in this video we're going to talk about the cathode ray tube experiment this is an experiment that was performed by jj thompson in the past and he used it to discover the presence of electrons inside of atoms and also he was able to calculate the charge to mass ratio of an electron so let's talk about the cathode ray tube experiment so inside this device is an evacuated chamber the pressure is very very low most of the gas molecules have been removed such that the pressure is as low as .01 pascals at sea level the pressure is one atm one atmospheric pressure which is equal to 101 325 pascals so you can see the difference between the air pressure that we breathe and the very low air pressure inside of this evacuated chamber if the pressure is too high the electrons will collide with the gas particles and you won't get the same effect it won't be visible now inside the cathode ray tube we have something called a cathode and an anode these are two different electrodes the cathode is a negatively charged electrode and the anode is a positively charged electrode now when the cathode is heated by this heating element nichrome wire is a good heating element when it's heated and if there's a high voltage applied between the cathode and the anode an electron beam is going to emanate from the cathode and it's going to accelerate towards the anode electrons are negatively charged so they're attracted to a positively charged plate so the anode accelerates this electron beam towards the right now the glass of this chamber is coated with a phosphorus material known as zinc sulfide and so when the electrons strike the glass they create this characteristic green glow these cathode ray tubes also known as crts they were very useful in making tvs in the old days those big large tvs they contained the cathode ray tube device inside of it and so when the electron beam strikes the screen it will produce a characteristic image based on the voltage variance signal that is applied to it now here is a question for you why was this experiment called the cathode ray tube experiment and not the anode ray 2 experiment what would you say the reason for this is because the electron beam appears to emanate from the cathode and not the anode and so it's called the cathode ray now here is another question to think about what about this experiment help jj thompson to conclude that all atoms contain electrons negatively charged particles how did he determine that this beam consists of negatively charged particles well the first thing is that this beam consists of charged particles because if you were to put a magnet next to it the beam would deflect a magnet will only deflect moving charges it won't deflect stationary charges so any object that is charged and is moving can be deflected by a magnet the second thing is if you apply let me put a positively charged plate here and a negatively charged plate here the beam will also be deflected would you say it will deflect in the upward direction or in the downward direction what would you say in this experiment the electron ray was deflected towards the positively charged plate so therefore we know that opposites attract that means that the beam must consist of negatively charged particles so that's how jj thompson came to the conclusion that this beam of particles must be negatively charged it's due to the fact that it was deflected towards the positively charged plate electrons are attracted to positive charges opposite charges attract as was mentioned before now another thing that he experimented was with the use of different anode and cathode materials it doesn't matter what metal the anode and the cathode were made of if we use zinc if we use aluminum iron metal copper silver all of these metals can emit a cathode ray so the fact that these different metals can emit a cathode ray help them to conclude that all atoms not just certain types of atoms but all materials all atoms contain negatively charged particles which we now know as electrons so now we understand how jj thompson was able to use the cathode ray tube experiment to determine the fact that atoms contain negatively charged particles known as electrons but now what about calculating the charge to mass ratio of an electron how did he use this experiment to get that number well now we need to jump into the realm of physics so let's talk about an electron if we have a positively charged plate and a negatively charged plate the electron will fill a force that will attract it or accelerate it towards the positively charged plate it will also fill another force that will repel it from the negatively charged plate so electrons can be accelerated by electric fields they can also be accelerated by magnetic fields as well a magnetic field can cause an electron to change direction not necessarily speed up but it can accelerate in a way that it can cause it to change the direction it could deflect it and we're going to talk about that so let's say we have an electron that is moving towards the right that is in the positive x direction and we have a magnetic field that is coming out of the page the electron will fill a force that will accelerate it in the north direction or you could say in a positive y direction if you view it from a two dimensional perspective in a three-dimensional perspective that would be the z-direction now the electron is moving towards the right but it feels a force that is accelerating it in that direction where will it go in this case it's going to turn it's going to deflect in this direction and notice that you could extend this to make a circle so by calculating the radius of curvature and knowing the strength of the magnetic field and the strength of the electric field you can actually calculate the charge to mass ratio so let me make a neutron with this so let's say this point represents the electron it's moving towards the right so it has a velocity component in the positive x direction the magnetic field is going to be the magnetic field is represented by the symbol b and it's going to be in a positive y direction from a 3d perspective and a force the magnetic force acting on the electron let's put f sub b to indicate magnetic force that is in the positive z direction and so the electron is going to travel it's going to turn in the direction of the force and then we can calculate the radius of curvature so now let's go over some physics equations the magnetic force f sub b that acts on a moving charge not a stationary charge but a moving charge is equal to the strength of the magnetic field b which is measured in units of tesla times the charge of the electron times the velocity of the electron so if it's not moving the velocity will be zero the magnetic force will be zero but as the speed of the electron increases