Question

Find the average of magnitude of linear momentum of helium molecules in sample of helium gas at temperature 150pi K .mass of helium molecules =166/3×10^-27kgand R=25/3j-mol k

Answer 1

The average of magnitude of linear momentum of helium molecules

$$p=mv_{\rm{ave}}$$

The average speed of molecules

$$v_{\rm{ave}}=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8RT}{\pi mN_A}}$$

So,

$$p=m\sqrt{\frac{8RT}{\pi mN_A}}=\sqrt{\frac{8mRT}{\pi N_A}}$$

$$=\sqrt{\frac{8\times 166/3\times 10^{-27}\times 25/3\times 150\pi}{6\pi \times 10^{23}}}$$

$$=3\times 10^{-23}\;\rm{kg\cdot m/s}$$