 guys today we are going to take up topic x-ray okay x-ray is an electromagnetic radiation now electromagnetic radiation study of that was being done for centuries now and first study of em waves what do you think could be the source sunlight is the source of that right so people have started understanding about em waves by analyzing what are the wavelengths in the sunlight so visible spectrum was very easy to find right and then due to the phenomena of radioactivity and things like those they came to know about gamma rays as well and simultaneously there was a research going on wherein scientist named Hertz was conducting several experiment to with with electric field and magnetic field in order to generate some sort of wave so he came up with radiation called radio waves which we are using in Wi-Fi devices okay it was William wrong turn who was doing some experiment with with the gases and discharge of you know waves from the gases he has accidentally found out a wavelength which was never you know observed and this particular of em waves of the particular of this wavelength is called x-ray okay because it was strange and William was not aware of this so he started calling it x-ray alright and he also got a Nobel Prize for it but then it was Coolidge who was the first one to devise an experiment to formally you know to he has formally put up an experiment to create x-ray fine so in this topic we are going to learn how x-ray is produced okay and what are the formulas governing the production of x-rays and how what is the wavelength and things like those okay so let us first understand how an x-ray could be generated alright so suppose there is a nucleus there is this positive charge nucleus right and it has surrounding electrons in K K shell and this is L shell so the electrons are revolving around it okay and if I fire an electron from the left-hand side it goes suppose like this okay suppose it do not touch any of the electrons so what are the things we have observed this electron which is coming towards the atom is it accelerating or not it is accelerating right it is coming under the influence of nucleus and it is deviating from its path little bit so there is some acceleration fine now since there is an acceleration of the electron which you have fired there must be em wave that must be produced isn't it so since charges accelerating it will create an em wave fine and this em wave will have frequency which is between ultraviolet rays and the gamma rays and this is one of the frequency for the x-rays right similarly there could be various scenarios where electron could be accelerated less could be accelerated more so you will get a range of frequencies okay now once in a while something strange will happen okay so once in a while what will happen is this electron that is coming from outside may hit an electron which is revolving now fine if this electron hits the electron which is in suppose k orbit okay and suppose due to the collision this outside electron supplies sufficient energy to this K shell electron then this K shell electron may get knocked out okay then what will happen K shell right and we know that energy of K shell is the least compared to L and M shells right so this L and M shell electrons they will try to occupy this position because every matter tries to have minimum energy as less energy as possible so when the electron is in L shell it has higher energy so it is suppose it has an opportunity to jump to K shell so it will just jump from L to K shell right so it was earlier in L shell now it will go in the K shell so its energy is decreased so what will happen to the rest amount of energy it will get emitted as em wave okay so we have generated em waves using the same electron in two different ways one way is when electron accelerates under the influence of nucleus it will create one wavelength right and second way of generating this em wave is when this electron knocks out orbital electron then the higher shell electron will try to occupy the lower shell electron and because of this transition some wavelengths will be emitted right so this is what is the phenomena that we are going to learn in this entire section okay fine let us try to draw a graph between characteristic energy of a wavelength and what is a wavelength of that energy okay suppose this is E lambda E lambda is nothing but total spectral energy for a particular wavelength okay and this is suppose wavelength fine so what kind of graph you will observe you will observe continuous graph or discontinuous graph it will be continuous graph right because there are several ways there are infinite way number of ways electron could be accelerated and every type of acceleration will emit a particular type of wavelength okay so this is what is observed so this is the kind of graph that is being observed when you plot characteristic energy for a spectral with the wavelength okay now let us try to understand what is happening here in this case you will have some lambda minimum this let us call it lambda minimum so you will not see any energy which is less than sorry you will not see any energy whose wavelength is less than the lambda minimum so all the photons will have wavelength which is more than lambda minimum fine so what does it mean there will lambda minimum correspond to maximum frequency isn't it so there is a maximum frequency after that you cannot observe a particular photon why it is that the electron suppose has energy k okay so how much maximum amount of energy a photon can have which is generated because of that electron it can have maximum energy of k only isn't it so maximum amount of energy an electron can transmit is k so that corresponds to maximum frequency or minimum wavelength okay now here you will see that there are two strange peaks what are those these are the wavelengths where you will these wavelengths will be generated because the electron knocks the electron that is coming is knocking the orbital electron and when there's a transition going on it will emit these two type of wavelength which is of course will be slightly different from the graph which you are plotting for the electron with when it is accelerating isn't it so this is these are the two wavelength so we have till now observed theoretically how the x-ray is produced now let us understand how the Coolidge tube experiment looks like this is an actual experimental setup that is used by Coolidge to generate x-ray okay so this is how it is you have a glass tube which looks like this this yellow outer shell if you see that and then inside the left part you'll have a molybdenum cylinder okay and on the right hand side you have a copper wedge which is this okay this is the copper piece or wedge and on the periphery of the copper there is tungsten and molybdenum coating fine and coming to the left side again inside the molybdenum cylinder molybdenum cylinder you have a tungsten filament all right now tungsten filament is given suppose a voltage of V so what will happen a tungsten filament will heat up right because it has high resistance so it will get heated up and because of the heat that is generated the electron inside the tungsten will may get sufficient energy to come out of the metal okay so this is called thermionic emission we have learned photoelectric emission right so in photoelectric emission when photon falls on the metal surface it absorbs the sufficient energy and comes out of the