Question

Calculate the  average speed of N₂ on the surface of Ganymede (molecular weight = 28.013 atomic mass units, Avogadro’s Number = 6.022 × 10²³ molecules/mole, surface temperature T  = 107 K.

Answer 1

vm = (3kT/m)^1/2

k = 1.38 x 10^-23J/k

Mass of one N₂ molecule m = 28.013/(6.022 x 10²³)

m = 4.65 x 10^-23g = 4.65 x 10^-26kg

v_m = ((3 x 1.38 x 10^-23 x 10⁷)/(4.65 x 10^-26)^1/2 = (95.26 x 10³)^1/2

v_m = 308.5m/s = 0.308km