Drift velocity formula derivation confusion

[swap1996]

In the derivation of drift velocity i have seen two variations and want to know which one's correct.

• s=ut +\frac{1}{2}at^{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 traveled 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.

 

[projjal]

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]

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.

It is appropriate when the limits of the validity of such an approach is taken into account. The Drude model is based on such an approach (which is where we get the beloved Ohm's Law). So it is valid whenever appropriate.

Zz.