Physics Lesson 22.10.2 - "Elementary Particles" in Various Temperatures of Matter

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Welcome to our Physics lesson on "Elementary Particles" in Various Temperatures of Matter, this is the second lesson of our suite of physics lessons covering the topic of Big Bang Model and Temperature, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

"Elementary Particles" in Various Temperatures of Matter

The term "elementary particle" is relative. In the micro-world, such as in atomic physics etc., the elementary particles are protons, electrons and neutrons. The same is true for electromagnetism. In the structure of matter, the atom is considered as the building block of matter. We can say the same thing in chemistry, and so on. In other words, elementary particles can be molecules, atoms, atomic nuclei, nucleons, quarks or leptons, depending on the amount of energy involved in the process. Hence, a certain particle can be elementary in one situation but not in another. Based on this logic, galaxies are considered as the elementary particles of Cosmology.

The effect of temperature is different for different elementary particles. Let's consider a virtual experiment to explain this point. Suppose we have an oven, where there is some water inside it. Let's suppose we can heat up the oven as much as we want (practically this is impossible as the oven itself will melt at certain temperatures). Here, we will consider the following stages the water experiences when heated.

1. Initially, the oven is at room temperature, i.e. at 300 K. The energy per molecule of water expressed in electronvolt is E = 0.025 eV. At this temperature, water is at liquid state. The "building blocks", i.e. the elementary particles of water at this stage are the water molecules (H2O). The dominant type of interaction at this stage is the electromagnetic one.
2. Water is heated to the boiling temperature (T = 373 K and E = 0.032 eV). At this temperature, water evaporates and the energy of collision between molecules exceeds their binding energy in the liquid. However, the dominant type of interaction at this stage is still the electromagnetic one.
3. Water vapour is heated to 10 000 K (E ≈ 1 eV). Particles gain and exchange large amounts of energy sufficient to break up the structure of the water molecule. At this point, the elementary particles are not molecules anymore, they are individual atoms of hydrogen and oxygen instead. The dominant type of interaction is still electromagnetic. The excitation occurring in electronic layers results in photons generation, which are more and more present with the increase in temperature.

All the three stages explained above are dominated by chemical bonds.

4. Matter in the oven reaches a temperature of T = 105 K (E ≈ 10 eV). The energy is sufficient to break the atomic bonds. Electrons are detached from nuclei and the oven at this point contains material in a fourth state of matter known as "plasma". It contains a mixture of positive electric charges (protons and oxygen nuclei) and negative ones (electrons). The interaction between particles is much stronger than in previous cases. Plasma also contains photons, as well as bosons as carriers of EM interaction, which become denser with the further increase in temperature.

From Section 19, we know that elementary particles create and cancel out according the relation

where γ are high energy photons. The first reaction takes place when the photon has a higher energy than the rest energy of particle and antiparticle taken together. Only thermal movement is able to supply such high amounts of energy to photons. Based on the mass-energy relation of Einstein:

it is evident that the rest energy varies depending on the type of elementary particle. For example, the rest mass of electron is 0.51 MeV and that of proton and neutron is 940 MeV.

4. As the temperature reaches the value T = 1.2 × 10¹⁰ K (the corresponding energy is E = 1 MeV). At this point, the electron-positron pair is produced. This process further increases the presence of electrons in the plasma.
5. When the temperature of matter in the oven becomes T = 10¹² K the process of oxygen nuclei decomposition begins to occur. This is because the binding energy of nucleons in the atomic nuclei (E_b = 8 MeV) is smaller than the energy of collision between the particles involved in the process (E = 100 MeV). At this point, plasma is populated by protons and neutrons.
6. When the temperature inside the oven is higher than 10¹³ K, the process of neutron-antineutron creation begins to occur in addition to electron-positron one (which continues taking place with even higher rates). All these particles create, disappear, recreate again and so on. Plasma at this temperature is full of protons and antiprotons. Likewise, protons and neutrons begin their decomposition process and split into u and d-type quarks, that start moving freely in the plasma. With the emission of quarks, other elementary particles such as hadrons and other massive particles with strange behaviour (strangeness ≠ 0) appear in the process - particles that we have discusses in Section 21 of this course. All of them require very high amounts of energy to activate.

As you see, after the termination of chemical binding processes, weak and strong interactions start to appear in the process. They become more and more relevant with the increase in temperature in the interaction processes between elementary particles. On the other hand, despite gravitational force always being present in massive particles, it becomes less influential in high temperatures (but not very high, as we will see in the following part of this tutorial).

Since the occurrence of the Big Bang, the Universe has gone through all of the above processes but in the reverse order, i.e. from the highest to the lowers temperatures. This is because when spreading out in the space, celestial objects get colder.

Example 2

Using the equation

calculate the average kinetic energy (in eV) of a single particle corresponding to the:

1. Room temperature
2. Boling temperature of water
3. Temperature of water molecular structure break up
4. Temperature of nuclear structure break up

Solution 2

1. For convenience, we can use the value of Boltzmann constant in eV/K found in the previous solved example, i.e.
   k = 8.625 × 10^-5 eV/K
   Thus, for matter at room temperature (T = 300 K), we have
   E_exchanged ~ k ∙ T
   = (8.625 × 10^-5 eV/K) ∙ (3 × 10² K)
   = 25.875 × 10^-3 eV
   = 0.025875 eV
2. Boling temperature of water is T = 373 K. Thus, we have
   E_exchanged ~ k ∙ T
   = (8.625 × 10^-5 eV/K) ∙ (3.73 × 10² K)
   = 32.171 × 10^-3 eV
   = 0.032171 eV
3. Molecular structure breakup occurs as T = 10 000 K = 104 K. The energy required for this process is
   E_exchanged ~ k ∙ T
   = (8.625 × 10^-5 eV/K) ∙ (10⁴ K)
   = 8.625 × 10^-1 eV
   = 0.8625 eV
4. Nuclear structure breaks up at T = 10¹² K. Hence, we have for energy involved in this process:
   E_exchanged ~ k ∙ T
   = (8.625 × 10^-5 eV/K) ∙ (10¹2 K)
   = 8.625 × 10⁷ eV
   = 86.25 MeV

As you see, all the above values are close to those given in theory (when explaining the theory, all values were rounded up).

You have reached the end of Physics lesson 22.10.2 "Elementary Particles" in Various Temperatures of Matter. There are 6 lessons in this physics tutorial covering Big Bang Model and Temperature, you can access all the lessons from this tutorial below.

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