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## Physics library

### Unit 17: Lesson 4

Nuclei- Mass defect and binding energy
- Nuclear stability and nuclear equations
- Types of decay
- Writing nuclear equations for alpha, beta, and gamma decay
- Half-life and carbon dating
- Half-life plot
- Exponential decay formula proof (can skip, involves calculus)
- Exponential decay problem solving
- More exponential decay examples
- Exponential decay and semi-log plots

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# Writing nuclear equations for alpha, beta, and gamma decay

Alpha, beta, and gamma decay are all ways that an unstable atom can decay into a more stable form. Let’s model each type of decay through equations.
Created by Jay.

## Want to join the conversation?

- A beta particle is an electron. But I was told that it doesn't behave like one. It can't take the place of an electron in a regular chemical reaction. Why is that?(18 votes)
- A beta particle can be either an electron OR a positron. If it is a positron, it will not act like an electron because it has a positive charge, which will repel it from anything that an electron would interact with. Most often they will be annihilated by colliding with an electron eventually.

If it is an electron though, and has a negative charge as usual, it will fly away from the atom at a high energy until it crashes into something, and then will react with whatever it crashes into. Hope this helped!(34 votes)

- When Thorium performs beta decay and becomes protactinium, would the product be an ion since a proton was added, and a beta particle was released out of the atom, not keeping the charges equaled?(5 votes)
- Probably, but also probably not for very long, since any free electrons in the area will be attracted to it's positive charge.

In studying nuclear physics we really are focused on what's going on in the nucleus. What happens with the electrons doesn't matter much.(5 votes)

- Is neutron made up of proton and electron and antineutrino? If yes, do the sum of these masses equal the mass of neutron? If no, what else is neutron made up of?(6 votes)
- No, a neutron is not made of a proton, electron and antineutrino. It is made of two down quarks (charge -1/3) and one up quark (charge 2/3).

When it decays, the weak force causes a down quark to change into an up quark, effectively making it a proton. This process also releases an electron and an antineutrino.(3 votes)

- How do you know charge and nucleons are conserved? Reason?(4 votes)
- We do not "know" that a given conservation law is true, instead we have observed, over and over again, that in every reaction things like the total electric charge stays the same. From this, scientist have created a model that up to now has always shown to be correct.(6 votes)

- So he talks about the three types of radioactive decay, but how do you know what kind of decay say, Uranium, for instance, would give off? Or any other element for that matter?

Thanks!(5 votes)- We measure it using detectors. Each particle can be detected using different methods due to its ability to penetrate materials. So, for U-235 for example, when it decays via α-decay, a Geiger counter will only detect it if there is no 'window' on the detector as alpha particles cannot penetrate through solid matter very far. Scintillation counters can use different materials specialized for specific types of radiation as well.(3 votes)

- I have a bunch of confusion how the Gama ray decays. Sal had't clarify about the Gama decays. Can any one help??(2 votes)
- Gamma rays are produced by an acceleration of charged particles. Usually, in terms of high energy decay, this is due to a rearrangement of nucleons in a nucleus into a lower energy state (this is what is referred to as gamma decay), nuclear fission, or various other means. Many of the other types of decay can also produce gamma radiation of various energy levels.(6 votes)

- At6:55, how can nucleus become excited? Wasn't that electrons?(1 vote)
- The nucleus has nuclear energy levels, just like the atom has atomic energy levels. The reason for this is that you get energy levels whenever you have things bound together. The electron is bound to the nucleus by the electric force, so you get quantized energy levels related to that "system" of nucleus + electrons. But inside the nucleus, the nucleons are bound to one another by the strong nuclear force, so you also get quantized energy levels for that smaller system. Since the strong force is much stronger than the electric force at subatomic range, the energy levels in the nucleus are much larger than those for the atom, and this is why the energy released in nuclear reactions is so much greater than the energy released in chemical reactions (eg a nuclear electric power facility produces energy from a lot less fuel than a similarly powerful coal-fired electric power facility)(3 votes)

- He didn't mention positron decay, which I am still very confused about. Can someone explain that or link to a video that better explains it? I've got a test coming up soon and I cannot fail.(2 votes)
- How can we predict what type of radiation might happen to a certain isotope? I recall learning about an N/Z ratio (using the belt of stability), but I'm really confused about it. Any help would be appreciated, thanks!(3 votes)
- If it is a Radioactive isotope it will then depend on what element it is in. Usually it is gamma decay but some radioactive synthesizers can tell you what radiation is has in its isotope.(1 vote)

- How do we know which elements will undergo which kind of decay without actually observing them? E.g, why can't U-238 do beta decay?(1 vote)
- You can't. You would need to look it up in a reference source. Some atoms can decay in more than one way, and you can't predict which one will happen first.(4 votes)

