The wavelengths of the photons at which a radiation field of temperature T radiates most intensely is given by . We have to show (a) that the energy E in MeV of such a photon can be computed from

(b) We have to find the minimum temperature at which a photon can create an electron-positron pair.

Solution:             Click For PDF Version

(a)

The wavelengths of the photons at which a radiation field of temperature T radiates most intensely is given by . The energy E of a photon of wavelength will be

(b)

The rest mass energy of an electron (positron) is 0.51 MeV. Therefore, the minimum energy photon that can create an electron-positron pair will be 1.02 MeV. The blackbody temperature that will radiate most intensely at wavelength corresponding to energy of 1.02 MeV will be