Chem 1010 Lecture Notes

Radioactivity - How Unstable Atoms Decay

There are three types of nuclear reactions: fusion, fission, and radioactive decay. When an atom undergoes radioactive decay, a small particle comes out of the nucleus, causing it to change into a different element. Several different kinds of particles are possible, as we shall shortly see.

Why Atoms are Radioactive

Not all atoms are radioactive. This is a good thing, because the high energy particles that result from radioactive decay aren't good for living things. However, this raises the question of why some atoms are radioactive and some are not.

The simple answer is that radioactive atoms have an unstable nucleus. So when we say that an atom is radioactive, we mean that its nucleus is unstable, and prone to radioactive decay.

What makes an atom stable or unstable? There are two important factors: the size of the nucleus, and the ratio of protons to neutrons.

Once a nucleus gets past a certain size, it is unstable. The largest stable nucleus is bismuth-209. All isotopes larger than this are unstable, while nearly all elements smaller than this have at least one stable isotope (exceptions are technetium and promethium).

Notice that the elements that don't have any stable isotopes aren't exactly the same ones as the ones we've previously referred to as “artificial,” or not naturally occurring. Uranium, as it turns out, doesn't have any stable isotopes, but it does have some that last quite a long time before undergoing radioactive decay, so we can still find it around. And when it decays, it turns into some smaller elements like thorium, francium, and so on, so that even though they are unstable and don't last long, a little more of them are being generated, so we can find small amounts in nature.

Large nuclei are unstable because the strong force that holds the nucleus together only works over short distances. In a very large nucleus, the protons on opposite sides are too far apart to be held together by the strong force, so they begin to repel each other. This makes the edges of the nucleus want to come off from the rest of it.

To look at the ratio of protons to neutrons, it is helpful to make a chart with the number of protons going up, and the number of neutrons going across (this is often called a nuclide chart). In the chart below, the stable isotopes are shown in green, while unstable isotopes are shown in yellow.

The red line shows where the number of protons is equal to the number of neutrons. For small atoms, this is the most stable ratio (1:1). For example, oxygen-16, magnesium-24, silicon-28, and calcium-40 are all stable atoms. As the atoms get larger, they diverge from this line, and are stable with more neutrons than protons (the maximum ratio is 1.3:1). Larger stable atoms include gold-197, tungsten-184, and indium-115, all of which have more neutrons than protons. The most logical explanation for this is that since neutrons are neutral, they don't repel each other, but are attracted by the strong force, so they held offset the repulsion of the protons.

Types of Radioactive Decay

When an atom is unstable, it undergoes radioactive decay in order to become more stable. If it is too big, then it needs to become smaller. If the proton/neutron ratio is too far from the stable range, then it needs to change.

There are three types of radioactive decay that we will study. They are named after the particle that comes out of the nucleus during the reaction. They are called alpha decay, beta decay, and positron emission. What are these particles, and what new isotope results when they are emitted? Let's analyze some examples and find out.

Alpha decay

Alpha decay is relatively straightforward. An example of alpha decay is radium-224, which emits an a particle and becomes radon-220.

²²⁴Ra --> ²²⁰Rn + a

The atomic mass goes from 224 to 220 – a loss of 4 amu. Two protons are lost – radium's atomic number is 88 and radon's is 86.  Finally, two neutrons are also lost – radium-224 has 136 neutrons and radon-220 has 134.  The lost mass, protons, and neutrons make up the a particle – a ⁴He nucleus. Other isotopes that undergo alpha decay also lose 4 amu, two neutrons and two protons, and therefore you can recognize alpha decay if given the starting nucleus and what is produced. Here are two more examples.

²³⁹Pu --> ²³⁵U + a

²⁴¹Am --> ²³⁷Np + a

Beta decay

Tritium undergoes beta decay. It gives off a b particle and turns into a helium-3 nucleus.

³H --> ³He + b

b particles were found to have the same charge and mass as electrons – in fact, they are electrons. However, a question arises because an electron came out of the nucleus of an atom, where no electrons are supposed to be. The answer is found in the change in the number of protons and neutrons. Tritium has the same mass as helium-3, but a proton was lost, and a neutron was gained. It turns out that a neutron turns into a proton plus an electron: n^o --> p⁺ + e^-.