metal right instead of photoelectroelectric emission or the energy given by the radiation we are giving energy due to the heat itself so when this filament gets heated up the electron from the filament will come out okay and this molybdenum cylinder and this copper piece they are connected by a huge potential difference of 20 kilo volt approximately so there's a small change in the figure earlier we have taken copper to be positive more positive potential than molybdenum now we have switched the polarity so what Coolidge have done he has taken copper to be at very high potential compared to molybdenum cylinder by connecting a huge potential across these two so when electron that comes out of filament it experience a repulsion from all lateral sides of the molybdenum cylinder because it is in negative potential so electron will converge to a narrow stream it looks like a pencil nib okay so it becomes a narrow this thing and it hits the tungsten molybdenum or molybdenum coating so because of that what will happen the same thing which you have just learned that suppose this is tungsten only that coating so tungsten will have nucleus and it will have electron in KLM shells so electron which is coming out of this tungsten filament will come and pass through the atoms of tungsten coating okay and after that due to the acceleration of the electron there might be some em waves that is coming out of the tungsten coating okay so this is how the entire experiment is conducted okay okay now we are going to say how mathematically we can analyze the whole situation okay so now if an electron that comes out of filament experience a potential difference of V between molybdenum cylinder and copper so how much kinetic energy the electron will have the maximum kinetic energy that is available to the electron is charge of electron which is E times potential difference which is suppose V okay so E times V is the maximum kinetic energy that is available to the electron okay and suppose if you want to find out what is the maximum frequency or minimum wavelength for which will be produced due to this electron then how much maximum energy this electron can give to create em wave maximum energy the electron can give is whatever energy is available to the electron itself which is E times V so suppose entire energy which is E times V gets converted into energy of a photon which is H mu or H c by lambda then I can get an expression for lambda minimum okay so this is the expression for lambda minimum now this comes in a graph if you see this this is a graph and this is the wavelength right so this is what the lambda minimum is fine now we are going to do what we are going to do is we want to get what are the wavelengths of these peaks okay these peaks are called characteristic x-rays because they are the characteristic of what is a material here isn't it this belongs to the material because the k shell of every nucleus will have different energy right so if electron jumps from l to k okay then there will be energy difference corresponding to what material it is so that is why it is called characteristic x-rays right so we are going to learn now how we can deal mathematically with characteristic x-rays okay so we know that for characteristic x-rays one of the electron from the shell is knocked out from the electron gun right so suppose from the k shell one electron is knocked out so how will it get electron now it can get electron from higher shells from l or m okay if it get electron from l we call it k alpha okay and if it get an electron from m we call it k beta rays okay so let us try to find out how we can get the wavelength of those now if you remember for hydrogen or hydrogen like atom we have a direct formula when electron jumps from higher orbital to lower orbital what is that 1 by lambda is equal to rickberg constant z square 1 by n1 square minus 1 by n2 square right this is the formula for the hydrogen like atom what is hydrogen like atom in a hydrogen like atom we have only one electron suppose you take helium okay you knock out all its sorry you knock out all its electron other than just one electron so helium plus is a hydrogen like atom lithium 2 plus is also hydrogen like atom but when i take this experiment this tungsten and molybdenum they are not hydrogen like atoms right they can have multiple electrons fine so if you have learned already about screening effect you may know that the atomic number due to the screening effect behaves as if it is less than the actual atomic number okay so there is some screening factor over here so this formula for for a generic scenario where it is not a hydrogen like atom looks something like this 1 by lambda is rickberg constant z minus b whole square 1 by n1 square minus 1 by n2 square fine so b is the screening constant of a material all right so let us first try to get what is a wavelength for k alpha so for k alpha n1 is 1 and n2 is right and you should remember that for k shell generally value of b is 1 okay so just write it down for k shell b is approximately equal to 1 the screening factor is 1 so for k alpha radiation we have 1 by lambda equals to rickberg constant z minus 1 whole square into 1 by 1 minus 1 by 2 square right so if i simplified further we get rickberg constant z minus 1 whole square this is 3 by 4 so suppose i multiply left hand side and right hand side with speed of light i will get an expression of what frequency this is my frequency right so frequency is 3 by 4 times rickberg constant speed of light z minus 1 whole square so after this if you take a square root you will get root of mu is under root of 3 rickberg constant c by 4 into z minus 1 fine so this is what you get an expression for k alpha radiation okay so for k alpha radiation we have just arrived at some relation between root of frequency and atomic number right so the graph between root of frequency and atomic number is a straight line it is like this okay and what is the slope of this straight line slope of this straight line is under root 3 r h c by 4 okay and suppose you do not assume that screening constant is 1 then what this expression will look like this expression will look like this under root mu will be equal to root over r h c by 3 r h c by 4 into z minus b right because you haven't assumed value of b to be 1 so you can get the value of b from here also this x coordinate here is the value of b okay where root of frequency becomes 0 root of frequency will become 0 when atomic number is equal to b okay so this is how you can deal with k alpha radiation what about k beta for k beta value of n 1 is 1 and n 2 is 3 fine and everything will follow like this only and there could be other characteristic wavelengths also for example electron rather than getting knocked out from k shell get knocked out from l shell then what is the value of n 1 n 1 will be now 2 and electron will jump to that second orbit from n 2 equal to 3 4 5 like that okay so when electron is jumping to l shell from higher shell suppose it jumps from m to l it is called l alpha and n to l it is called l beta okay these are just naming convention so this is k alpha and we know k beta is when it jumps from m to l right so this is how you deal with entire x-ray topic and i hope you will be able to solve questions on your own and we are anyway going to take a few example in the later video wherein you can understand how we can use whatever we have learned in a form of question okay