We have to calculate the wavelength of the maximum spectral radiancy and identify the region of the electromagnetic spectrum to which it belongs for each of the following: (a) The 2.7-K cosmic background radiation, a remnant of the primordial fireball. (b) Human body, assuming a skin temperature of . (c) A tungsten lamp filament at 1800 K. (d) The Sun, at an assumed surface temperature of 5800 K. (e) An exploding thermo nuclear device, at an assumed fireball temperature of . (f) The universe immediately after the Big Bang, at an assumed temperature of . We may assume cavity radiation conditions throughout.

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The wavelength at which spectral radiation emitted at temperature T has its maximum is given by the Planck’s formula

.

We will use this result for answering (a) to (f).

(a) , microwave region;

(b) , far infra red;

(c) infra red;

(d) visible;

(f) ultra-gamma

ray.