# Homework Help: Speed of an electron and potential difference

1. Jun 20, 2007

### grscott_2000

I have a question here where a potential difference is applied to a stationary electron. I have calculated the energy translated to the electron already and I know the mass energy of the electron.

If I want to find its final speed I assume that I use a rearrangement of the relativistic formula? And if so, what value would I use for Energy? Would it simply be the total energy : mass energy + translated energy?

Thanks for any help

Last edited: Jun 20, 2007
2. Jun 20, 2007

### malawi_glenn

There are many formulas you can use,

$$E_{tot} = E_{k} + mc^{2} = \gamma mc^{2}$$

$$\gamma = \dfrac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$$

remember that you can not take the rest mass of the electron in the expression of the kinetic energy.

Last edited: Jun 20, 2007
3. Jun 20, 2007

### grscott_2000

Would that be Ek as in translated kinetic energy?

4. Jun 20, 2007

### malawi_glenn

Well E_k is kinetic energy, what you mean by "translated kinetic energy" I do not know.

You can also use this:

(E_tot)^2 = (pc)^2 + (mc^2)^2

where p is the momentum:
p = gamma * mv, v is velocity.

And from this we can get:

v = c * sqrt[1 - (mc^2 / E_tot)^2 ]

5. Jun 20, 2007

### grscott_2000

I see... So if I have calculated the kinetic energy of an electron to be for example 6 x 10^-12J, then I can calculate the total energy as

(6 x 10^-12J) + mass of electron * speed of light^2 ?

And once this is established I can use one of the formulas to give me v?

Last edited: Jun 20, 2007
6. Jun 20, 2007

### malawi_glenn

How did you calculate the kinetic energy of electron?

You took:

Potential (electrical) energy = qV, where V is the electric poteintal, and then
qV = Kinetic energy?

Well then it is ok, and if you want to find out the velocity of the electron, you must calculate relativistic. (if the kinetic energy is approx 10% or more of the rest mass energy of electron)

7. Jun 20, 2007

### grscott_2000

yes thats exactly it.... potential difference(100V) x charge of electron(q).

I understand that relativistic formulas are used when the particles speed become close to the speed of light. Is this right? Otherwise the classic Newtonian formula 1/2 mv^2 can be used?

8. Jun 20, 2007

### malawi_glenn

yes, as I said, when the kinetic energy is apporx 10% or more, it may be good to use relativistic. The bigger the E_k is compared to the rest mass, the better to use the relativistic =)

9. Jun 20, 2007