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Elementary Particles Revision Notes

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21.1Elementary Particles


In these revision notes for Elementary Particles, we cover the following key points:

  • What are quantum numbers? How many quantum numbers are there?
  • What are atomic orbitals? What do they represent?
  • How to find the electronic distribution in various orbitals?
  • What does Pauli's Exclusion Principle say on electronic configuration in atomic orbitals?
  • What are elementary particles? Where do they come from?
  • What is the phenomenon of "pair annihilation"? When does it occur?
  • What did Yukawa predicted?
  • What are mesons? Why are they called so?
  • How to find the lifespan and energy of elementary particles?

Elementary Particles Revision Notes

Quantum numbers represent a method used to define the trajectory and movement of an electron within an atom. There are four quantum numbers for every electron in an atom, which are combined to give a unique configuration. They are:

n - the principal quantum number that expresses the energy levels (atomic orbitals). The principal quantum number n is always an integer (n = 1, 2, 3, 4).

- the azimuthal or angular momentum quantum number that describes the subshell. The angular momentum quantum number is also an integer, which represents the value of an electron's orbital (ℓ = 0, 1, 2, , n - 1).

mℓ (or simply m) - the magnetic quantum number that symbolizes the orientation of the orbital. The integer values of magnetic quantum number range from -ℓ to +ℓ.

ms (or simply s) - the spin quantum number expressing the spin, that is one of two types of angular momentum in quantum mechanics (the other is orbital angular momentum). The spin quantum number has a half-integer value, which is either - 1/2, known as 'spin down' or + 1/2 called 'spin up'.

Atomic orbitals represent the space or region around the nucleus where the electron are calculated to be present. The four atomic orbitals in use are s, p, d and f where s can hold a maximum of 2 electrons, p can hold 8 electrons, d can hold 18 electrons and f can hold 32 electrons (that is 2n2 where n is the principal quantum number).

In general, the number of orbitals is found through the formula

N = 2l + 1

where is the azimuthal quantum number. This means the number of maximum electrons that each s-orbital can hold is two, regardless of the number of principal quantum number (n). Each p-orbital can possess at maximum two electrons which means six electrons in total; two electrons for each of three p-orbitals. The total number of electrons in d-orbitals and f-orbitals is 10 and 14 respectively.

Spin of every two electrons in each orbitals will be always in opposite direction.

Pauli's Exclusion Principle says that in a single atom no two electrons will have an identical set or the same quantum numbers (n, l, ml and ms). This means each electron in an atom has a unique configuration regarding quantum numbers and their orientation.

Elementary particles represent the smallest known building blocks of the universe. They are thought to have no internal structure, meaning that they are considered as as zero-dimensional points that occupy no space. We can identify a number of elementary particles only through the radiation coming from remote stars by means of cosmic rays, which provide one of our few direct samples of matter from outside the solar system. Some of elementary particles detected in cosmic rays include neutrons, electrons and neutrinos. The positive electron (in short positron) was another elementary particle identified experimentally in cosmic rays but also in terrestrial conditions. It has a positive charge of + e and a spin of 1/2.

The related but opposite elementary particles such as electron and positron are known as antiparticles. More precisely, an antiparticle is a subatomic particle having the same mass as a given particle but opposite electric or magnetic properties.

Positron does not exist in the structure of common matter; the electron-positron pair appears only during the collision with matter of charged particles or high-energy gamma rays. This process is known as "pair production". The minimum energy needed for pair production process must be

Emin = 2me ∙ c2=1.64 × 10-13 J

Schematically, the process of electron-positron pair production is written as:

γ → e- + e+

The reverse process may also occur. Thus, when an electron enters in contact with a positron, a gamma particle is produced. More specifically, if a positron encounters an electron on its way, this electron-positron pair is transformed into a pair of gamma quants according the reaction

e- + e+ = γ + γ

The energy of this pair of gamma quants is not less than 2 me · c2, This radiation propagates in opposite direction to the movement of original particles. Thus, when a particle and an antiparticle collide with each other, they are annihilated, emitting energy. This process is (not so rightfully) called "pair annihilation".

The "Strong force" - the scientific name of nuclear force (as one of the four fundamental forces acting in nature) - appears inside the nuclei to balance the effect of electric force between protons. This force however is evident only in very small distances (1 - 2 × 10-15 m). It decreases drastically with the increase in distance between particles. Because of this, when two electrons repel each other, one of them emits a photon and the other electron absorbs it.

According to Heisenberg's uncertainty principle, a short-term state has an uncertainty of energy ΔE given by the relation

∆E ∙ ∆t ≥ h/

where Δt is the time interval during which the process occurs. Based on this principle, the generation of photons having the energy ΔE is possible with the condition that the generation time not exceeds the time interval Δt provided in the Heisenberg formula. Such a photon having a lifespan as much as allowed by Heisenberg uncertainty principle is known as "virtual photon."

In 1935, the Japanese scientist Hideki Yukawa introduced the idea that the strong interaction between nucleons is made possible through the exchange of certain particles of mass 200-300 times the mass of electron.

A few years later, scientist were able to identify a particle of mass 207 times the mass of electron. Since this value of mass is between the mass of nucleons and electrons (nucleons are more than 1800 times heavier than electrons), the particle discovered was named "μ-meson" ("meson" means medium value in Greek language) or "muon". It was initially identified with the particle predicted by Yukawa but later on, scientists realized that such particles almost do not interact with atomic nuclei. That means they cannot be the carriers of nuclear interaction. The true carriers of strong interaction were discovered in 1947 by Cecil Frank Powell - an English scientist. These particles were the π-mesons (pi mesons) or simply "pions" predicted by Yukawa.

After accurate measurements, it resulted illustrated that three types of pionsexist: π +, π - and π 0 with these bearing electric charges of +e, -e and 0 respectively. As for their masses, we have:

mπ + = mπ - = 273 me and mπ0 = 264 me

All nucleons pass some part of their lifespan by experiencing one of the four transformations shown below:

p ⇄ n + π+
p ⇄ p + π0
n ⇄ p + π-
n ⇄ n + π0

Hence, every nucleon is surrounded by a cloud of π-mesons which form the field of its nuclear force. The exchange of π-mesons between nucleons results in the strong nuclear interaction.

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