Electronic Charge and Mass

in our first atomic physics we saw how cathode rays were discovered and then we saw how hid torque in 1869 was able to cast shadows with cathode rays and come to the conclusion that cathode rays travel in straight lines and then a year later Sir William Crookes showed that cathode rays have momentum and energy by making a little pinwheel turn around by their impulse or impact he was able to show they have energy and momentum now today we're going to first take up a third important experiment concerning cathode rays a discovery made by Jean Perrin in France some years later some 25 years later to be exact Peron found that cathode rays are charged particles charged particles this was an important discovery his apparatus was similar to that drawn here on the board in which I'm going to demonstrate later and for you a discharge tube made of glass a long tube here with a metal electrode here connected to the negative side of a battery and called the cathode and here a positive piece of metal called the positive electrode and because it's connected to the positive side of the battery often referred to as the anode the anode now from the cathode their screen these cathode rays now Perrin put into the discharge tube a metal disc or screen here that the cathode rays had to hit and in the center of it a little slot through which some of the cathode rays could stream and since they knew at that time and he knew that fluorescence would be produced by the cathode ray striking fluorescent materials he put a long screen in here painted the fluorescent paint so he could see the stream of cathode rays as they went down the length of the tube then he placed around the tube here a magnet so that there was a magnetic field here perpendicular to the beam and he found that the beam would Bend now it would only Bend if the cathode rays were electrically charged furthermore by knowing the direction of the magnetic field in the direction of motion he could conclude whether they were negatively charged particles or positively charged particles now let me show you the experiment here's the apparatus consisting first of all of an induction coil that produces the high voltage and a switch for turning it on the battery is under the table the high-voltage electrodes are the induction coil are connected to the two ends of this class two now in this particular tube the cathode is over here on your right and the little screen with a slot in it is here just in front of it just beyond it and the cathode rays coming in here will strike this little piece of metal strip of aluminum here that's been painted the fluorescent paint now the cathode rays as they stream down there will make a path that'll pair blue in color or as a bright streak if you're seeing this in black and white and here is a horseshoe magnet and I'm going to place this magnet over the beam like this and we'll see that it bends either up or down now the North Pole of the magnet is this one here and I'm first going to put the magnet down with the North Pole nearest Jill so that the magnetic lines now you see will cross between the North and South Pole here horizontally going away from you and the beam then going through here will have a force on it either up or down you see at right angles to both now let's turn this on and see what so what happened without the magnet there you see the beam I'm turning it off so you can see the beam appear [Music] now I'll leave it on and now I'll turn the magnet around so that the South Pole is nearest you that reverses the magnetic field and the beam bend down back down now the North Pole there's two bends up so one sees that this beam is bent by the application of a magnetic field at right angles to the stream now you remember with the North Pole nearest you the beam bent up now let's apply the left hand rule assuming these are negative charges to see if that's the way they would they should Bend the left-hand rule says put the thumb in the direction of motion since their cathode rays coming from a cathode we know they're traveling from right to left so we imagine grasping this beam with our left hand the fingers then point in the direction of the magnetic field due to the magnet on the underside of the beam where the field then is strengthened and exert a force on this charged particles away from that strong field up now had the beam bent down with the North Pole nearest you here then we would have had it conclude that they were positively charged particles but by knowing this as a North Pole and by knowing the direction of the beam one concludes that they are negatively charged particles beam params discovery of these charged particles and that they were negatively charged now soon after params discovery many people began experimenting with these charged particles to learn other things about them and JJ Thompson an Englishman found was the first to answer a number of very puzzling questions about cathode rays JJ Thompson asked the question and many others did too our cathode rays these particles these native charged particles are they all alike are they all like this was the major question and by all alike one means first of all do they all have the same charge exactly well now the beam you saw bent as a whole one would think they were probably all other they were all alike probably they all had the same charge but do they could one measure the charge do they all have the same charge third do they all have the same mass do they all have the same way or mass if the since they mend alike again you might conclude they're all the same mass but are they really might not some of them be twice as heavy as others and carry twice as much charge and therefore be bent the same amount in the magnetic field these were important questions to try to answer and there were a number of years passed by and a number of very famous experiments performed before these questions could be answered and I'm going to describe two important classic experiments today but to the scientists are considered classics of the past these experiments were done around the turn of the century one of them around 1900 