Estimate the average thermal energy of a helium atom at:
$(i)$ room temperature $(27^{\circ} C)$,
$(ii)$ the temperature on the surface of the Sun $(6000\; K)$,
$(iii)$ the temperature of $10$ million kelvin (the typical core temperature in the case of a star).

(N/A) The average thermal energy of a gas molecule is given by the formula $E = \frac{3}{2} kT$,where $k$ is the Boltzmann constant $(1.38 \times 10^{-23} \; J/K)$.
$(i)$ At room temperature,$T = 27^{\circ} C = (27 + 273) \; K = 300 \; K$.
Average thermal energy $= \frac{3}{2} \times (1.38 \times 10^{-23}) \times 300 = 6.21 \times 10^{-21} \; J$.
$(ii)$ On the surface of the Sun,$T = 6000 \; K$.
Average thermal energy $= \frac{3}{2} \times (1.38 \times 10^{-23}) \times 6000 = 1.242 \times 10^{-19} \; J$.
$(iii)$ At the core of a star,$T = 10 \; \text{million} \; K = 10^7 \; K$.
Average thermal energy $= \frac{3}{2} \times (1.38 \times 10^{-23}) \times 10^7 = 2.07 \times 10^{-16} \; J$.