The positron is a fundamental particle with the same mass as that of the electron and with a charge equal to that of an electron but of opposite sign. When a positron and an electron collide, they may annihilate each other. The energy corresponding to their mass appears in two photons of equal energy. Find the wavelength of the radiation emitted. [Take : mass of electron `= (0.5//c^(2))MeV` and `hc = 1.2 xx 10^(-12) MeV-m`, where h is the Planck's constant and c is the velocity of light in air.

Answer

`2.48 xx 10^(-12) m`

Explanation

Total mass annihilated `2m_(e)=1/c^(2) MeV`
Total energy produced `=mc^(2)=1/c^(2) MeVxxc^(2)=1 MeV`
Energy of 1 photon `=0.5 MeV`
`lambda=(hc)/E=(1.2xx10^(-12))/(05)=2.4 p m`