Discovery of Subatomic Particles

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. The electron is far too small to see, and far too light for any weighing balance. Yet every chemistry book gives its mass, correct to four digits! So how did anyone weigh it? Strange, right? Today, you will find out. And look, questions on these particles come up often in JEE, okay? So, let's begin.

0:27Cathode rays in a discharge tube

So, it all starts with a discharge tube: gas at a very low pressure, and a high voltage. Now rays travel from the cathode to the anode, in straight lines. We call them cathode rays. Okay? Now, the rays bend towards the positive plate. So tell me, what charge do they carry? Yes, exactly! Negative charge, because opposite charges attract. And this double arrow you see on screen means so, or therefore. Right? Next, the rays turn a light paddle wheel. Only something with mass can push a wheel. So cathode rays have mass. With me? Now the big question. Change the gas inside the tube, or change the material of the electrodes. Do the cathode rays change? No, they don't! Same properties every time. So these rays are made of something present in every material. Cathode rays are streams of electrons. That's it! Clear?

1:25The three fundamental particles

First, the electron, written e with a small minus sign at its top right, discovered by J J Thomson in eighteen ninety seven. Its charge is minus one point six zero two times ten to the power minus nineteen coulomb. The cross means times, and the capital C stands for coulomb. Its mass is nine point one zero nine times ten to the power minus thirty one kilogram. Okay? Next, the proton, written p. It was found by Goldstein, through anode rays, and by Rutherford. Its charge is plus one point six zero two times ten to the power minus nineteen coulomb: the same size as the electron's, just positive. And its mass is one point six seven three times ten to the power minus twenty seven kilogram. Right? And the neutron, written n, discovered by Chadwick in nineteen thirty two. Charge zero, and mass one point six seven five times ten to the power minus twenty seven kilogram. Almost the same as the proton, just a little heavier. Now, the electron and the proton have charges exactly equal in size. So their masses should be similar too, right? No, no, not at all! The proton is about one thousand eight hundred and thirty six times heavier than the electron. On screen, m with a small p below is the mass of the proton, m with a small e is the mass of the electron, and the wavy equals sign means approximately. And the relative charges: electron minus one, proton plus one, neutron zero. Got it?

2:58Specific charge, and how the electron was weighed

Now, the key idea of this lesson: specific charge. It is e over m, charge divided by mass; the slash on screen means divided by. In eighteen ninety seven, Thomson was the first to measure e over m for the electron. His value was rough, and it was only the ratio, not the mass. Remember our puzzle? This is where it starts. The accurate modern value is one point seven five eight eight two zero times ten to the power eleven coulomb per kilogram. The unit, C kg to the power minus one, means coulomb per kilogram. Clear? So, think like a scientist. We know e over m. What one more number do we need, to get the mass? Yes, exactly! The charge e itself. And that came in nineteen oh nine, from Millikan's oil-drop experiment. He found that every charge is a whole number times e, never a fraction of it. Okay? And e is one point six zero two times ten to the power minus nineteen coulomb. Now divide e by e over m, and the mass pops out. m e, the mass of the electron, comes to about nine point one times ten to the power minus thirty one kilogram. That's how the electron was weighed, without any balance! Puzzle solved.

4:15Common trap: anode rays are different

Now, one trap that comes up often. There are also anode rays, or canal rays. They are positive ions of the gas in the tube. Okay? We already saw that cathode rays have the same e over m, whatever the gas. Electrons are the same in every material, right? So anode rays should also have the same e over m for every gas. Correct? No, no, careful! Anode rays are ions of the gas itself. Change the gas, and the mass of the ion changes. So their e over m depends on the gas. Got it? And it is largest for hydrogen. Hydrogen gives the lightest positive ion, H plus, which is just a proton. Smallest mass, so the largest e over m. Simple!

5:01Example 1: specific charge e/m of the electron

Now, Example one, a quick warm-up. Calculate e over m for the electron, from e equal to one point six zero two times ten to the power minus nineteen coulomb, and m e equal to nine point one one times ten to the power minus thirty one kilogram. Pause the video, and try it first. Done? Okay, let's check. e over m equals e on top, divided by m e at the bottom. Just put the numbers straight in. Okay? Now, ten to the power minus nineteen, divided by ten to the power minus thirty one. What power do you get? Very good! When we divide, we subtract the powers: minus nineteen plus thirty one, which is twelve. Careful: many students write minus fifty. Completely wrong! And one point six zero two divided by nine point one one is about zero point one seven six. So, zero point one seven six times ten to the power twelve. With me? Shift the decimal one place: one point seven six times ten to the power eleven coulomb per kilogram. That is the accurate value of the ratio Thomson first measured, roughly, in eighteen ninety seven. Easy marks!

6:13Example 2: unit charge from Millikan oil-drop data

Now Example two, a step harder. In an oil-drop experiment, the charges on three drops were three point two, four point eight, and eight point zero, all times ten to the power minus nineteen coulomb. What is the largest unit charge consistent with these? Pause the video, and try it. Done? Okay, let's check. Many students grab the smallest charge, three point two, and call it the unit. Looks fine, right? No, no, wait! Test it. Four point eight divided by three point two is one point five. One and a half units? Not possible! Every charge must be a whole number times the unit. So three point two is out. So try half of it, one point six. Three point two is two times one point six, four point eight is three times one point six, and eight point zero is five times one point six, all times ten to the power minus nineteen. Whole numbers every time. Correct! Now, the question says the largest unit. Look at the multipliers: two, three and five. They have no common factor other than one, so no bigger unit can divide all three charges. Got it? So the largest unit charge is one point six times ten to the power minus nineteen coulomb. And look, that is just the size of the charge on one electron, rounded off. See how fast that was?

7:36Quick revision: charges, masses, cathode vs anode rays

So, quick revision. Relative charges: electron minus one, proton plus one, neutron zero, and the proton is about one thousand eight hundred and thirty six times heavier. Thomson's e over m and Millikan's e together give the mass of the electron. And cathode rays have the same e over m for every gas, but for anode rays it depends on the gas. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!