How Do You Calculate the Energy of an Electron Beam in an Electron Gun?

[joker_900]

Hey guys

Apparently I have to know how to find the energy of accelerated electron beams for a test, and I'm not sure how. Any help?

I'm assuming it's talking about electron guns: I think this consists of a heated cathode which emits electrons via thermionic emission, and an anode which accelerates them. But how do you actually get the cathode and anode (i.e. what are the circuits and how does one make each electrode charged). Is the electron beam energy just the voltage between the cathode and anode multiplied by Q (=It)?

Thanks, Jonty

 

[Hootenanny]

I'll give you a big clue and say that the definition of potential difference (or voltage) is work done per unit charge. The circuitry does not matter in the slightest, there's only one thing you need to know about the electrodes.

 

[kyle8921]

Hello Jonty,

You are correct in your understanding of electron guns and beams. The energy of an accelerated electron beam can be calculated using the formula E=1/2mv^2, where m is the mass of the electron and v is its velocity. The velocity of the electron can be found using the formula v=sqrt(2eV/m), where e is the charge of an electron and V is the accelerating voltage between the cathode and anode.

To make the cathode and anode charged, you can use a power supply to provide a potential difference between the two electrodes. The cathode is typically heated using a filament to release electrons through thermionic emission, while the anode is positively charged to accelerate the electrons towards it.

I hope this helps with your test preparation. Good luck!