# Drift velocity formula derivation confusion

## Main Question or Discussion Point

In the derivation of drift velocity i have seen two variations and want to know which one's correct.
• s=ut +$\frac{1}{2}$a$t^{2}$
Assume that the drift velocity of any electron in any conductor is :
$v_{d}$=l/t
Due to the electric field the acceleration of electrons in any conductor is:
a=eE/m
Now the distance travelled by an electron after a long time (initial thermal velocity = 0)
l=$\frac{at^{2}}{2}$
the time between the collisions is τ ∴
l=$\frac{eEτ^{2}}{2m}$
thus the velocity is
$v_{d}$=$\frac{eEτ}{2m}$

• In another proof i saw the author using v=u+at⟹$v_{d}$=$\frac{eEτ}{m}$
My question is which of the the two equations of motion can be used in the proof? Can they be used at all.

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Since we are talking about 'average velocity' so the former derivation would be appropriate.However i don't think using classical mechanics for finding the velocity of particles like electrons would be appropriate,i think this requires quantum mechanical approach.

ZapperZ
Staff Emeritus