Parallel Plate Electric Fields

Hi there, again I just wanted to see if anyone could help with the answer to this past examination question as I don't have the answers so not sure if I'm doing them correctly!

Thanks in advance.

An electron is liberated from the lower of two parallel plates seperated by 5mm. The upper plate has a potential of 1000v relative to the lower plate. How long does it take to reach the top plate?

(Neglect gravity)

Ok, well I thought it best to work out the field strength so I did E=V/d giving E=2.0x10^5N/C

Then I said that F=ma=qE so a=qE/m and since the chrage of electron is e, this gives a=eE/m=3.5x10^16!

Surely this is much to greater acceleration!

I then used s=ut + 1/2at^2 to get the time taken, which gives t = 3.78x10^-10.

I'm thinking these figures look way out!

Any help much appriciated.

Mike