We have to show (a) that the number N of photons radiated, per unit area per unit time, by a cavity radiator at temperature T is given by

In evaluating the integral, we will ignore “1” in the denominator of . (b) We have to show that to the same approximation, the fraction of photons by number, with energies greater than 2.2 MeV at a temperature of is .

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The radiated power per unit area that extends from to is given by the Planck’s blackbody radiation law,

.

The energy of a photon of wavelength is . Therefore, the number of photons having wavelength emitted per unit area per second by a blackbody at temperature T will be given by

,

and therefore, the number N of photons radiated, per unit area per unit time, by a cavity radiator at temperature T will be given by

In evaluating the integral, we will ignore “1” in the denominator of . In this approximation

For evaluating this integral, we make the change of variable

Stefan-Boltzmann constant

We thus find that

(b)

We will show that to the same approximation, the fraction of photons by number, with energies greater than 2.2 MeV at a temperature of is . Photons with energy greater than 2.2 MeV will have wavelength ,

Therefore,

And,

Therefore,

And,