Surface temperature of Sun has to be estimated for this most probable energy 
for photons emitted by a black body of temperature T is found. Intensity is proportional to 
i.e., 
. The Balmer lines of hydrogen span the visible frequency range. The human eye has evolved to be most sensitive to sunlight. If 
is the number of photons with energy E then distribution of 
is given by 
(i) The most probable energy E for photons emitted by a black body of temperature T is -
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Ans.
(i)
Sol. If 
is the number of photons with energy E, then the distribution of 
is given by
The most probable energy 
of photons satisfies the equation 
Giving 
.
(ii)
Sol. The Balmer lines of hydrogen are emitted when electrons transit from energy levels of 
to that of 
. Thus, the maximum energy of the Balmer line photons is
and the minimum energy is
with 
being the Rydberg constant. Hence the energy of a Balmer line photon is between 1.9 eV and 3.4 eV.
(iii)
Sol. If the human eye is most sensitive to sunlight and the visible light is the most probable frequency band of the Sun's light emission, and furthermore, the visible light corresponds to the frequency range of the Balmer lines, the surface temperature of the Sun is given by
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