So far when we've looked at chemical reactions, we've focused only on how reactions involving electron behavior. In nuclear reactions, the nucleus of the atom undergoes changes. As a brief reminder: in the notation $$^{A}_{Z}X$$ `Z` is the number of protons, `A` is the number total number of nuclides aka protons plus neutrons, and `X` is the atomic symbol. For example, the carbon-14 isotope would be written as $$^{14}_{6}C$$
Consider the following nuclear reaction:
$$^{238}_{92}U →^4_2He + ^{234}_{90}Th$$
There are two important things to note about this reaction:
1. The `U` atom is emitting an atom of `He`
2. The original atom (`U`) changes into an atom of a different element (`Th`)
Both of these are processes that we have yet to observe. In fact, we were explicitly told that the second wouldn't happen; one of the first things we learn about atoms is that the "number of protons in an atom remains constant." It turns out that through radioactive decay, atoms can change their identities.
Since nuclear reactions deal solely with the stability of the nucleus, we have to examine both protons and neutrons in order to predict radioactive behavior. The rest of this section will go towards understanding the conditions in which atoms will undergo nuclear decay and how we can predict the specifics of the decay.
We say that a nucleus is stable when the nucleus has the optimal ratio of protons to neutrons. Stable nuclei are those that are unlikely to undergo radioactive decay, whereas unstable nuclei are more likely to decay in order to reach an optimal ratio.
If we plot the number of protons vs the number of neutrons, we get a pretty insightful chart:
If the number of neutrons increased by 1 everytime the number of protons increased by 1, we would see a straight line corresponding to the `Z=N` line. Instead, we see a distribution where the number of neutrons increases more quickly than the number of protons do. We can make a general statement that as the atomic number increases, the ratio of neutrons to protons increases. Carbon has a neutron:proton ratio of `1:1` whereas a "heavy" element like mercury has a ratio of `1.53:1` .
If we look at the distribution, we can see a region that consists of many colors surrounded on both sides by blue. The colored region is referred to as the zone of stability and atoms in this zone are said to have stable nuclei. On the other hand, the blue region consists of atoms that have a less-than-optimal neutron:proton ratio and are therefore likely to undergo radioactive decay.
On a final note, there are certain "magic numbers" of protons/neutrons that exhibit high nuclear stability. This is similar to how certain atomic numbers corresponding to the noble gases (2, 10, 18, 36...) are particularly stable. For nuclear stability, atoms with 2, 8, 20, 28, 50, or 82 protons or neutrons are particularly stable.
The type of decay that an unstable nuclei undergoes is, for the most part, dependent on the neutron:proton ratio. There are 5 main types of decay:
1. Alpha Decay: in alpha decay, a helium-4 particle, also referred to as an α-particle, is emitted. This type of decay is primarily seen in very heavy nuclides.
$$^{238}_{92}U → ^{234}_{90}Th + ^{4}_{2}He$$
2. β-particle Production: β-particle production involves the emission of a β-particle. A β-particle is another name for an electron.
$$^{131}_{53} → ^{131}_{54}Xe + ^{0}_{-1}e$$
Notice that the overall number of nuclides (protons + neutrons) remains the same, but the number of protons has increased by 1. Thus, we can say that the net effect of β-particle production is that one neutron changes to a proton.
Because of this effect, we can say that atoms above the zone of stability are likely to undergo β-particle production. This is because atoms above the zone of stability are those with neutron:proton ratios that are too high. Undergoing β-particle decay will subsequently reduce the ratio and bring the atom closer to the zone of stabilility.
3. Electron Capture: in electron capture, an inner shell electron is "captured" by the nucleus. This can be thought of as the opposite of β-particle production
$$^{81}_{36}Kr + ^{0}_{-1}e → ^{81}_{35}Br$$
4. Positron Production: in positron production, a positron is formed. A positron is a molecule with the same mass as an electron but with a positive charge instead of a negative charge.
$$^{22}_{11}Na → ^{22}_{10}He + ^{0}_{1}e$$
The net effect of positron production is the opposite of the effect of β-particle production. In positron production, a proton is converted into a neutron. This is desired for atoms below the zone of stability.
