# What is the energy of a free electron?

1. Apr 27, 2012

is it just E=mc^2 or does it have KE,I mean can a electron be stationary,so that its wavelength is zero.

2. Apr 27, 2012

### Naty1

The total energy E of a particle is explained here:

http://en.wikipedia.org/wiki/Relati...ion#The_relativistic_energy-momentum_equation

m is the rest mass of a particle, so mc2 is it's equivalent energy 'at rest'...that is, in the same frame of reference as the particle. If you speed up, then so does the electron relative to you and it appears to acquire KE. You travel further into a gravitational potential, it will appear to acquire PE....relative to you.

Any electron 'is stationary' when you move in the same frame as it. But that does not mean
it's debroglie wavelength is zero. The DeBroglie relations are explained here:

http://en.wikipedia.org/wiki/Debroglie_Wavelength#The_de_Broglie_relations

3. Apr 27, 2012

its stated as lamda=h/mv right ; when v=0,lamda=infinite.. does that mean electron which is away from the atom when left with zero force has infinite wavelength

4. Apr 27, 2012

### Staff: Mentor

v=0 as exact value would imply that the electron is distributed over the whole space (uncertainty relation!).

The kinetic energy (distribution) and its wavelength (distribution) depend on the system in which you look at the electron.

lambda=h/p is a nice thing remember, but it is not sufficient to describe the wave function of particles, so keep in mind that there are situations where it is not useful to take this formula.

5. Apr 27, 2012

suppose we have a collider where electron is made to collide with electron.for this to happen electron is detached from a atom,during this process there may be a stage at which applied force by us equals coloumbs attractive force of nucleus and hence electron detaches outside,now we know electron has dual nature,but at this point of time appears to have purely particle nature because accelerating a wave is not possible right.? and also u know the region where detached electron is present by calculating net force on ejected electron,when net force is zero electron does not have enough KE to move to far from its source..does this mean it voilates dual nature of electron

6. Apr 28, 2012

### sweet springs

Hello.

It does not matter. We can measure exact value of energy and momentum of free electron in infinite time interval and infinite space distribution that do not matter in this question.

Regards.

7. Apr 28, 2012

### Staff: Mentor

No. There could be a position where these forces are equal (and even that is a classical approximation). But as the electron is not at a specific point, "the current force on an electron" is not well-defined.

You can accelerate the wave function of an electron. There is nothing wrong with that.

The question was how an "infinite wavelength" could be interpreted. And the answer is that this situation can occur only if the electron is distributed over the whole space.