Rutherford Atom

ofation is taking place due to the passage of a projectile carrying an unbalanced electric charge for alpha particles the electrical unbalance amounts to two positive Elementary charges today we are going to see how Ernest Rutherford used alpha particles to investigate the structure of the atom Rutherford knew a good deal about the alpha particle he had measured its mass he had measured its light charge as a matter of fact he had determined that an alpha particle is a helium atom without its balancing negative charge it's two electrons he had measured the velocities of alpha particles ejected from radioactive elements and it was after he had observed alpha particles passing right through gases liquids even metal foils and knew how to count them that he realized that he had at hand a tool with which to explore the inner structure of the atom let us look a little more closely at these Atomic probes these alpha particles this time we will use a cloud chamber of different design our radioactive source is polonium and it is held in place by the screw on the left beyond the alpha particle tract you can see a small wire scale that we have laid on the bottom of the chamber and against which we can judge how far the alpha particles travel notice that the longest tracks go out about four divisions on the scale now we can set up a barrier across the path of the alpha particles using a metal foil this is gold foil similar to that Rutherford and his assistants used it is very very thin only a few thousand atoms thick and it's hard to handle nevertheless we've managed to get our Cloud chamber fitted with its barrier you see it here as a fuzzy light line across the face of the source the alpha particles pass right through it to look at the tracks you'd think the gold foil was not there at all the particles go through it with ease but there is a little difference showing up distance now the longest tracks go out only about three divisions on our scale they don't seem to travel as far the foil has reduced their energy slowed them down a little and they are consistently stopping short of their former range there is another effect that the gold foil has on the alpha particles that we cannot see just by examining these wispy tracks by eye the tracks are ever so slightly deflected rarely by more than one degree Rutherford suggested a study of this deflection to his colleague Hans Gyer who was already on the way to perfecting the now famous Geer counter this is how guer proceeded at one end of a glass tube evacuated and about a meter and a half in length he radium Source partway down the tube he placed a slit to give him a narrow well-defined beam of alpha particles at the other end he placed a cellation screen he used a microscope to see the flashes produced by the alpha particles as they hit the cator when he used gold foil he placed it over the slit with this equipment he recorded the distribution of alpha particles with and without the gold foil and prepared a graph of his findings here is the center of the beam of alpha particles 0° these figures represent the angles of deflection of the alpha particles in degrees and of course the vertical coordinate represents the number counted this is the beam as he saw it without any gold foil present you can see that it is only 1 Dee wide and had very sharp edges this second graph shows the effect of the gold foil the beam fuzzed out at the edges about half the particles were deflected through one degree a few to three degrees but none Beyond five the equipment for our demonstration is arranged a little differently our polonium source is on a rod here in a cylindrical brass tube here's the aperture through which the alpha particles emerge and we have made our aperture quite large so that a great number of particles will pass through the gold foil in a short period of time where garer beam was about 1° wide ours is in fact about 70° wide the gold foil is here and our electronic detector is here and is movable in an arc about the gold foil since we are not using a vacuum as guer did our components must be grouped closely together this is the tube containing our polonium Source here's a thin gold foil and here's the detector we will use to count the alpha particles that penetrate the foil it's a brand new device made out of a transistor it gives a sharp electrical impulse as an alpha particle hits it here it is connected through an amplifier to an asso scope and a loud speaker this arm pivots letting us move our detector in an arc across the beam of alpha particles and out of it on either side at any angle our detector is light sensitive so we'll place a shield over it and read its angle by this marker now we'll switch on the amplifier and hear a snap from the loud speaker for each Alpha partic we also see a pulse on the cathod ray tube even though we are working with a much broader beam of alpha particles then guer did we can still see on our counting equipment the rapid fall off at each edge of the beam here are the alpha particles about a half a million per second in the beam the beam goes from here over to here diminishing rapidly and we'll mark this as the edge of the beam and the same way on the other side here they diminish rapidly and we'll mark this as the other edge of the beam and now if we go beyond we find none perfectly quiet none of the alpha particles are deflected more than a few degrees from their original Direction what was that a count at this angle that's 25° out of the beam there's another that was three is the gold foil really responsible for these counts let's see silence now let's put the gold foil back now the G oils back in the beam of alpha particles and we'll wait and see there's a count