda)]rArr lambda=(2hc)/(10.2BeV)`
Here h = ` 6.63 xx 10^(-34) J - S, c = 3 xx 10^(8) ` m/s , 1 BeV = ` 10^(9) eV = 10^(9 ) xx 1.6 xx 10^(-19) ` J
` rArr lambda = ( 2 xx 6.63 xx 10^(-34) xx 3xx 10^(8))/(10.2 xx 10^(9) xx 1.6 xx 10^(-19)):. lambda = 2.436 xx 10^(-16) ` m