the magnetic force will be increased as well proportionally so you can increase the magnetic force acting on an electron by increasing the electron speed or by increasing the strength of the magnetic field now there's another type of force that occurs when an object moves in a circle and this is known as a centripetal force the centripetal force is not a force in itself it is caused by another force that causes the object to turn in a circle so if you think of how the moon orbits the earth gravity provides the centripetal force in that case in the case of the electron turning the magnetic force provides the centripetal force so any force that causes an object to move in a circle is a centripetal force and is equal to mv squared over r so because the magnetic force provides this centripetal force in this example we can set these two forces equal to each other so we could say that b q v is equal to m v squared over r if we divide both sides by v we're going to get b q is equal to mv over r where m is the mass of the electron v is the speed or the velocity of the electron and r is the radius of curvature so to get the charge to mass ratio we need to get q over m so i'm going to multiply both sides by 1 over b and also by one over m so on the left b is going to cancel on the right m is going to cancel so q over m is equal to v over b times r q is the charge of the electron m is the mass of the electron v is the speed v is the strength of the magnetic field and r is the radius now we can easily determine the strength of the magnetic field because we can control the amount that we apply in the experiment and we can measure the radius of curvature but measuring the speed of an electron is not going to be easy to do and so we need to remove it from the equation the magnetic force acting on a moving charged particle as we said before is equal to bqv the electric field or rather the electric force acting on any charged particle regardless if it's moving or if it's stationary is equal to the charge of that particle times the electric field now what we need to do is we need to set this experiment in such a way that these two forces are equal and that they cancel out if we can do that then we can set bqv equal to q times z dividing both sides by q we get b times v is equal to e and dividing both sides by b we get that the speed of the electron is equal to the electric field divided by the magnetic field if we design the experiment in such a way that these two forces are equal so we can replace v with e over b so we have q over m is equal to one over b times r and then times v which is e over b so the charge divided by the mass is equal to the electric field divided by the square of the magnetic field times the radius of curvature so let me show you how we can set this experiment up such that the magnetic force cancels the electric force so let's say we have two plates one is positively charged and the other is negatively charged and let's say we have an electron beam that is traveling in this direction there's going to be an electric field that emanates from the positively charged plate and flows towards the negatively charged plate now a positively charged particle like a proton will fill a force an electric force that will accelerate it in the direction of the electric field in this case it's going to accelerate towards the negatively charged plate a negatively charged particle like an electron will fill an electric force that will accelerate it in the other direction that is opposite to the direction of the electric field and so it's going to be accelerated towards the positively charged plate so the electrons in this electron beam they will want to deviate towards the positively charged plate and this is due to the electric force acting on them now if we have a magnetic force that is directed into the page using the right hand rule you could determine the direction of the magnetic force on the electron so let me see if i still have my uh drawn skills so what you want to do is using your right hand you want to place your four fingers into the page and your thumb you want it directed in the direction of the electrons so you want your thumb pointing towards the right your four fingers pointed into the page your right hand should be opening in the upward direction the magnetic force will be in the upper direction for a positively charged particle but for a negatively charged particle it's going to be in the opposite direction using the right hand rule now if you want to learn how to use it there's a video that i created on youtube so if you go to right hand rule i mean let me say that again if you go to youtube and type in the search bar right hand rule organic chemistry tutor you'll find it and it can show you how to determine the direction of a magnetic force on a moving charge particle but we need to know is that when the magnetic field is directed into the page the electrons will fill a force that will direct them this way due to the magnetic force now if we can design the experiment in such a way that these two forces are equal they will cancel out and so the electrons will continue to move straight to the right and so that's why we could set fb equal to fe to get this equation it all depends on if we can balance those two forces if we could then we can calculate the charge to mass ratio using this formula now once the beam of electrons passes through the electric field what's going to happen is it's going to turn because the magnetic field is still active everywhere and let's say we have a material here what's going to happen is once it escapes from the electric field and the magnetic field is the only force acting on it it's going to turn and it's going to hit somewhere along this spot and then we can calculate the radius of curvature so now we know the strength of the electric field that we're applying the strength of the magnetic field and the radius of curvature we can now calculate the charge to mass ratio so jj thompson discovered that the charge to mass ratio of an electron is negative 1.76 times 10 to the 8 coulombs per gram now we actually know the charge of an electron and the mass he didn't know at the time but we know what it is the charge of one electron is negative 1.602 times 10 to the negative 19 coulombs the mass of an electron is 9.11 times 10 to the negative 28 grams it's 9.11 times 10 to the minus 31 kilograms but one kilogram is a thousand grams so you get this number in grams so dividing those two numbers will give you the charge to mass ratio of an electron and so that's basically it for this video so now you understand the basic ideas behind the cathode ray tube experiment and how jj thompson use it to discover the fact that all atoms contain negatively charged particles known as electrons