and the other around to 1910 within several years one way or the other now the first experiment is known as JJ Thompson's experiment in it he determined the charge divided by the mass of the electron and also the speed of cathode rays his apparatus consisted of a discharge tube made of glass but has the shape shown here and this shape is not greatly different than the modern television receiver screen and the oscilloscope tube with which some of you are familiar and in principle is a great deal like it now in this glass tube which was highly evacuated he had a cathode over here or metal electrode a cathode to produce cathode rays these electrons we now know they are and then the anode would in the form of a little disc with a hole in the center tiny pinhole and another here with another pinhole so that he could get a very narrow beam of cathode rays coming down the tube then at the far end of the tube here was some fluorescent paint so that the stream of cathode rays and cathode rays are invisible we only see them when they strike some fluorescent material they would produce a bright spot right here at the center but now in the path of these beams he he was able to produce an electric field try to deflect them or a magnetic field or both inside the tube were two metal plates here and by connecting them to a battery he could produce here an electric field and exert forces on these charged particles and bend them in their path to a new point on the screen or by applying a magnetic field here by the circle represents the poles the two poles of a magnet scene end on a magnetic field the lines being perpendicular to the board he could bend the beam up or down as he likes but here it's shown that up to another spot on the screen so he could apply an electric field or a magnetic field now I'm going to spend a little time discussing the bending of particles in electric and magnetic fields because these principles we will see applied over and over again in many different ways not only in atomic physics but in nuclear physics later on the principles of cyclotrons atomic accelerators and many other pieces of apparatus used today in the laboratory are based upon these fundamental equations and principles so I want you to play a very close attention and particular to the equations they're very simple and form and they're simple and application they may seem a little complex at first now here is a diagram first of all of two metal plates representing the two plates inside of Thompson's apparatus - the two plates he applied a different voltage and giving the upper plate a negative charge the lower plate a positive charge now this produces between the plates an electric field B of intensity II remember we represent field between plates uniform electric field by the letter e now these cathode rays or electrons that come in from the left are designated here by three quantities first of all small e represents the amount of charge on these particles and we're given the negative sign because it's negatively charged he is the amount of negative charge M represents the mass of the electron and small V represents the speed or velocity three things we want to know about electrons we do not know yet or Thompson did not know this this nor this may be things he wanted to know and others wanted to know now these particles come streaming into this field and as soon as they enter this electric field between these plates there's a force on them they're attracted by the lower plate repelled by the upper one there's a force on them and you remember the force on a charged particle is given by the electric field strength times the charge at any rate this force however these particles moved is always straight down because that's the directional field and so this path is the path of a parabola it's the same kind of a path you have when the projectile is projected horizontally and the earth pulls on it with a constant force it follows a parabolic path well here the force is parallel and it follows a parabolic path now the electric field intensity e you remember is given by this equation the voltage applied to the plates divided by the distance between them and meters volts per meter now the force on the charged particles force is given by the electric field intensity times the charge on the particles now you can measure V and D but this quantity is an unknown however this equation shows that the force on those charged particles are given by the electric field intensity times the charge on the electron now let's look at the magnetic field the equations and the principles involved in the magnetic field the magnetic field in here you see by this little circle represents the two poles of a magnet coming in and then you're looking in Don now here is a detailed diagram of that arrangement this circle represents one of the poles of the electromagnet circular in form and you're looking and on at the magnetic field lines the lines would be coming out from the board in this case from north to south be coming out from the board be the magnetic induction we say is out now here is our stream of electrons here's one of them coming streaming in from the left charge e velocity V and mass M again now they enter a magnetic field now they experience a force given by the rules we've had before from a direction of motion charge the forces at right angles to the field and at right angles to the direction of motion now if B is out in this diagram and these are negatively charged the force is up just as it enters the field here the force will be straight up but as it moves then annex curved path always the force stays at right angles to the direction of motion and when it gets up here the force will be in this direction at right angles to the direction of motion see this is different from an electric field the force here changes Direction all the time and furthermore the force will depend upon the velocity the force F will depend on the velocity whereas that wasn't true in the electric field the velocity had nothing to do with the force if you just given by the electric field strength time the charge so these this particle now will