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## Broadening of Spectral lines Due to Temperature

The temperature of a gas is due to random kinetic energy of its atoms and molecules. For a gas at temperature
$T$
consisting of atoms of mass
$m$
with root mean square speed equal to
$v_{RMS}$
we can write
$Average Kinetic Energy= \frac{1}{2} m v^2_{RMS} = \frac{3}{2} kT \rightarrow v_{RMS} = \sqrt{\frac{3kT}{m}}$

The surface temperature of our Sun is about 6000 degrees Kelvin and the surface consists mostly of ionized hyrogen - electrons and protons.
$v_{RMS} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 6000}{1.67 \times 10^{-27}}} =12000 m/s$

This will result in a broadening of the spectral lines
Considered as a redshift we have
$z=\pm \frac{12200}{3 \times 10^8} = \pm 4.07 \times 10^{-5}$
.