Saturday, February 18, 2023

Quarks: UNIZOR.COM - Physics4Teens - Atoms - Elementary Particles

Notes to a video lecture on


Let's recall the steps of progress of our understanding of the structure of matter.

1. Splitting a drop of water or cutting the wire we gradually reached the smallest particle that retains the properties of an original object - molecule.

2. Then we realized that thousands of different molecules consist of different combinations of about a hundred of different atoms that have their own characteristics.

3. Later discoveries led to inner structure of every atom as consisting of a nucleus surrounded by shells filled with moving electrons.

4. Farther experiments proved that nucleus itself is a combination of protons and neutrons. So, three main particles - electrons, protons and neutrons - are the building blocks of all atoms.

5. Thousands of experiments showed the existence of other particles that differ from the main ones mentioned above. More than 200 particles have been discovered by physicists through numerous experiments. The number of these new particles made the picture of the structure of matter that we had in mind significantly less "structural" or, plainly, just messy.

It's time to go deeper into inner structure of all particles.
Are there any small number of smaller than proton or neutron particles, whose combinations make up already discovered particles inasmuch as about a hundred different atoms make up thousands of different molecules by grouping in different combinations?

The first theoretical answer was suggested in 1964 by Murray Gell-Mann and George Zweig. It was partially confirmed by experiments and, as a result, is accepted as a working model.

Their proposal was that protons and neutrons are not elementary particles, but, in turn, are composed of smaller particles called quarks.
The usefulness of such an approach can be demonstrated using an example from the previous lecture about isotopes.

Recall how isotope carbon-14 is formed.
Cosmic radiation hits the atoms in the upper layers of the atmosphere, breaking them into individual particles and producing free neutrons.
A free flying neutron hits an atom of nitrogen in our atmosphere, kicks off one proton, replacing it with itself, and frees up an electron.
Kicked off proton and an electron combine into a hydrogen causing the following reaction
714N + 01n → 614C + 11H

The process of carbon-14 decaying is rather complex, but can be described in an oversimplified form as follows.
A neutron in the nucleus of unstable carbon-14 transforms into a pair proton+electron. This does not change the electric neutrality of the atom, does not change the atomic mass, it remains 14, but atomic number increases by 1, thereby creating an atom of stable nitrogen.

This nuclear reaction can be described (in an oversimplified form) as
614C → 714N + e + ?
where ? signifies additional participants in this transformation that we cannot discuss at this point because it requires knowledge of other elementary particles beyond the main ones (electron, proton and neutron).

While a transformation of an atom of nitrogen into an atom of carbon-14 is physically easy to understand (a neutron kicks off a proton and electron, replacing and taking place of a proton in a nucleus), the reverse transformation of a neutron to proton and electron via decay is less understandable, as it seems to happen without material physical factors.

It would be more understandable if this transformation can be expressed as replacing of something with something else, as in the transformation of nitrogen into carbon-14 by replacing a proton with a neutron.

Developing this idea, physicists came to a model of neutron and proton based on some smaller elementary particles and a transformation of one into another as a replacing of one elementary component with another.

The first obstacle to overcome is electric charge of a proton and electric neutrality of a neutron. If these main particles have smaller elementary components, the electric charge must be distributed among them.
Taking electric charge of a proton as +1, its components must have it as a fraction.

Here is one way to implement it.
Assume, a proton is a combination of two elementary particles, X with an electric charge +½ each, and a neutron is a combination of a particle X with an electric charge +½ and a particle Y with electric charge −½.
Then the total charge of a proton (X+X) is +½+½=+1 and for a neutron (X+Y) it is +½−½=0 as it should be.

Consider a different model.
Particle X has charge +2/3 and particle Y has charge −1/3. Then a proton can be composed of X+X+Y with charge +2/3+2/3−1/3=1, while a neutron can be composed of X+Y+Y with charge +2/3−1/3−1/3=0.

The next characteristic to satisfy using this type of modeling protons and neutrons as consisting of smaller components is mass of a particle.
These components must have masses, sum of which is equal to corresponding larger particles. Actually, almost equal because of mass and energy relationship E=m·c².

What's more difficult is to come up with a model that satisfies not only charges and masses of protons and neutrons, but also other particles observed in experiments (antiprotons, antineutrons, pions, barions, mesons etc.).
Mathematically, it means to solve a system of many linear equations (as many as the number of particles we consider as consisting from the components times the number of parameters we have to match, like electric charge and mass, separately) with as few unknowns as possible.

The latest solution to this problem is so called Standard Model that proposed relatively few elementary (not divisible any more) particles with certain characteristics.

According to Standard Model, six different "flavors" of elementary (not divisible) particles called quarks are the building blocks of about 200 observable particles.
These different quarks are called Up (u), Down (d), Charm (c), Strange (s), Top (t) and Bottom (b).

Each quark has an electric charge (positive, negative or zero), mass and other characteristics.
Here is an electric charge table with the unit of charge 1 being associated with proton (+1) or electron (−1):
Up: +2/3
Down: −1/3
Charm: +2/3
Strange: −1/3
Top: +2/3
Bottom: −1/3

They are combined into different combinations, producing different particles.
For example, proton is made from two Up and one Down quark:
p = uud
Electric charge of proton is +2/3+2/3−1/3=+1, as it should.
Neutron is made from one Up and two Down quarks:
n = udd
Electric charge of a neutron is +2/3−1/3−1/3=0, as it should.

The process of transformation of a neutron into a proton and electron can be imagined as replacing one u quark with a d quark.
Where the new d quark comes from, how electron is created and where a released u quark goes to is a separate issue, which is beyond the scope of this lecture.

But complexity of the Standard Model is, actually, higher than this.
For each quark of the above six types there is an anti-quark.
Its electric charge is opposite to the corresponding quark.

In addition, quarks have a characteristic called color with values red, green and blue. These "colors" have nothing to do with the colors observable by our eyes, they are just used to characterize particular quarks or their combination.

Electron belongs to another group of particles, it's not constructed from other particles, it's an elementary particle. So are muons and tau particles.

Yet another group of elementary particles (not quarks) is responsible for carrying forces between particles (electrostatic, strong, weak etc.) One of the particles in this group is photon that carries electromagnetic force. Gluon is a particle responsible for strong forces inside a nucleus.

In a word, the contemporary model of the structure of particles is very complex and requires deep studying to understand it completely.

This complexity is well represented by the following illustration of the Standard Model authored by Chris Quigg and taken from the Web site

(to view all the details, click the right button and open it in a new tab)

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