Counting Electrical Charges in Motion (1961)

meters meters meters they're everywhere around this measuring all sorts of things a very great many of them measure the strength of electric currents these meters are called ammers because they're calibrated in units called amp by now you know that electric current is just the flow or motion of Elementary charges the natural unit then in which to measure this current is just the number of Elementary charges which pass any given point in the circuit during each second now how many Elementary charges per second is in an ampere a single Elementary charge is too smaller unit to be used conveniently in measuring electric currents so we use a package which contains 6.25 * 10 18th Elementary charges we call this package one Kum you'll see a little later in the study of electricity just why we choose a package this size a unit this size now the flow of this many Elementary charges per second we call 1 ampere [Applause] here we have a simple electric circuit a battery a variable resistor so that I can change the current and a small bulb let me connect them together and I'll adjust the variable resistor so that the bulb is about that bright now to measure the current flowing in this circuit I'll insert an ammeter now it doesn't make any difference where in this series circuit I insert the ammeter because the current is the same everywhere the meter indicates a current of about 1 ampere now this brings us to an important question how can we be sure that this meter is accurate if the manufacturer had one accurate meter he could calibrate all the other ones he produces from it but how do you calibrate that first meter one way to calibrate it is to put it into a circuit where you can count by a foolproof method the actual number of Elementary charges flowing past any point in the circuit per second it is possible to get a direct indication of the number of Elementary charges flowing in a current by doing an electrolysis experiment the type usually called a faraday experiment you have probably all done an electrolysis experiment like this one the water has been made conducting by adding a little salt I'll connect the batteries and you see that the water decomposes hydrogen bubbles up at the negative electrode on the right and oxygen bubbles up at the positive electrode on the left if I let the current that I'm using here flow for 10 minutes I collect this much gas after the bubbles settle down I can measure the volume of the gas I've collected so from avagadro's law I can determine the number of molecules of gas either of hydrogen or of oxygen now you probably recognize this figure it's avagadro's number under normal conditions 22.4 L of any gas contains 6.02 * 10 23rd molecules of that gas for easy figuring let's round this number off to 6 * 10 23r many experiments have shown that there are two hydrogen atoms in each hydrogen molecule so that in 22.4 L of hydrogen gas there are 12 * 10 23rd atoms of hydrogen now in just a moment I'm going to do an experiment where I'll collect 22.4 cubic mm of hydrogen gas 1 millionth of this value that volume should contain 12 * 10 17th atoms of hydrogen so that I'll be collecting 12 * 10 17 atoms of hydrogen in a volume of 22.4 cubic mm this is the equipment with which I'll do the quantitative electrolysis experiment this battery is connected through these wires to a pair of electrodes in this Beaker the water has been made conducting just as in the previous experiment the electrodes are very fine Platinum wires positioned beneath two small tubes when I connect the electrodes to a battery hydrogen bubbles off the wire on the right oxygen off the wire on the left left you can see the gas collecting in the tubes and displacing the water between the two tubes you can see thin black lines drawn on a white background these lines mark off lengths of tubing which have a volume of about 22.4 cubic mm now I'll disconnect the battery and release the gas here is a meter it's a fairly sensitive meter and I've covered the numbers on the face so that the face is blank now I want to calibrate one point on this meter when it's in the circuit in terms of the actual number of Elementary charges flowing through the circuit per second I'll connect connect it in series with this circuit now and I'm going to allow the current to flow until I've collected 22.4 cubic millim of hydrogen here which you will remember is 12 * 10 17 atoms of hydrogen now it's important to know that there are just as many Elementary charges flowing in the circuit as there are atoms of hydrogen coming off at the negative electrod let me illustrate that with a drawing on the board let these represent the electrodes this the battery this is the positive electrode and this the negative electrod hydrogen ions in solution have a positive charge and are attracted to the negative electrone where they pick up a negative charge and go off as a hydrogen atom while this is going on oxygen ions in solution are giving up their negative charge to this terminal thus making available free negative charge to the Circuit here for each free negative charge placed at this point the battery makes available a negative charge here for combination with a hydrogen ion in solution so that each each hydrogen atom which comes off at this point it represents the flow of one Elementary charge around the circuit if we count say three hydrogen atoms coming off here per second and have a meter in the circuit over here the meter will point to a position which represents the flow of three Elementary charges per second through the circuit now we can't count this small a number so if you'll remember we're going to count 12 * 10 17 atoms of hydrogen coming off at the negative electrone in some given interval of time now I'll need a timer in this experiment and I'll use this stopwatch I'll mark the position on this meter where the needle comes to rest now let me Mark the zero position since it'll take a little while to collect this bubble of gas I'll be turning on the stopwatch at the same time I connect the battery I'll then turn them both off when it seems to me that the bubble of gas is down to this first black line now I guess we're ready to go this current causes the needle to stop at this point you can see the hydrogen collecting in the right hand tube when it reaches the first black line I'll shut off the current and the timer there that was about 20 seconds so now let's uh organize our information here we actually counted 12 * 10 17 atoms of hydrogen in 20 seconds so that we counted 6 * 10 the 16 atoms per second each atom represented the flow of one Elementary charge through the circuit so that we actually were counting a flow of 6 * 10 the 16th Elementary charges per second now you remember that 1 ampere is equal to 6.25 * 10 18 Elementary charges per second and we counted 6 * 10 16th Elementary charges per second which is a ratio of about 1.04 * 10 2 over 1 or just about 100 to 1 so we had a current about 01 100 of an ampere so in this experiment we had a flow of current of 100th of an ampere 10 milliamp measured directly by counting the number of Elementary charges flow now let's take a look at this meter this Mark represents 100th of an ampere or 10 milliamp now if I