move in the arc of a circle the force is always at right angles to the direction it's like a centripetal force you see Stone on the end of the string the force is a central force now that our small R represent the radius of that circular path now we come to the formulas now here is our first important equation and you better write this down the force on a charged particle in a field moving at right angles to the magnetic induction is given by the strength of the field that is the magnetic induction B times the charge on the particle times the velocity force on a charged particle is given by B times e times V now this force causes it to move in a circle because it acts like a centripetal force and one can write then from mechanics centripetal force is M V squared over R where m is the mass of our particle the mass of the electron V again is its velocity and ours our radius of its path that you can marry so we have to form fundamental formulas here one for mechanics one from electrostatic or from from electrodynamics now this force is the one that gives rise to this centripetal force that makes it moves in circles so you can you can place those two things equal to each other and write B times e times V is equal to MV squared over our electromagnetic force is equal to the centripetal force because that is the force that produces the centripetal force that makes it move in a circle now you see you can cancel this as V times V over here V squared you can cancel one of those V's with this one and then juggle these letters around and can obtain finally e divided by M see these are quantities about the electron is charge divided by its mass equals the velocity divided by the magnetic induction times the radius of the circle all of these quantities are known these two quantities are known this one is not known now this is what Thompson did he noted that by applying these two fields at the same time he could neutralize one field with the other and hence make some calculations possible that were not otherwise possible you see if he applied the electric field alone and bent the beam away from this point down to here then if he applied the magnetic field he could bend it back up again see with a magnetic field alone he could bend it from here up to here exert an upward force on it in here in the magnetic field or he could observe downward force to the electric field or he could exert both forces by turning on both fields and by varying the current in the magnet he could adjust the upward force upward deflection an upward force so it was exactly equal to the downward one and then the beam would come right straight through again but two forces would be balanced if they came right straight through well now that you could do very easily because you could locate the spot without any field then turn on the fields and adjust them until it comes back in the same spot now what what good the dis do it well he could say with the electric field he attained a force F equals E times E with a magnetic field the force is b times e times b he could say these two are equal to each other they're exactly equal and you could replace EE plus pdv you could write this equality only under those circumstances where the fields were balanced now you see the charge on the electron cancels out and one obtains e equals B times B putting the B on the other side you get a over B is equal to V in other words the velocity is simply given by the ratio of the two field strengths now one could measure calculate this because you know the voltage you applied in the distance between the plates B you can calculate because you know the current in the electromagnets and you know their size and dimensions and so he found he calculated be that with 10,000 volts apply between the anode and cathode of his discharge tube that the velocity of the cathode rays the electrons was equivalent to 60 million meters per second this is about one-fifth of the velocity of light about 36,000 miles a second a very very high speed so this was an important discovery how fast were the electrons moving how fast were these cathode rays moving about one-fifth of velocity of light now then his next step was the following knowing the speed of the electrons or cathode rays in here he applied the magnetic field alone the field due to the magnet alone and deflected the beam from here up to here and by measuring that deflection he could calculate the radius of the path in here knowing how big the pole was he could calculate small R and from small R from knowing that then he could put that in this formula he could put in the radius here the magnetic induction here known and his velocity one-fifth the speed of light and find this ratio he over m now this ratio is a very important ratio in atomic structure it's the ratio of the charge on electron to its mass in kilograms e in coulombs divided by the mass in kilograms now Thompson found by his experiments and one has since bound by many repetitions of this and similar experiments but a / M has a value 1.7 six times 10 to the 11th power coulombs or / this should be kilogram not seconds 1.76 times 10 to the 11th power coulombs per kilogram now all this number really means to us here really is that it's a very large number but it's the ratio between e and M it means that the charge on the electron and coulombs compared to the mass and kilograms is a very large number it's specific value however is of importance now we turn to the second classic experiment of the past and the not-too-distant past either around 1910 to 1915 the famous oil-drop experiment of RA Milliken an American scientist who determined for the first time with any precision at all the charge e on the electron now what Milliken did is diagrammed human board Milliken set up two metal plates parallel to each other again to form an electric field an electric field here which now is such that the force would be would be up on a negatively charged particle and then into this field through a pin hole in the top center of the top plate he would obtain the tiny drop of oil and this he did by using a perfume atomizer here with a little oil in it and squeezing