 Hello Okay, we've gone through all of the graphs and the changes that can be made Now I want to talk about formula derivation I've just borrowed some formulas from the stage to our year 12 physics, South Australian curriculum formula sheet and The key thing here is to remember that the maximum kinetic energy of an electron when it slams into a tungsten nucleus and stops Transfers all of that kinetic energy to the maximum frequency x-ray So the key formula associated with it is f max is equal to e delta v on h Which is the maximum frequency x-ray is equal to the charge in an electron Times the change in voltage across the tube or the potential difference across the tube divided by Planck's constant We need to be able to derive that formula So remembering that you've got yourself an electric field and the electron accelerates across the field It's accelerating must mean that it it's experiencing a force And it's going to gain energy. So how do we get that energy? Well You see here this borrowed from electricity and magnetism work is equal to the charge times the change in voltage There's a difference between q and e and the two formulas given that when we're talking an x-ray to we're only talking about Electrons so that the e represents the charge in an electron, which is a 1.6 by 10 to the negative 19 coulombs We're not dealing with calculations here. Just yet. This is a formula derivation So w work is measured in joules and there is work done on the electron as it accelerates across the gap So what we can say is that the energy that the electron has as across as the gap is equal to The charge in an electron which we'll now call e and then delta v Calling it e because it's an electron. We're talking about no other particle The energy of a photon is this formula here So e again will be measured in joules is equal to Planck's constant Times the frequency of the photon you're going to get out of it Now in making the assumption that all of the energy all of the kinetic energy of the electron is transferred To the photon itself this e Is going to equal the other e? So you can now smash these formulas together The charge in an electron times the change in voltage will equal Planck's constant times the frequency and that's going to be the f max of the x-ray So then we can simply rearrange this formula so that f max Will equal the charge in an electron times the change in voltage divided by Planck's constant