The electron is ejected as radiation, and the presence of the new proton causes the atomic number to increase by one.  Another isotope that undergoes beta decay is carbon-14.  It gives off a b particle (an electron) and becomes nitrogen-14: ¹⁴C --> ¹⁴N + b. Cobalt-61 emits a beta particle and becomes nickel-61: ⁶¹Co --> ⁶¹Ni + b.

Positron emission

The last kind of radioactive decay is positron emission. An example is when fluorine-18 emits a positron and becomes an oxygen-18 atom.

¹⁸F --> ¹⁸O + e⁺

What is a positron? It is a positively charged electron – a particle of antimatter. It is formed when a proton changes to a neutron plus a positron: p⁺ --> n^o + e⁺.

The positron comes flying out of the nucleus, leaving it with the same mass, but one atomic number less. Other examples include: ¹⁵O --> ¹⁵N + e⁺, and ¹¹C --> ¹¹B + e⁺.

To summarize:

You should be able to determine the product of an alpha decay, a beta decay, and a positron emission, determine the parent isotope if the product is given, or to tell what type of reaction has occurred if you are given both the reactant and product nuclei.

Predicting radioactive decay

We can often predict what kind of radioactive decay will occur by looking at what the change does to the size of the nucleus and the ratio of protons to neutrons.

When an atom undergoes alpha decay, it loses two protons and two neutrons. This reduces the mass of the nucleus without changing the proton/neutron ratio. So atoms that have an appropriate ratio, but are too big, are likely to undergo alpha decay.

When an atom undergoes beta decay, it gains a proton but loses a neutron. This doesn't change the mass, but it alters the proton/neutron ratio so that there are fewer neutrons than there were before. Atoms that have too many neutrons, or in other words, isotopes that are unusually heavy for that element, are likely to undergo beta decay.

When an atom undergoes positron emission, it loses a proton but gains a neutron. This also doesn't change the mass, but it alters the proton/neutron ratio in the opposite direction as beta decay, so that there are more protons than there were before. Atoms that have too many protons, or in other words, isotopes that are unusually light for that element, are likely to undergo positron emission. This isn't as common as beta decay, but it does happen.

If we look again at the nuclide chart showing stable and unstable nuclei, we can predict the most likely radioactive decay reaction that different kinds of unstable nuclei will undergo. Atoms that are above the stable ones will undergo positron emission to get closer to the stable ratio, while atoms that are below the line will undergo beta decay to get closer to the stable ratio. Atoms that are along the line but too big will undergo alpha decay so that they can become smaller without changing the proton/neutron ratio.

The most common isotope of carbon has a mass of 12, as we can see from the atomic mass given on the Periodic Table. Carbon-11 is therefore unusually light, and will likely undergo positron emission to get rid of a proton and be a smaller element which will be more stable with a mass of 11. Carbon-14, on the other hand, is unusually heavy, and will likely undergo beta decay to get rid of a neutron and be a larger element which will be more stable with a mass of 14. Plutonium-241, on the other hand, is simply too big to be stable, and is likely to undergo alpha decay so that it can be smaller.

Radioactive decay series

Even though radioactive decay can help an atom become more stable, many times one radioactive decay reaction isn't enough. The product of a radioactive decay may not be stable either.

When this happens, the atom will undergo more than one radioactive decay, forming a radioactive decay series. One isotope decays to another, then to another, and another, until finally a stable isotope is reached.

Here is an example of a decay series:

thorium-232 --> radium-228 + a

radium-228 --> actinium-228 + b

actinium-228 --> thorium-228 + b

thorium-228 --> radium-224 + a

radium-224 --> radon-220 + a

radon-220 --> polonium-216 + a

polonium-216 --> lead-212 + a

lead-212 --> bismuth-212 + b

bismuth-212 --> polonium-212 + b

polonium-212 --> lead-208 + a

Lead-208 is a stable isotope, so the series ends there.

A decay series can also be shown on a nuclide chart, like the one below. It shows the path followed across the nuclide chart until a stable isotope is reached (this is a different series than the one described above).

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Copyright 2006 Sarah Morgan Black