 Hello everyone I'm going to talk to you today using a question from the 2020 South Australian Certificate of Education end of year exam. It's going to be different for different students in different states but at the end of the day this gives you an idea of the kind of questions that get asked at the end of year 12. The diagram below shows an x-ray tube. Electrons are accelerated towards the target by applying a potential difference of 1.25 by 10 to the 4 volts across the x-ray tube. The key piece of that question being the 1.25 by 10 to the 4 volts. So describe the purpose of the target in the x-ray tube. And I've gone ahead and here's an answer I've provided before. The target provides the means by which the x-rays are generated by the tube. Made from a dense metal the target has a large amount of metal nuclei which acts to slow down or stop the electrons. They provide a breaking force. It is this force which causes the kinetic energy of the electrons to be converted into x-rays as the electrons slow down. Show that the electrons gain 2 by 10 to the negative 15 joules of energy from the potential difference across the x-ray tube. Now knowing that we've got 1.25 by 10 to the 4 volts you're going to use again W work is equal to Q delta V, Q being the charge on an electron. So 1.6 by 10 to the negative 19 coulombs by 1.25 by 10 to the 4 volts gives you 2 by 10 to the negative 15 joules. Calculate the speed of the electrons as they strike the target in this x-ray tube. Now this is a good example of where the question has gone outside of the maximum frequency formula for an x-ray and actually go on to the use of some information from the earlier motion in two dimensions and energy and momentum topic. So we're talking the kinetic energy formula here. That's how you get the velocity of something which is moving. So you're going to have to rearrange the formula itself knowing the kinetic energy is half MV squared. If you follow through the derivation to make velocity the subject of the equation you'll end up getting velocity is equal to the square root of 2 times the kinetic energy divide the mass of an electron. The mass of an electron being 9.11 by 10 to the negative 31 kilos. You'd note there that there's a step where it says EK on a half is equal to MV squared. Divide anything by a half is the same as timesing it by 2. That's why EK on a half becomes 2 EK on the next line. When we run the calculation we get 2 by 10 to the negative 15 joules and that's the kinetic energy that it's going to have and where did that come from? The previous question w is equal to q delta v. So 2 by 10 to the negative 15 joules we migrate that into the equation itself and you'll end up getting 6.63 by 10 to the 7 meters per second. Quite fast. Now one of the key things to notice about this question here is that even if you couldn't answer B you could still use the information from B to go forward and answer C. The idea when you write a good exam question is that if you can't do the previous calculation you can still go ahead and do the next part of the question so that then you're not penalized. Calculate the maximum frequency of the x-rays produced well that's just the fmax formula again except you're going to need to involve Planck's constant 6.63 by 10 to the negative 34 joules seconds. I'd just like to cover off on the units that we're looking at here. If you look at the maximum frequency formula you'll see e charge on an electron times the change in voltage across the x-ray tube divide Planck's constant. Now these all have units. The charge on an electron is measured in coulombs. The change in voltage, the potential difference is measured in joules per coulomb understanding that one volt is one joule given off by one coulomb of electrons which is a set amount of electrons and Planck's constant is joules seconds. So if we put that all together you've got a coulombs on the top from the charge on an electron and on the bottom from the delta V so they cancel out. You've also got a joules on the top from the delta V but again another joules on the bottom because that Planck's constant is on the bottom of the equation and they cancel out and you're left with one on seconds. Now you might be aware that one on seconds can kind of be included in frequencies equal to one on period. Period being the time it takes for the wave to go through one complete oscillation and that's where we get that hurts from. So you can see that the units themselves cancel out. Certainly not part of the South Australian curriculum. I'm not sure about other states but it's definitely done when you get to university. They'll make you to all carry the units all the way through to the end. It's really fun.