connect the battery again we see that the pointer points to the mark which represents 10 milliamp now if I uncover the face to show the factory markings you can see that the 10 mli division Falls where we made our Mark we can assume our experiment was quite accurate and thus can say the meter is in fact well calibrated by counting atoms of hydrogen in this experiment we got a direct one: one count of the number of Elementary charges flowing through this circuit we were dealing with basic units of charge when we calibrated this meter later more evidence will show that these Elementary charges involved in the electrolysis experiment are the same Elementary charges which are in the migan experiment now we were using a rather small current here 10 milliamp and collected a small volume of gas but still we were dealing with a large number of atoms per second 60 million billion Elementary charges per second this amount of current was a fairly steady current the needle on the meter didn't fluctuate much but suppose I could count only 60 Elementary charges per second this counter is measuring a current of even less than 60 Elementary charges per second in fact it's measuring less than 20 it clicks once for every second electron because of the design of the circuit to which it's connected to measure currents this small accurately is a bit tricky I'm standing beside the apparatus devised to do this it was designed by Mr Madson here Borg could you turn it off for now to better understand what we're going to do here let's take a look at the various pieces of apparatus this meter can be used as a very sensitive am meter it is been accurately calibrated by the manufacturer if I set the rain Swit switch on the meter to its most sensitive position the meter will indicate a current of 10- 11 amp at full scale deflection of the needle in other words when the needle points here to 10 naturally then a reading of only 1 a tenth of full scale reading would indicate a current of 1 * 10-2 amp but if we want to measure just a few Elementary charges flowing per second then we must extend the range of this meter this tube is an electron multiplier let me take off the light Shield so that we can see the interesting part with the tube we'll extend the range of this meter by a factor of a million let me show you something about the details of this tube in this closeup you see the fully assembled tube in order to take a better look at how this tube operates we'll remove some of the supporting wires and the resistors these are the plates of the tube we call them dines they are connected to a battery in such a way that each plate is more and more positive going from right to left as you look at it here the filament is located here the filament is heated and some of the electrons which boil off of it pass pass through a small hole in a shield the electrons are accelerated to the first dinod the dines are especially treated so that when an electron hits a dyode it knocks a few more electrons out of it each of these electrons is then accelerated to the next dyode and each of these electrons in turn knocks out some more from that dyode and so on through to the last stage we can adjust the batteries so that for each electron that goes to the first dyode there are just about a million coming out of the last stage and being collected on the output Wire by connecting an AM meter into the circuit at the output stage we can measure the Amplified current to adjust our tube for a gain of a million we will have to compare the output current with the current from the electron gun alone we disconnect all the dines except the first one then putting an ammeter into the circuit from the first dyode we measured just the current of the electron gun we've compared the measurement of the electron gun current with its Amplified current from the final output of the multiplier and have adjusted the batteries so that for each electron coming from the gun we get a burst of 1 million from this final output stage of the multiplier having actually done the calibration we're ready to use the tube Mr madson's going to turn on the filament and adjust the current so that it is very weak when it flows through the electron gun this meter is connected directly to the electron gun and the multiplier is not in the circuit we'll read the current on the meter now as you remember when the needle is at 1 the current is 1 * 10 -2 amp you'll notice the needle holds pretty steady about this point he doesn't have any trouble measuring a current this size let's try a smaller one Mr Madson is going to change the con C so the multiplier is now in the circuit then he's going to adjust the current from the electron gun so that it is only one time 10-7 amp he can't check this current directly on the ammeter the meter isn't that sensitive but he knows when he's got it because the output current which he can measure is just 1 million times as large or 1 * 10- 11 amp we'll adjust the meter so that when we have this output current the needle will point to 1 the meter will in effect then be responding to the electron gun current of 1 * 10 -7 amp which is 60 Elementary charges per second now let's see the meter is set and board will change the current from the electron gun the needle is moving there it is pointing just about at one we really can measure this very weak current of about 60 Elementary charges per second but the needle won't hold still it fluctuates back and forth on both sides of one this fluctuation which isn't noticeable in larger currents illustrates a basic fact about all electric currents the elementary charges that make up a current don't go through the circuit with perfect regularity in this case there are sometimes more than 60 per second sometimes less the exact moment at which any charge goes by is just a question of probability let's see if we can make this more evident in several other ways first of all you can hear it you hear the Amplified sound of the elementary charges in this very weak current now I'll make the current even weaker now the rate is between 15 and 20 per second secondly we can see a visual trace of each Elementary charge if we display them on the oscilloscope tube face the large pulses you see are made by amplifying each electron in this weak current the narrow line below them comes from other parts of the circuit and the osilloscope and not the output of the multiplier to if I cover up the narrow line I think you can see see that the pulses made by the electrons in our current don't make a perfectly spaced pattern on the tube but appear at random intervals across the screen just the way the electrons pass randomly through the circuit if we use this equipment we can actually count the number of Elementary charges which constitute this very weak electrical current and in fact by using this method of direct ly counting Elementary charges we can calibrate that same ammeter which we used earlier and we get exactly the same results as we got by doing it by electrolysis from this you should recognize that it is really the average number of charges that pass per second which designates the strength of an electric current whether it be in this small current or the larger currents we measured earlier by electrolysis e