Voltage,electron energy and electrode spacing I am trying to calculate what is theoreticaly maximum energy electron will gain between two electrodes.The electrodes are 100 micron apart and one is +50V,and other is -50V.
I learned that eV unit equals electron being accelerated across potential of 1V,but electrons cant accelerate instantly since they have mass.In the ideal scenario that the electrons begins at the surface of negatively charged electrode a fly straight towards positive electrode,will it gain 100 eV considering the gap is only 100 micron?
How fast can the electron accelerate,isnt the 100 micron gap with 100V potential just too small to give the electron the full 100eV energy? I mean consider the extreme case,that electron is between electrodes 1 nm apart and there is potential 1 giga volts,the electron wouldnt go from being stationary to 1 giga eV energy in 1 nano meter distance.
How can I calculate if the electron can gain the full potential energy in specific gap distance and voltage combinations? I want to look at gap distance,voltage,and tell how much energy can electron have in those gap spaces.
I would like to have some kind of rule of thumb in my head,something like a electron will go from zero to 1000 km/h in 1mm gap with 100V potential in 1 microsecond or something like that.
 A: It will always be the case that as the electron moves across the gap:$$\text{KE gained = PE lost} \ .$$So if the electron starts from rest$$\frac{1}{2}m v^2=e \Delta V$$If the electron travels from a negative to a positive electrode with a given pd between them, the separation of the electrodes doesn't affect the final speed of the electron. What you suggest in your third paragraph simply isn't the case.
A rule of thumb that I use is that a pd of 2500 V will accelerate an electron initially at rest up to approximately $\frac{1}{10}$ of the speed of light. 
At this energy (2500 eV) there is an error of about $\frac{1}{2}$ % in using the $\frac{1}{2}mv^2$ formula for kinetic energy. The error gets worse and worse at higher energies and you need to use the relativistic formula $$KE=(\gamma - 1)m c^2$$ in which $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.$
The time that the electron takes to go from one electrode to the other does depend on the separation and shape of the electrodes. The easiest case is when the electrodes are plane and parallel and the gap between them is small compared with their length and breadth (or diameter). In that case the field between them is uniform and the acceleration of the electron is constant, so the time taken is plate separation divided by the mean velocity of the electron, which is half its final speed if it starts from rest on the negative electrode. 
A: 
I would like to have some kind of rule of thumb in my head,something like a electron will go from zero to 1000 km/h in 1mm gap with 100V potential in 1 microsecond or something like that.

Adding to this answer:
For low potential differences $\Delta V$ where we don't need to worry much about relativity, you can write
$$v = \sqrt{ \frac{2 \Delta V}{m c^2}}$$
For an electron $m c^2$ is about 511,000 (eV).
An electron accelerating through a 1 volt difference will reach a speed of 593.5 km/sec which is 368.8 miles per second or 1,328,000,000 miles per hour.
That's 1.3 billion miles per hour for a 1 Volt difference!
If it accelerates from rest to that velocity $v$ over a gap width $x$ we can also write
$$t = 2x/v$$
For a 1 mm gap and a 1 Volt difference, it will accelerate to 1.3 billion miles per hour in 3.36E-09 seconds, or about 3.4 nanoseconds. For comparison the speed of light is about 300 millimeters per nanosecond or a foot per nanosecond for those who use them.
That's an acceleration of 393 million miles per hour per nanosecond!