already too this wide angle scattering seems to be caused by the presence of the gold foil all right what is going on this is what Rutherford wondered when a discovery of these wide angle scatterings was first made by Ernest Marsden a young graduate student under his Direction Maron found that on the average about one alpha particle out of every 8,000 was deflected through more than 90 de what was there about the structure of matter that would give rise to such violent changes of direction for a few alpha particles and scarcely any for the vast [Applause] majority here is a model that will enable us to examine this problem more closely these steel ball bearings will represent alpha particles the ramp will launch them with uniform energy this of course represents our gold foil now let's launch some there goes one these hot ball bearings leave tracks as they cross our specially prepared waxed paper there's a fourth and a fifth but this one was deflected through a large angle two more straight another one straight another straight another straight and another one we have set off 11 in all of the 11 10 have followed the kind of course guer observed but one has under gone a large deflection of the kind that maren observed let's run out about 200 now we have our sensitized paper record about as full as we can make it how did we make out how many violent collisions 1 2 3 4 five six these points in our gold foil looks suspicious let's see what's there aha hard steel fins no wonder the balls bounced our model gold foil is not really uniform in structure it consisted partly a fuzzy felt space through which our so-called Alpha partic penetrated with ease and partly of small massive scattering centers this sort of possibility is what Rutherford guessed at he knew that atoms were full of electricity ionization electrolysis and so on suggested that atoms had had lots of electricity in them despite their being electrically neutral when undisturbed and he knew the negatively charged electrons were very light compared to the mass of their atoms so he proposed that all of the mass of the atom except the little part belonging to the electrons might be [Applause] concentrated really concentrated in a minute space at the center of the atom leaving the rest of the atom empty except for the light electrons then if this massive core were to carry a large electrical charge the electrostatic force between this charged core and the charged alpha particle might explain the wide deflections now if this view of the atom were true how could it be checked rufer turned to the very deflections that had created the puzzle he would make an accurate record of the deflection angles tell him what kind of collision had taken place can you tell from a series of collisions what force is responsible for the deflections do you remember the toy train cars they made a collision at a distance because of the forces of repulsion between two magnets for magnets not Guided by tracks a magnetic deflection looks like this or this you can see the angle of incidence and the angle of emergence sometimes that's all you can see but a study of the angles of deflection can often tell us a great deal about the nature of the force that produced the Collision here's another Collision you are familiar with it is often called A Hard sphere Collision nothing happens until the Spheres appear to come into contact now this is a type of collision you may not have seen before this is a very light dry ice puck it seems to be working all right and this is a small vandag graph generator let's switch it on when it's charged up it has a large positive charge now let's share the positive charge on the Vander grass sphere with the sphere on the dry ice pip [Applause] when the two spheres are charged they have the same type of charge and they repel each other with a Kum force a force which varies inversely with respect to the square of the separation of the two spheres now let's see an electrostatic [Applause] Collision there was a wide encounter and a deflection angle of about 45° now let's charge the sphere again it gets hot to handle by hand let's try more direct encounter there it goes slowly in and deflect it almost directly backwards a deflection angle of about 150° now let's charge it again and see another encounter each of these encounters shows a deflection angle that's connected with the encounter distance in a way characteristic of the electrostatic force let's charge it again [Applause] that encounter produced about a 90° deflection we have seen three types of collisions magnetic contact or hard sphere and kulum or electrostatic and the types of deflections each produced as a matter of fact any type of force at work in a collision produces its own characteristic deflections Rutherford strongly suspected a kulum type interaction rather than magnetic or hard sphere or any other kind so he set about calculating the deflection pattern that is positively charged minute Atomic core would produce using kum's law he deduced the angles through which the alpha particles would be deflected as a function of how directly they were aimed at the center of the atom square at the center an alpha particle would turn through 180° and come right straight back if it approached a little off center as this one does it will be deflected through a large angle say 125° and come out here another one approaching a little further off center as this does look go through a lesser angle and come out here another one approaching still further out like this would come out here and another one approaching way out here would only be deflected by the coolum force through a small angle say 45 5° each of these trajectories and all the intervening paths rord