 Hello, we're going to do an example of a calculation using the x-ray tube formula Here's something I prepared earlier According to Wikipedia an x-ray tube can operate between 30 to 150 kilo volts What is the f max of the x-ray released from the tube operating at 75 kilo volts and what is its lambda? Remember that f max is the maximum frequency of the x-ray kilo means by 10 to the 3 and lambda is wavelength So let's break it down Key information here is you're looking for an f max You're looking for a wavelength and the operating voltage is 75 kilo volts You can see here that I've written 30 to 150 kilo volts That's an example of information that is not necessary for answering the question that's asked the question that is asked is underlined So the first thing you have to do is to start using the relevant formulas and This is w is equal to q delta v w being energy and that's the work done by the Electric field to accelerate the electrons across So you get the charge in an electron, which is 1.6 by 10 to the negative 19 coulombs and times it by the voltage that it's going to be Accelerated across in this case. We've got the charge on the electron here. That's q. We've got the voltage here Giving you the total kinetic energy of the electron Arriving at the other side of the electric field being 1.2 by 10 to the negative 14 joules Then we proceed to use this formula here energy is equal to Planck's constant times the frequency So if we assume that every joule Has been converted into an x-ray i.e. we're talking about the electron being stopped in its tracks by a metal nucleus Then we can rearrange this formula to suit and use all the energy out of the w equals q delta v To determine the maximum frequency of the x-ray itself so Knowing that the energy of the x-ray is going to be equal to the work done to accelerate the electron We can now rearrange the formula e equals hf max. We're calling it f max because it's the f maximum frequency x-ray So the energy on Planck's constant will equal the maximum frequency Knowing the Planck's constant is six point six three by ten to the negative thirty four joule seconds If we follow through on the calculation here, then we get the figure one point eight one by ten to the nineteen hertz and That is the frequency of the x-ray Now of course the frequency is not the wavelength So you've got another step here, and we're using the formula the speed of light is equal to frequency times wavelength The speed of light in a vacuum is three by ten to the eight meters per second And we want to determine the wavelength so we need to rearrange the formula hence the speed of light over the frequency Equals the wavelength so we've got three by ten to the eight Divide one point eight one by ten to the nineteen which is our answer from the previous slide and You're gonna end up with the amount which is one point six six by ten to the negative eleven meters However, if you have a look at orders of magnitude, you'll see the ten to the negative twelve is p code So you could actually represent it as sixteen point six picometers. However, this answer here is perfectly acceptable to get full points