Calculate the rms speed of free electrons

[Chele]

Hi and thanks for checking this out! :)

Homework Statement

The temperature and pressure in a star's atmosphere are 1.20E6 K and 0.0400 Pa. Calculate the rms speed of free electrons (mass = 9.11 10-31 kg) there.

Homework Equations

What am I doing wrong and why do they give the pressure if that's not needed in the formula!?

The Attempt at a Solution

I'm using this formula:

v=$$\sqrt{kT/m}$$

k=1.380658E-23 J/K
T=1.2E6 K
m=9.11E-31 kg

Seems like a simple "plug and chug" type problem. My answer was 4.3E6 m/s. This is not the correct answer.

 

[Doc Al]

I'm using this formula:

v=$$\sqrt{kT/m}$$

That formula is incorrect. The average KE equals (3/2)kT (you must include all three translational degrees of freedom).

 

[Astronuc]

. . . why do they give the pressure if that's not needed in the formula!?

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kinthe.html#c3

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/molke.html

 

[Chele]

That formula is incorrect. The average KE equals (3/2)kT (you must include all three translational degrees of freedom).

That's what I get for trying to do homework at 330am. Thanks, I can't believe I missed that.

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kinthe.html#c3

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/molke.html

Thanks for the information, I'll check those out!