Question

Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at 0°C. Mass of a helium molecule = 6.64 × 10⁻²⁷ kg and Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹.

Answer 1

Here,
​m = 6.64 × 10⁻²⁷ kg
T = 273 K

$$\begin{gathered} \mathrm{Average}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{He}\mathrm{atom}\mathrm{is}\mathrm{given}\mathrm{by} \\ {\mathrm{V}}_{\mathrm{avg}}=\sqrt{\frac{8kT}{\pi m}} \\ =\sqrt{\frac{8\times 1.38\times {10}^{-23}\times 273}{3.14\times 6.64\times {10}^{-27}}} \\ =1202.31 \end{gathered}$$

We know,
Momentum = m × V_avg
= 6.64 × 10⁻²⁷ × 1201.35
= 7.97 × 10⁻²⁴
= 8 × 10⁻²⁴ kg-m/s