Gas Molecule Escape: Can Diatomic Hydrogen Escape Earth's Gravity?

Could diatomic hydrogen molecules escape earth's gravity at a temperature of 9567K?

Select an answer and submit:

a. No, the rms speed is too slow.

b. Yes, all the molecules will escape.

c. Yes, some molecules could escape.

Final answer:

Some diatomic hydrogen gas molecules at a temperature of 9567K could escape earth's gravity due to their root mean square speed exceeding the planet's escape velocity, although not all molecules would be moving fast enough to escape.

Explanation:

The escape of gas molecules from a planet's gravitational field is determined by their root mean square speed related to the planet's escape velocity. The root mean square speed is a statistical measure of the speed of particles in a gas, given by v_rms = sqrt(3kT/m), where k is Boltzmann's constant, T is the temperature and m is the molecular mass. On the other hand, Earth's escape velocity is approximately 11.2 km/s.

If the root mean square speed of the molecules is greater than the escape velocity, then they can overcome the planet's gravitational pull, provided they are moving in the right direction. However, not all molecules will have velocities above this average speed, so not every single molecule will escape. Therefore, for a gas of diatomic hydrogen molecules at a temperature of 9567K near the surface of the Earth, some molecules could escape earth's gravity.