The Three Kinds of Decay

Transcript

0:00Introduction

Hello everyone! Let me start with a puzzle. In beta decay, a nucleus shoots out a fast electron. But there are no electrons inside a nucleus, only protons and neutrons! So where does that electron come from? Today we meet the three kinds of radioactive decay, alpha, beta and gamma, and see how one element turns into another. This topic is in the JEE Advanced syllabus, and it was in JEE Main until twenty twenty three, so let's begin.

0:33Writing a nucleus, and alpha decay

So, how do we write a nucleus? Capital X is the nucleus. The small capital A at the top left is the mass number, the number of protons plus neutrons, and the small capital Z at the bottom left is the atomic number, the number of protons. Okay? Now, one rule drives everything today. In every decay, charge, nucleon number, energy and momentum are conserved. So the total nucleon number and the total charge stay the same. Right? Now the first kind, alpha decay, with the Greek letter alpha. An alpha particle is a helium nucleus, two protons and two neutrons. So when a nucleus throws one out, what happens to its A and its Z? Yes, exactly, it loses two protons and two neutrons. The arrow means changes into: X changes into a new nucleus Y, plus helium four, with four on top and two below. So Y has A minus four at the top and Z minus two at the bottom. And since Z has changed, Y is a different element altogether. With me?

1:42Beta minus decay: where does the electron come from?

Now, back to our puzzle. This is beta minus decay: the Greek letter beta with a small minus sign. The nucleus throws out an electron, e with a small minus sign. But there are no electrons in it. So where does this electron come from? Here is the answer. Inside the nucleus, a neutron, small n, changes into a proton, small p, and at that moment an electron is created. Along with it comes nu, the Greek letter like a v, with a bar on top: the antineutrino. Got it? So here is beta minus decay. One neutron became one proton, so the nucleon count, A, is unchanged, but there is one more proton, so the bottom number is Z plus one. Be careful, because many students reduce the mass number in beta decay too. Don't do that, okay?

2:35Beta plus, electron capture and gamma decay

Now the opposite, beta plus decay, beta with a small plus sign. Here a proton becomes a neutron. Out come e plus, the positron, with charge plus e, and nu without the bar, the neutrino. So the mass number A is unchanged, and the bottom number falls to Z minus one. Right? Now a tricky question. Can a free proton, all alone outside a nucleus, turn into a neutron this way? No, it cannot, because a free proton is lighter than a neutron. So beta plus decay is possible only inside a nucleus. Clear? Electron capture also turns a proton into a neutron. The nucleus captures an electron: p plus e minus gives n plus nu. Same effect as beta plus decay: the mass number is unchanged, and Z falls by one. Okay? Finally, the third kind, gamma decay, with the Greek letter gamma. An excited nucleus drops to a lower state and emits a photon. The photon has no charge and no nucleons, so A and Z are both unchanged. Got it?

3:41Trick: count the alpha and beta minus particles

Now let me share a topper's trick. Say a parent nucleus with A and Z goes through a chain of alpha and beta minus decays, and ends with A prime and Z prime; the little dash is read as prime. So tell me first, which of these two decays changes the mass number? Yes, only alpha decay, and each alpha takes away four. So n alpha, n with a small alpha below, equals A minus A prime, over four. Clear? Now look at the atomic number. Each alpha lowers Z by two, and each beta minus raises it by one. So the alphas pull Z down by two times n alpha, and the beta minus particles bring it back up to Z prime. Right? That gives n beta, with a small beta below, equals two times n alpha, minus bracket Z minus Z prime. Always find n alpha first, then n beta, and keep the bracket as parent minus final. With me?

4:41Properties of alpha, beta and gamma radiation

In this figure, the rays come up from a source in a lead block and pass between two charged plates, and the E with an arrow on top is the electric field. Alpha is a helium nucleus, charge plus two e, where e is the electron's charge in size. It is heavy, so it bends only slightly, towards the negative plate. Okay? Beta is a fast electron, charge minus e, or, in beta plus decay, a positron, charge plus e. Being very light, beta minus bends sharply, towards the positive plate. Right? And gamma is a photon with no charge, so it goes straight up, with no deflection at all. Clear? Now, alpha has the greatest ionising power of the three. So does it also have the greatest penetrating power? No, it is exactly the opposite, and that is a common trap. Ionising power goes alpha, greater than beta, greater than gamma, and penetrating power goes the other way: gamma, greater than beta, greater than alpha. Got it? So a sheet of paper stops alpha, beta needs a few millimetres of aluminium, and gamma needs centimetres of lead. With me? Last, let us look at the energies. Alpha and gamma come in sharp lines, but beta energies are continuous, up to a maximum. That is because the energy is shared between the electron and the antineutrino. Okay?

6:08Example 1: products when U-238 emits alpha, then beta minus

Uranium, U, with mass number two hundred and thirty eight and atomic number ninety two, emits an alpha particle, and the product then emits a beta minus particle. Identify the two products. Pause the video and try it first. Done? Okay, let's check. In alpha decay the mass number falls by four: two hundred and thirty eight minus four gives two hundred and thirty four. The atomic number falls by two, to ninety, and that is thorium, with helium four going out as the alpha particle. Right? Next, thorium emits a beta minus particle, an electron, along with an antineutrino. The mass number stays two hundred and thirty four, and the atomic number rises by one, to ninety one, which is protactinium. So, thorium first, then protactinium. Clear?

7:02Example 2: alpha and beta particles from U-235 to Pb-207

Now a harder one. How many alpha and beta minus particles are emitted when uranium two hundred and thirty five, atomic number ninety two, changes to lead two hundred and seven, atomic number eighty two? Pause the video and try it first. Done? Okay, let's check. Alpha first: two hundred and thirty five minus two hundred and seven gives twenty eight, and twenty eight over four gives seven. So seven alpha particles. Got it? Now, the atomic number fell from ninety two to eighty two, that is, by ten. But tell me, seven alpha particles alone would lower Z by how much? Seven alphas lower it by two times seven, which is fourteen. That is four too many, and each beta minus raises Z by one. So n beta equals fourteen minus ten, which is four. Right? Let's check it. Ninety two, minus fourteen, plus four, gives eighty two, which is lead. So the answer is seven alpha particles and four beta minus particles. See how quick that was?

8:14Quick revision: A and Z changes, counting rule, penetration

So, quick revision. Alpha gives A minus four and Z minus two, beta minus gives Z plus one, beta plus gives Z minus one, and gamma changes neither. To count particles, find n alpha from the mass numbers first, then n beta. And ionising and penetrating powers go in opposite orders. Now try the practice problems on this page. All the best!