The thermal speed of an electron at room temperature

[Edge5]

I am trying to find the thermal speed of electron at room temperature.

kT = (1/2)mv^2

which gives v=√((2kT)/m)

but answer says it should be √((kT)/m)

Where did that 2 go?

 

[dextercioby]

I am trying to find the thermal speed of electron at room temperature.

kT = (1/2)mv^2

which gives v=√((2kT)/m)

but answer says it should be √((kT)/m)

Where did that 2 go?

By the equipartition theorem, there is a factor of 1/2 kT for each kinetic degree of freedom. Assume the electrons moves only in one direction as a classical point particle. You then get the sqrt formula without the 2 in it.