Question

A He atom at 300k is released from the surface of the earth to travel upward no collision other molecules how high will it rise before coming to rest?

Answer 1

Given temperature T = 300K

Atomic mass of Helium = 6.64*10^-27 Kg

We know that, Energy E = 3/2kT ---(1)

k is boltzmann constant (i.e.) k = 1.38 x 10^-23 m2 kg s-2 K-1

While atom comes to rest, kinetic energy = 0

Potential energy E=mgh ---(2)

From the two equations, 3/2kT = mgh

h = 3kT/(2mg)

= (3 * 1.38 x 10^-23 * 300 )/ (2 *6.64*10^-27 * 9.8)

= 1242 * 10^-23 / 130 * 10^-27

h = 95432 m

Helium raises to 95.4 km