What is the average kinetic energy of an atoms at temp 5700K?

Question

The surface of a star consists mostly of hydrogen atoms (not molecules) at a temperature of 5700 K. What are the average translational kinetic energy per atom and the rms speed of the atoms.

Answer 1

v² rms = 3RT/M, where M is molecular weight in kg/mole, since the joule is 1 kg*m²/sec²

For H atom, v = √(3) (8.314 J/K*mole) (5700 K) / (0.001 kg/mole);

v = 11923 m/s, or about 12 km/sec.

Remember KE = 1/2 mv², so KE = (3/2)RT. Therefore KE is independent of MW of the gas:

KE = (3/2) (8.314 J/K*mole) (5700 K) = 71089 J/mol, or about 71 kJ/mol.