The surface of the sun consists mostly of hydrogen atoms (not molecules) at a temperature of 5700 K.?

Question

What are the average translational kinetic energy per atom and the rms speed of the atoms?

Answer 1

Use Maxwell's distribution equation: -

v = √(3kT/m)

Where T = 5700 K, k is Boltzmann's constant 1.38 x 10^-23 J/K and m is the the mass (here, the non-relativistic rest mass ) of a proton 1.672 x 10^-27 kg.

Thus: -

v =  ÃƒÂ¢Ã‚ˆÂš(3 x 1.38 x 10^-23 x 5700/1.672 x 10^-27)

Hence, the average translational velocity: -

v = 1.188 x 10^4 m/s

Or the kinetic energy is: -

E = 0.5mv²

or

E = 0.5 x 1.672 x 10^-27 x (1.188 x 10^4)²

Hence, the average translational kinetic energy per hydrogen nuclei or atom is: -

E = 1.179 x 10^-19 J (rounded to 3 DP)

Answer 2

E=3kT/2 =1.38*10^-23 *3*(5700+273)/2=1.2364*10^-19J

v^2=2*1.2364*10^-19*6.022*10^23=1.489*... m/s

Answer 3

The surface of the Sun is 5770K.

Answer 4

See the ref. for explanation and formulas.

Mean KE = 3(kB)T/2 = 1.18046160973975E-19 J

v(rms) = sqrt(3RT/M) = 11923.8474069157 m/s

where

M = molar mass of H atom = 0.001

R = universal gas constant = 8.31451093470238 J/(mole-degK)

kB = Boltzmann's constant = R/Avogadro = 1.38065685349678D-23 J/(molecule-degK)