Question

Calculate the average speed of molecules of CH₄ (molecular weight = 16.043 amu) on the surface of Charon (T = 37k) and determine whether Charon can retain this compound.

Answer 1

v_m = (3KT/m)^1/2

Mass of a methane molecule = 16.043/(6.022 x 10²³)

= 2.664 x 10^-26kg

v_m = ((3 x 1.38 x 10^-23 x 37)/(2.664 x 10^-26))^1/2 = (57.5 x 10³)^1/2

v_m = 239.7m/s = 0.239km/s

6 × v_m = 1.438 km/s  

 v_e = 0.630 km/s 

Methane can escape from Charon because 6 × v_m = 1.438 km/s is greater than the escape velocity (v_e = 0.630km/s).