## Video transcript

- [Voiceover] Let's look at three types of radioactive decay, and we'll start with alpha decay. In alpha decay, an alpha particle is ejected from an unstable nucleus, so here's our unstable
nucleus, uranium-238. An alpha particle has the same composition as a helium nucleus. We saw the helium nucleus
in the previous video. There are two protons in the helium nucleus and two neutrons. So I go ahead and draw
in my two neutrons here. Since there are two protons, the charge of an alpha
particle is two plus. So for representing an
alpha particle in our nuclear equation, since an alpha particle has the same composition
as a helium nucleus, we put an He in here, and it has two positive charges, so we put a two down here, and then a total of four nucleons, so we put a four here. Trying to figure out the other product from our nuclear equation, I know nucleons are conserved, so if I have 238 nucleons on the left, I need 238 nucleons on the right. Well, I have four from my alpha particle, so I need 234 more. So 234 plus four gives me a
total of 238 on the right, and so therefore nucleons
are conserved here. In terms of charge, I know
charge is also conserved. On the left, I know I have 92 protons, so 92 positive charges on the left. I need 92 positive charges on the right. We already have two positive charges from our alpha particle, and so we need 90 more. So we need 90 positive charges. We need an atomic number here of 90. The identity of the other product, just look it up here at our table, find atomic number of 90, and you'll see that's thorium here. So thorium-234 is our other product. So we think about what's
happening visually, we're starting off with a uranium nucleus which is unstable, it's going
to eject an alpha particle, so an alpha particle is
ejected from this nucleus, so we're losing this alpha particle, and what's left behind
is this thorium nucleus. So this is just a visual representation of what's going on here,
in our nuclear equation. Let's do beta decay. So in beta decay, an electron
is ejected from the nucleus. We saw in the previous video that you represent an electron, since it has a negative one charge, you put a negative one down here, it's not a proton, nor is it a neutron, so we put a zero here. So here's our electron and an electron ejected from the nucleus
is called a beta particle. We could put a beta here,
and it's an electron, so a negative one charge,
and then a zero here. If a beta particle is
ejected from the nucleus of a thorium-234, so we're
starting with thorium-234, this nucleus ejects a beta particle, so we go ahead and put
a beta particle in here, so zero and negative one,
what else is produced here? What else do we make? Well, once again, the number of nucleons is conserved, so I have
234 nucleons on the left, I need 234 on the right. I have a zero here, so
I need 234 nucleons. Charge is also conserved,
so I have 90 positive charges on the left, I have 90 protons. On the right, I have a
negative charge here, so I have a negative one charge, and so I must need 91 positive charges, because 91 positive charges and one negative charge gives me 90 positive charges on the right. So I need an atomic number of 91. If you look at the periodic table, and you find the atomic number of 91, you'll see that this is protactinium. So we're going to make
protactinium here, so Pa. What is happening in beta decay? Let's look at it in a
little bit more detail. We already talked about
the number of protons, so we have 90 protons on the left, how many neutrons do we have? Well, 234 minus 90, 234 minus 90 gives us the number of neutrons. That's 144 neutrons. On the right, we have 91 protons, how many neutrons do we have? Well, that'd be 234 minus 91. So 234 minus 91 gives us 143 neutrons. So we went from 144 neutrons on the left to 143 neutrons on the right, and we went from 90 protons on the left, to 91 protons on the right. So we lost a neutron,
and we gained a proton. You could think about the
neutron turning into a proton, and this is an oversimplified
way of thinking about it. Let's go ahead and write that down here. So a neutron turning into a proton. So a neutron has no charge,
so we put a zero here. And a neutron is a nucleon,
so we put a one right here. So a neutron is turning into a proton, so let's go ahead and
write our proton here. A proton has a plus one charge, and it's a nucleon so we put a one here. When we think about what else is made, we know that nucleons are conserved, so we have one nucleon on the left, one nucleon on the right. Therefore, we would have a zero here. In terms of charge, if we
have zero charge on the left, plus one on the right, we
need negative one right here. This of course represents the electron, so this is the electron that's
ejected from the nucleus. This is our beta particle. And also actually,
something else is produced. You're also going to
make an anti-neutrino, and that's just really
not part of this video, so we'll just ignore it for now. So a neutron has turned into a proton, and we're also getting a beta particle ejected from the nucleus. When this conversion, this process is actually governed by the weak force, the weak interaction, so there's a lot of stuff going on in the nucleus which we just won't
get into in this video. The important thing is to be able to look at a nuclear equation, recognize it as beta decay, and be able to write everything in your nuclear equation. Let's do one more type of decay. This is gamma decay. Gamma rays are given off, and a gamma ray has no charge and no mass; it's pretty much just energy,
if you think about it. These are pretty easy decay problems. Let's start with technetium-99m, and the m right here
stands for metastable, which means a nucleus
in its excited state, so a nucleus in its excited state, so it has more energy. It's going to give off a gamma ray, so let's go ahead and draw in our gamma ray here, so zero and zero. Since we're dealing with zeroes, so these zeroes aren't
going to affect our numbers, so if we start with nucleons, we have 99 nucleons on the left, we're going to have 99
nucleons on the right. And in terms of charges, we have 43 positive charges on the left, we need 43 positive charges on the right. And since the atomic
number isn't changing, it's 43 on the left, it's 43 on the right, we're dealing with technetium here. It's still technetium; it's
just in the ground stage. It's no longer in the excited state. It's in the ground state. It's given off energy in the form of gamma rays in this example here. So technetium-99m is actually used in several medical imaging
and diagnostic procedures, because we have ways of
measuring the gamma radiation, and so this is very useful in medicine.