5. Gamma Emission: gamma emission involves the emission of a high energy photon, called a gamma (γ) ray. The gamma ray is written as a massless and chargeless particle.
$$^{238}_{92}U → ^{234}_{90}Th + ^{4}_{2}He + ^{0}_{0}γ$$
Gamma ray emission usually occurs alongside another type of radioactive decay as a way to release the extra energy. Notice that this corresponds to the emission we learned about when first learning about the structure of the atom! In the example provided, the gamma ray emissions occurs alongside α-decay.
We can summarize the different modes of decay through the following chart:
| Mode of Decay | Emission | Most likely for |
α-decay |
$$^{4}_{2}He$$ |
Heavy atoms |
β-particle production |
$$^{0}_{-1}e$$ |
atoms above zone of stability |
Electron capture |
absorb $$^{0}_{-1}e$$ |
|
Positron production |
$$^{0}_{1}e$$ |
atoms below zone of stability |
Gamma emission |
$$^{0}_{0}γ$$ |
excess energy |
Heavier elements will often undergo multiple decay steps before arriving to a stable nuclear arrangement. This is called a decay chain. Below is the decay chain of Neptiunium-237.
At this point, many of the heavier radioactive elements have decay chains that have been well-studied and understood.
The significance of decay chains is to show that, in order to reach a stable nucleus, atoms often undergo multiple smaller decay steps instead of a singular step. If you look at the image, you'll notice that each of the decays corresponds to a type of decay we've learned.
Nuclear decay follows a first-order rate law:
As we learned before in kinetics, first-order processes have a half life that is independent of the amount. It doesn't matter if we have 10,000g or 1g, the half life of the process will remain the same. For nuclear decay, the half-life is calculated through the half-life formula for first-order decay:
`t_(1/2)=0.693/k`
Where `k` is the proportionality constant for the process.
1. Nuclear reactions involve changes in the nucleus of an atom.
2. In nuclear reactions, the fundamental identity of an atom can change.
3. Nuclear stability is dependent on the neutron:proton ratio. The zone of stability is the region on a neutron-proton graph that all nuclides want to be at.
4. There are several kinds of nuclear decay that occur under different conditions.
5. Heavy atoms tend to be radioactive and emit α-particles.
6. Heavy atoms tend to undergo multiple decay steps before finally reaching a stable state.
7. Nuclear decay is a first-order process.
#1. The iron nucleus is the most stable nucleus.
We know from earlier posts that the noble gases have the most stable electron configuration. In terms of nuclear stability however, it turns out that iron has the highest.
This is interesting because it introduces the concept of nuclear stability. Iron is the most stable nucleus because it has the optimal proton:neutron ratio and thus contains the lowest binding energy of all of the elements. To produce either a heavier or lighter atom through nuclear processes would require an input of energy as the new atom cannot have a more stable nucleus than that of iron.
The iron-54 isotope is often found at the center of stars because of how stable it is. Under the immense pressure of the star collapsing inward, elements are combined together under they eventually become iron-54. Once all of the atoms become iron-54, no more nuclear processes occur because to change from iron-54 would require an input of energy.
#2. Dangers of radioactivity (comparison between different sources)
We often hear about the dangers of radiation in the news and see radioactive waste as a source of superpowers in our favorite superhero movies. What is it about radiation that makes it dangerous?
As we learned in this post, radiation is the process in which nuclides emit particles in order to achieve higher nuclear stability. Most of the time, these emitted particles travel at incredibly high speeds (100,000 miles/second). When these particles collide with the cells in our body, they collide violently in a way that can cause cancer to proliferate.
Our bodies are constantly bombarded with radiation, but the dose is low enough that we're shouldn't be too worried about cancer. Interestingly enough, every individual particle that's emitted has a risk of causing cancer, but the chance of that happening is fortunately really low. For fun, here's a chart of various radiation doses, courtesy of XKCD.
#3. Is alchemy possible?! (mercury to gold)
One of the main pursuits of alchemy was the transmutation of ordinary metals into the noble metals of silver and gold. It turns out, through radioactive decay, that this is possible!
Consider the following nuclear reaction in which mercury undergoes electron capture:
$$^{196}_{80}Hg + ^{ 0}_{-1}e→^{196}_{79}Au$$
By this process, we can technically turn mercury into gold, atom by atom. The bad news is that the process occurs very, very slowly; so slowly in fact that we can hardly recognize it. The good news is that we can speed up the process by slamming a neutron into the mercury atom in a particle accelerator. The second piece of bad news is that this is extremely expensive, moreso than gold is actually worth.