Question

Determine the proportion of oxygen molecules on the surface of the Earth which have sufficient speed to escape the gravity of the Earth.

Answer 1

Solution:

Let us go to the basics first.

The squared average of the speed can be found from the Maxwell-Boltzmann distribution, it is given by <v²> = 3 k T / m.

The mass of a oxygen molecule is ~ 32 × (1.6605× 10^-27 kg).

The RMS is then
v = √<v²> = √(3 k T / m)
= √[3 × (1.381 × 10^-23) (293.15 K)/(32 × (1.6605× 10^-27 kg))]

[where, k =Boltzmann constant; T = average temperature on surface of earth = 20°C = 293.15 K]
= 1.90 × 10³ m/s

=>V = 478 m/s = 0.478 km/s

But we know that escape velocity, V_esc on earth is 11.2 km/s.

Since, V < < V_esc , thus, oxygen molecules on the surface of the Earth HAVE NOT sufficient speed to escape the gravity of the Earth. (Answer)

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