The density of a monatomic gas remaining constant, at what temperature will the $\mathrm{rms}$ speed of the gas molecule which is initially at $100°C$ fall to $\frac{1}{3}rd$ of the original value?

Estimate the average thermal energy of helium atom at room temperature $27°\mathrm{C}$

Estimate the average thermal energy of helium atom at

the temperature on the surface of the sun $\left(6000\mathrm{k}\right)$,

Estimate the average thermal energy of helium atom at the temperature of the ${10}^7$ Kelvin (the typical core temperature in the case of a star). Given $k=1.38\times {10}^{-23}{\mathrm{JK}}^{-1}$.