found to be Hyperbole and it isn't just in this plane that these trajectories occur they occur all about the nucleus of the atom in this three-dimensional space here is a hemisphere that will help us picture the directions along which the alpha particles fly away from the nucleus after being deflected by the kulum force and I will ask you to picture another hemisphere under the table for everything that I say about angles on the upper hemisphere will apply equally well to the lower hemisphere when Rutherford was satisfied that he understood how each individual alpha particle would behave Under the Influence he turned his attention to a calculation of the fraction of the alpha particles that would emerge at each angle that is how they are distributed as they come out from this direction we can imagine a uniformly distributed R of alpha particles an alpha particle that falls at this point on the rim of this smallest Circle will follow a trajectory indicated by this wire go in toward the center of the atom and emerge along this direction One striking the same Circle at another Point say here will go in toward the center and come out along this this direction in fact particles striking anywhere on the rim of this circle will come out in directions like this through this Arc and I'll draw The Arc in a similar way a particle entering the coom field here at this point on the second Circle we'll go in along this trajectory and go out along here in the same way all around this circle and I can draw an arc to represent the places where alpha particles with exactly those trajectories will emerge from the nucleus and for this third circle the particles will fly out at Angles through this Arc lastly particles approaching somewhere out here will emerge through an arc along here now we have the spherical space about the nucleus of our atom marked out with certain limiting arcs which are determined by the trajectories we established before in fact each of these circles is directly related to each of these arcs for instance all of the AR Al particles approaching the nucleus within this Inner Circle will come out at Angles greater than those approaching right at its Rim that is they will come out through this cap Zone here now you can see that alpha particles entering outside the Inner Circle that is through this anular ring which I can Mark will come out through this Zone in other words each pair of arcs marks out a zone of emergence that is directly related to each pair of circles in the approach area particles going in through this annular ring will come out through here and particles going in through this largest anular ring which I will Mark come out here so now we're able to tell exactly where the alpha particles go that is at what angles they emerge and in fact we can also predict the quantities for the quantities going in through each circular area are exactly the same quantities that come out through the corresponding Zone on our sphere now let's think about the experiment to take counts in an actual experiment of this type we have to have a detector and on this scale the detector will be way out there for you remember that this model just represents the minute core or nucleus of the atom and a little of the atomic space about the nucleus for the purposes of argument let's assume that all the particles that come out through this Square on the spherical surface will hit our detector and that's true not only at this position but at any any angle on the sphere so our detector always sees a fixed fraction of the total spherical space about the atom can we arrange it so that our detector also sees a fixed fraction of the alpha particles coming through each Zone we can do it by choosing the areas of the zones to be equal how do we do that we do it by selecting the trajectories which divide up the zones in our particular case we wanted four zones so we chose four trajectories that would make the zones have equal areas this means that our detector always sees a fixed fraction of the alpha particles coming out through each zone so if the number of alpha particles emerging from one zone differs from the number of partic emerging through another Zone the fractions striking our detector have the same ratio so we have a uniform R of alpha particles passing through concentric circles of various sizes but emerging through spherical zones of equal size now look at this all the particles which go in through this Inner Circle emerge through this cap Zone and those that go in through this outer ring emerge through this fourth Zone and you can readily see that the number of particles that will go in through this outer ring is much larger than the number of particles that will go into this small Inner Circle so the number of particles emerging through this fourth Zone and going out to the detector will be much larger than the number of particles that goes out through this cap Zone and into the detector when it is out here here so the key to our problem is the relative size of those input areas with a uniform re of alpha particles the number entering the Inner Circle or any of the annular Rings is going to be directly proportional to the area of that Circle or ring so now we can write that the number capital n striking our detector is proportional to the input area a sub I now let's prepare a graph of the way we expect the data to appear we will let the vertical axis represent the predicted number of counts and the horizontal axis will represent angle and will extend from 180° to 0 de we will let the number of particles that goes in through the Inner Circle and comes out through the cap Zone into the detector be our unit number and the cap Zone extends from 180° to 125° so on our graph