# Frequency of an electron

1. Feb 24, 2009

### Christophe.V

I wanted to calculate the frequency of an electron. The problem is that I just don't get a realistic value.

E=hf

In which:
h=4.135 667 33×10 −15 eV s
E=mc2+30keV (-> e.g. the energy of a tv)
Masselectron=9.10938215×10 −31 kg
c=299 792 458 m s-1

So:
(9.10938215×10 −31 kg * (299 792 458 m s-1)2) + 30keV= hf

8.1871*10-14J +30 keV=hf
541000 eV=hf
(541000 eV)/(h)=f
(541000 eV)/(4.135 667 33×10 −15 eV s)=f
f=1.308*1020 s-1

Isn't this a non-realistic number? How can they accelerate electrons in an accelerator if the frequency is so big? Or (which is probably more realistic) where am I wrong? Thanks!

2. Feb 24, 2009

### malawi_glenn

You use wrong formula, that formula is for photons.

For particles in general you must use:

$$\lambda = \frac{h}{p}$$

where lambda is wavelenght, h is plack constant and p is relativistic momentum.

For photons, E = p, that is why E=hf is valid for photons (and other massless) particle only.

Next time, this should be put in the home-work part of the Forum, it seems to me that this is HW

Good luck

3. Feb 24, 2009

### Christophe.V

Thanks, I thought on it a whole time!

It was no homework. I'm building a linear particle accelerator at home (so not for school) and I wanted to calculate the frequency. BTW; I live in Belgium. We have holiday now .

4. Feb 24, 2009

### malawi_glenn

ok, cool

Good luck with that accelerator!

You know you can build an accelerator with just a couple of batteries yes? ;)

5. Feb 24, 2009

### Christophe.V

No, I just wanted to take the electron gun out of a tv and connect it to a vacuum tube etc.

What do you mean with the batteries?

6. Feb 24, 2009

### Vanadium 50

Staff Emeritus
Before you get too far with your particle accelerator, what exactly is this "frequency" you are looking for, and how does it effect what you are doing? Do you understand how the accelerator is supposed to work? (For example, in the equations you wrote, you never mentioned the velocity of the particle.)

7. Feb 24, 2009

### Staff: Mentor

Why do you think the frequency that you calculated has anything to do with accelerating the electrons?

8. Feb 24, 2009

### Christophe.V

I'm not yet building the accelerator, just researching the possibilities. I opened a crt monitor and saw how it worked. I think I'll make a hole in the screen and connect it to a tube. Then the electrodes will be attracted by a high voltage at the end of the tube and accelerate. First I thought of changing the voltage and placing different electrodes (see below), but if the frequency is that big, it would never be possible, right?

This is what I thought, correct me if I'm wrong:

An electron is accelerated by the positive voltage of the first electrode, after it comes out of the electron gun. When it is in the first electrode, the voltages becomes negative, so when it comes out of the electrode, it is pushed away to the next electrode, where the voltage is positive etc. If that's right, the voltage have to be changed very quick, isn't it? (see: http://upload.wikimedia.org/wikiped...e_linac_en.svg/800px-Wideroe_linac_en.svg.png)

I know that's not the way how a synchrotron works, but that's not what I wanted to make. Just a linac, based on a tv (btw: I have a hard deadline, in three weeks it have to be finished).

9. Feb 24, 2009

### DeShark

Just wanted to point out that there are some health issues that I hope you've considered. Basically, high voltages used plus possibility of x-ray emission when the electrons bombard a target. More info (not necessarily valid info), can be found at http://en.wikipedia.org/wiki/Cathode_ray_tube#Health_concerns

Having said that...

Do you understand what this frequency is and its implications? If looks like you're using quantum mechanics in a situation which doesn't really require it. I don't want to sound patronising, just trying to help.

Negative voltage here really just means abundance of electrons. Positive means lack of electrons. This potential difference sets up an electric field, which acts to accelerate the electrons from the negative electrode to the positive one. Once the electrons arrive at the positive electrode, they will have a certain amount of energy. Assuming that the positive electrode is an annular ring, you will want the electrons to pass through the ring. So you'll need some way of focusing the electrons through the ring. This is what happens in a TV set, so you might already have a focused beam of electrons.

Once the electrons have passed through the ring, they will now be working against the potential. At this point, you'll want to swap the potential in the electrode to a negative potential. Swap it too early and you start to slow down the electrons before they've even reached the ring. Swap it too late and the electrons will have already been slowed down. The electrons will then travel onwards to the next electrode. Since you should have swapped the field around, this next electrode will be positively charged. Once the electrons have passed, you will want to swap the field again. It is the frequency that you have to swap the field which is important, not the frequency of the electron (E=hf).

10. Feb 24, 2009

### Staff: Mentor

And the frequency at which you swap the field depends on the time it takes for the electron to travel from one electrode to the next, which depends on its velocity as it accelerates. You can consider the electron as a classical particle here (perhaps relativistic if you reach a high enough velocity), not as a quantum-mechanical one.

11. Feb 25, 2009

### Christophe.V

Would it be possible (but probably less efficient) to make a cascade of subsequent voltage differentials, + to - to + to -, each one shielded from the previous by a zero potential wall with a small hole through which the electrons will pass? This wall would prevent the electrons from "seeing" the positive voltage and being slowed down again by it. In that manner no switching voltages are needed and the same voltage drop can be applied again and again.

12. Feb 26, 2009

### DeShark

Not as far as I can see. If you want the electron to go from a high potential to a low potential, then from high to low and repeat, you have to keep taking the electron from a low potential and putting it in a high potential. This takes energy. So on average, you'd be getting no acceleration at all.

I was in my lectures yesterday and the professor started off on a bit of a tangent about particle accelerators and how they function. It made me think immediately of this thread. He mentioned something which seemed very clever and possibly possible for you to achieve. Basically, you set up an electric field as you suggest, + - + - + - + -, etc, then you start to move the field slowly. The electrons will want to sit in the + sections of the electric field, so as you start to move the field, so the electrons move as well. In this way, the electrons are almost surfing the wave of this changing field.

The first particle accelerators though, according to him, were created simply using one big + to - potential. And of course the particles had to be placed in a vacuum to stop them from interacting with particles in the air.

Then you'll need some sort of way of detecting what's going on, so that you know that something's happening (or not).

Edit: After thinking about this electron surfing a little more, it's become apparent to me that this is exactly what was going on in the first instance I recommended to you. Basically, to set up this accelerating electric field, you will need to oscillate the electric field in the same switching on and off of electrodes that I was talking about before.
Also, to elaborate, this changing electric field is the only way (that I can see) that you can accelerate particles without just having one continuous potential drop.
Additionally, particles are focused using quite clever quadrupole magnets or some other arrangement of magnets.

Edit 2: I found a nice diagram explaining this surfing electrons: http://particleadventure.org/accel_particles.html

Last edited: Feb 26, 2009
13. Feb 26, 2009

### lightarrow

I haven't controlled your computations, but there isn't anything strange in that result. Electrons are used instead of light in high resolution (electron) microscopes exactly for that reason (higher frequency = lower wavelenght = greater resolution).

E = hf is correct even for electrons.

Of course a particle's frequency has *nothing* to do with the accelerator's frequency.

Last edited: Feb 27, 2009
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