The Scattering Experiment

Transcript

0:00Introduction

Hello everyone! Let me start with a small puzzle. Fire fast particles at a sheet of gold, much thinner than a page of your notebook. Almost all of them fly straight through, as if nothing is there. But about one in eight thousand turns back, by more than ninety degrees! How can something that is almost empty throw a fast particle back? This one experiment gave us the nucleus, and JEE does ask questions on it, so let's begin.

0:30Thomson's model: the watermelon atom

So, first, the atom before this experiment. In eighteen ninety eight, Thomson said the atom is a sphere of positive charge; the plus sign on screen means positive. Its radius is about ten to the power minus ten metre, where the letter m stands for metre. Okay? And the electrons are embedded in this sphere, like seeds in a watermelon. Now, the positive charge is spread over the whole atom. So let me ask you this: can such a spread out charge push hard on a fast particle, anywhere inside? No, it cannot, because with the charge spread out, the electric field inside is weak everywhere, so the force is always small. The double arrow means so, or implies. So fast alpha particles, alpha being the Greek letter on screen, should be deflected only by very small angles. Clear?

1:21Geiger and Marsden's experiment (1911)

Now, in nineteen eleven, Geiger and Marsden tested this, at Rutherford's suggestion. Their source was bismuth two fourteen; the small two one four at the top left is its mass number. It gives alpha particles with five point five M e V, mega electron volts, of energy each. Got it? The target was a gold foil, about two point one times ten to the power minus seven metre thick. Really thin, and soon we will see why. With me? Now, an alpha particle is far too small to see. But each one that hits a zinc sulphide screen makes a tiny flash of light. So they counted these flashes at different angles. Okay?

2:02What they saw, and what it means

Now the results, in the picture. The alpha beam comes in from the left, and the dashed circle marked atom is one atom of the foil. Most particles, the blue lines marked undeflected, go straight through without turning. So tell me, if most particles pass through without hitting anything, what does that say about the atom? Yes, exactly, the atom is mostly empty space! Nothing in the way, so nothing turns them, right? But some particles, the green paths marked deflected, turn through large angles. And Thomson's model allows only very small angles, remember? And about one in eight thousand turn by more than ninety degrees; the small circle means degrees. They come back towards the source, like the orange path marked bounced back. That is really surprising, isn't it? These alpha particles carry five point five M e V each, so they are very fast. What could possibly turn such a particle back? Yes, exactly, only a tiny, massive nucleus can do that. The positive charge and nearly all the mass sit in this tiny centre, the orange dot marked nucleus. Only such a nucleus can exert a force large enough to turn an alpha particle back. This is Rutherford's nuclear atom. Got it?

3:22How small is the nucleus?

Alright, now the size. From the scattering results, the nucleus comes out between ten to the power minus fifteen and ten to the power minus fourteen metre. And the atom, as we saw, is about ten to the power minus ten metre. So how many times smaller is the nucleus? Work out both ends of the range. Ten to the power minus ten, over ten to the power minus fourteen, gives ten to the power four. And over ten to the power minus fifteen, it gives ten to the power five. So the nucleus is smaller by a factor of ten to the power four to ten to the power five. Clear?

4:00Electrons, a thin foil, and gold

Now, one doubt. Gold atoms also have electrons, and they are charged, so they pull on the passing alpha particle. So they should turn it a lot too, right? No, no, careful, that is the trap here. An electron is about seven thousand three hundred times lighter than an alpha particle. So a collision with an electron changes the alpha particle's velocity by a negligible amount. So electrons do not deflect the alpha particle appreciably. That is why, in scattering, we look only at the nucleus. Okay? Next, the foil is kept very thin, so that each alpha particle is scattered by no more than one nucleus. In a thick foil, many scatterings one after another would hide the effect, and the particles would also lose energy. With me? And gold was chosen for two reasons. It can be beaten very thin, and its nucleus is heavy, so it does not recoil much. Got it?

4:59Example 1: if the nucleus were 1 cm, how big is the atom

Now, example one, an easy one. If a nucleus were enlarged to the size of a marble of radius one centimetre, written c m, how large would the atom be? Take the ratio of radii as ten to the power five. Pause the video, and try it first. Done? Okay, let's check. Enlarge everything by the same factor, and the ratio does not change. So the radius of the atom is ten to the power five times the radius of the nucleus. Right? The nucleus is now one centimetre in radius, so the atom's radius is ten to the power five times one centimetre, that is, ten to the power five centimetres. Now change the units. How many kilometres is ten to the power five centimetres? Divide by one hundred, and ten to the power five centimetres becomes ten to the power three metres, which is one kilometre, written k m. So the atom would be about one kilometre in radius! Now you see why most alpha particles went straight through, right?

6:05Example 2: fraction of a gold atom's volume that is nucleus

Now a harder one. The radius of a gold atom is about one point four times ten to the power minus ten metre, and that of its nucleus about seven times ten to the power minus fifteen metre. What fraction of the volume of the atom does the nucleus occupy? Pause the video and try it first. Done? Okay, let's check. First, the ratio of radii, nucleus over atom. Seven over one point four gives five, and ten to the power minus fifteen, over ten to the power minus ten, gives ten to the power minus five. So the ratio is five times ten to the power minus five. Okay? So the nucleus occupies five times ten to the power minus five of the atom, and we are done, right? No, no, wait, the question asks for the volume, not the radius! The volume of a sphere is four thirds pi r cubed, where r is the radius; pi is the Greek letter, and the small three means cubed. The four thirds and the pi cancel in the ratio, so the fraction is the ratio of radii, cubed, as in the brackets. With me? Five cubed is one hundred and twenty five, and ten to the power minus five, cubed, gives ten to the power minus fifteen. So we get one hundred and twenty five times ten to the power minus fifteen, which is one point two five times ten to the power minus thirteen. That is a really tiny fraction, so the atom is almost empty, just as the alpha particles told us.

7:32Quick revision: Thomson model, 1 in 8000, nucleus size

So, quick revision. Thomson: charge spread out, so only very small deflections. The experiment: most alpha particles pass straight through, but about one in eight thousand turn by more than ninety degrees. So there is a tiny, massive, positive nucleus, ten to the power four to ten to the power five times smaller than the atom. Now go and try the practice problems on this page. All the best!