# Escape Velocity of Gas Molecules

What would the temperature of the Earth's atmosphere have to be such that the average speed of a hydrogen molecule(H2) is Equal to the Earth's escape velocity? What about an oxygen molecule (O2)?

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:46 pm ad1c9bdddfhttps://brainmass.com/physics/planets/escape-velocity-gas-molecules-10165

#### Solution Preview

The escape velocity for a planet or satellite is equal to the square root of 2 times the mass and gravitational constant, divided by the radius. For Earth, in SI units, this equals:

Vesc = SQRT (2*Mass*G/r)

Vesc = SQRT (2 * 5.976e24 * 6.672e-11/6378000)

Vesc = 11182 ms-1

Where G = 6.672e-11 Nm^2Kg^-2 is the ...

#### Solution Summary

Very clear solution which will enable you to do similar problems yourself.

$2.19