that portion looks looks like this 180° to 125° at unit number now the first annular ring is 1.8 times as large as the Inner Circle so 1.8 times as many alpha particles will pass through it and out through the first Zone as went in through the Inner Circle and come out through the cap Zone that Z Z extends from 125° to 98° and the count is 1.8 so that portion of our graph will look like this the second annular ring is 3.7 times as large as the Inner Circle so 3.7 times as many alpha particles will pass through it and out through its corresponding Zone this is 3.7 here and the angular extent of that zone runs from 98° to 74° so this portion of our graph will look like this finally the outer annular ring is 15 times as large as the Inner Circle there therefore 15 times as many particles will pass through it and out through its corresponding Zone as passed through the Inner Circle 15 is up here and the angular region of that zone is from 74° to 45° so that portion of our graph will look like this and now the character of the scattering pattern becomes apparent you can see that far fewer alpha particles are scattered through large angles than are scattered through small angles now we have taken this calculation in large angular steps if we had more time we could have taken smaller steps and more of them and we would have had a curve that look something like this you can see that the number of alpha particles varies continuously with angle instead of being averaged over large angular intervals now there's a great deal of approach area out here in the atom much more than the area we've considered Near the nucleus so most of the alpha particles in the rain hitting the atom go almost Straight Ahead as guer had first seen those alpha particles that are only deflected by a degree or two would be plotted here on our graph and there would be a great number of them this part of the graph shows you the kind of scattering pattern Ruther expected Geer and Maron defin at the larger angles here we have a carefully prepared graph based on his calculations as before the predicted count is plotted on the vertical axis and the angle of the detector is plotted on the horizontal axis here by contrast we have a graph derived in a similar way for hard sphere scattering and here is the curve you would expect if the deflecting force were proportional to 1 / R cubed instead of 1 R 2 as in the kulum force you can see that the three curves are different each curve provides a signature or fingerprint of the type of force that is at work in the collision by February of 1911 Rutherford had prepared the curves for the electrostatic case within a few weeks he had completed for publication a description of his nuclear atom model with the prediction that the scattering force was electrostatic then he set gerer and Marston to work at an experimental confirmation which we could approximate with our apparatus for each angular setting of The detector the rate at which alpha particle struck the detector was carefully recorded work which took them months we can do the day in hours with our modern accelerators after 18 months of painstaking effort the scattering pattern Rutherford had calculated was decisively confirmed gager and maron's Counting rates plotted against their counting angles fitted the curve characteristic of the 1/ R 2 Kum force their data did not fit the curve for hard sphere collisions and it didn't fit the 1 over R cubed curve to be even more certain they did experiments with foils of metals other than gold and with alpha particles of different Energies and they all fitted with the prediction of a 1 over R 2 kulum force field within the atom Rutherford's extraordinary piece of deductive reasoning had given the world an entirely New Concept of the structure of the atom for the first time it was seen as a sort of a minute solar system with the nucleus as Sun carrying virtually all the mass of the entire system with the bulk of the volume being empty space permeated by intense electrical fields and with the electrons distributed in this space balancing by their negative charge the positive charge of the nucleus did Rutherford come to any conclusion about how small the nucleus actually was he did for even the AL particles which approached the nucleus most directly scattered as he predicted they would under the influence of a pure Kum force and his calculation showed that the distance of nearest approach was less than 10us 11 cm in an atom which is 10us 8 cm in diameter this charged massive core must be concentrated in a space which is smaller than 10us 11 cm we can hardly see that on this scale let me give you an idea of the amazing image this creates let suppose this point of light 1 mm in diameter to represent an atomic nucleus I'm going to place it here and then I'm going to ask you to back away from it further further still there from there you should be able to see the whole of this circle it's 3,000 mm diameter and on the scale of this model it represents the outer dimensions of the atom now I'm going to take another point of light also 1 mm in diameter and let it represent a helium nucleus an alpha particle is it any wonder that most of the alpha particles travel through the gold foil as though it were empty space but it's a peculiar kind of empty space face its outer Dimension is as unassailable as the Greeks said it was with all this space why doesn't matter collapse why don't the charge particles of the other atoms move into this space another 20 years passed before before that question was answered that answer and everything else we know about the atam today are firmly built on Rutherford's Triumph with its brilliant analysis of the force Mass space relationship of the Earth