the bulb would produce a spray of tiny oil drops now when you atomized or vaporize oils or any liquid the particles the little drops become charged but in any rate as these little drops of oil would fall occasionally one would fall through this tiny pinhole on the top shown rather large here and here up here is represented one of these tiny oil drops now one can see these drops falling slowly through the space by looking through with a microscope so this circle represents what you would see looking in between the plates with a microscope to see the tiny oil drop one shines a bright light from an arc lamp and a lens in here and looking in the microscope it seems like a little bright star now the pull of gravity the downward pull of gravity is such as this little oil drop falls under the pull of gravity then when it gets down near the bottom he would close an electric switch over here applying a voltage to these plates and if the oil drop had a negative charge on it the upward force due to the electric field would cause it to rise if it had no negative charge it would go on down but if it had a negative charge it would rise then when we get up near the top here before hit the plate he would open the circuit take the charge off of here by sure grounding these two plates and the little oil drop would fall again under the pull of gravity now let's look at a detailed diagram of what he saw in the microscope here's the field of the microscope here's the little hole through which an oil drop has fallen and it falls down here due to the pull of gravity the mass of the oddness of the oil drop now don't confuse this with an electron this is an oil drop millions of times bigger than electron yet so small but it can just be seen under a microscope full of gravity on a downward it falls with a constant speed under the pull of gravity because of the air this is not in a vacuum this is an air atmospheric pressure you remember falling bodies reach a terminal velocity due to air friction objects falling fall faster and faster and faster until there comes a time on air friction pushing up is just equal to probably downward and then they fall with that constant speed we call terminal velocity now the terminal velocity for these part of these oil drops is rather small but from the rate of fall of the oil drop he could calculate from the known viscosity of air the mass of these oil drops not the mass of an electron but the mass of the oil drop now the way he did this was to have little crosshairs in here and a little scale and using a stopwatch he would time the fall of the drop as it passed this wire he would start his stopwatch and stop it when it passed here and then before to hit this plate he would turn on the electric field and this oil drop oftentimes would have a negative charge and it would rise and as it rose he would again time it from here up to here then he would short-circuit the plates discharge them and the it would drop again and he would time its fall again and sometimes he could run it up and down or maybe 15 or 20 times each time finding the time of fall and getting a better and better measure of the speed of fall and therefore better and better measure the mass of the oil drop and each time it rose he would get a measure of the charge on here on this oil drop because he knew the electric field strength and he could calculate Q of the oil drop now here's a little diagram to represent one of the oil drops as it falls down due to the pull of gravity air friction do the air has to stream by it exerts an upward force just equal to the downward force when the field was thrown on to the to the drop let's suppose that there was one electron on the oil drop and this represents an electron tiny tiny negative charge then the upward force here would be due to the electric field e times the small either charge on this particle and if this force were greater than this one the oil drop would rise and so he found that the oil drop one time might ride rather slowly showing a certain amount of charge on the oil drop the next time it would rise perhaps it would go a lot faster showing that perhaps several negative charges happen to be on the drop the next time it rose and then when he let it fall and let it rise next time there might be four on the next time he didn't know how many all he could do is measure the amount of charge on here now the equations for this experiment are just those we've had before the downward force due to gravity is the mass of the oil drop times acceleration of gravity the upward force when the electric field is on is just the charge on the oil times the electric field intensity now he found these cues and he listed them for a given oil drop all in a row and he what he found was this that if he divided all of these charges capital Q by one number that they all came out to be whole numbers in other words there were there always seemed to be a negative charge on the oil drop which was a whole number multiple of some unit of charge and that unit of charge that he found was divisible into all of the capital kills was one point six times ten to the minus nineteen coulombs one point six times ten to the minus nineteen coulombs so this is assumed to be the charge on the electron now since that time many hundreds of experiments not only this experiment but many others have confirmed this value once you have the charge on electron you can put it in JJ Thompson's value of e over m and calculate the only unknown the mass of the electron and one finds them at the mass on the electron the mass of the electron is nine point one times ten to the minus thirty-one kilograms nine point one times ten to the minus 31 grams a very very small mess and so today we've seen the important experiments whereby one has been able to determine experimentally the ratio a over M for electrons and second to determine the charge on the electron e by Milliken's oil-drop experiment and from the two experiments to determine the mass of the electron electrons have a very small charge a very very small mass and the two together go to make up this little thing no one has ever seen called the electron you