Wednesday, March 29, 2023

Alpha-, Beta-, Gamma-Decay: UNIZOR.COM - Physics4Teens - Atoms - Fission

Notes to a video lecture on

α, β, γ Decay

Experiments with radioactive elements (primarily, radium) around 1900 performed by Rutherford and Villar resulted in detection of some kind of rays emitted by a radioactive element.
These rays were subdivided into three kinds - those that carry positive electric charge (α-rays), those negatively charged (β-rays) and electrically neutral (γ-rays).

It was concluded that radioactivity is some kind of atom's transformations occurred under certain circumstances.

In this lecture we will address three types of transformations called α-, β- and γ-decay.

These transformations may occur spontaneously or as a result of some external force, like bombarding a nucleus with neutrons or under extreme heating etc.


An α-particle is a combination of two protons and two neutrons, which is the same as a nucleus of an atom of helium 2He4.
An α-decay is a process of spontaneous or forced emitting an α-particle from a nucleus of an atom, thus converting this nucleus into a different type.

Usually, an α-decay is observed with heavy elements. For example, an isotope of uranium-238 can spontaneously undergo an α-decay converting into an isotope of thorium-234:
92U23890Th234 + 2He4

An emitted α-particle is relatively heavy and does not travel far. It cannot penetrate a sheet of paper or human skin. However, if inside a body, α-particles can do significant tissue damage.
The famous case of poisoning of Russian spy Alexander Litvinenko with radioactive polonium is an example of such case.
Unstable radioactive isotope of polonium 84Po210 undergoes a spontaneous α-decay into a stable isotope of lead 82Pb206:
84Po21082Pb206 + 2He4
emitting α-particles.

When α-decay occurs spontaneously, there are certain statistics involved. Not every atom undergoes a decay, but every atom has certain probability of decaying during a certain period of time. To quantify this process, physicists use a concept of half-life - the average amount of time half of the atoms will decay.

For example, half-life of polonium 84Po210 is relatively short period of 138 days, so in the case of Litvinenko poisoning, in a couple of weeks he had a pretty damaging amount of α-particles destroying his cells, and he died.


Some experiments with radioactive materials resulted in detection of particles called β-particles at the time.
Later on it was determined that these particles are electrons.

At the same time, emitting electrons should create an imbalance of electrical charge of the atom, since the negative charge goes away.
The situation with β-decay is, therefore, more complex than seems on a surface.

The further experiments showed that the atomic mass of the radioactive element remained the same during β-decay, while its electric state remained neutral.
The only possible reason for this was a transformation of one of the neutrons in a nucleus into a proton and an electron emitted from the atom.

In a simplified form one of the examples of β-decay (symbolized as β) that involves unstable isotope of carbon-14 transforming into a stable isotope of nitrogen-14 is as follows:
β: 6C147N14 + e + ?
where ? at the end means that there are other particles in this reaction (in this case, anti-neutrino) not related to electric charge or atomic mass.

Emitting one electron with simultaneous transformation of a neutron into a proton maintains the atomic mass and atom's electric neutrality.


The γ-decay is a different kind of a process. Historically, it was called "gamma" as one of the three kinds of detected rays emitted by radioactive material:
alpha for positively charged (later on identified as a combination of four particles - two protons and two neutrons),
beta for negatively charged (identified as electrons) and
gamma for electrically neutral rays.

These electrically neutral γ-rays were later on identified as very high frequency oscillations of electromagnetic field that behaved like particles because of duality of the electromagnetic field, which, especially in very high frequencies, can be viewed as a flow of particles - photons.

While the penetrating abilities of α and β-particles are very limited (a thin sheet of plastic or aluminum foil can stop them) those of γ-particles are extremely high. The γ-radiation can penetrate walls and, if it's of high intensity, is dangerous for living organisms.
The real protection from penetrating γ-radiation is a layer of lead.

The γ-radiation is not related to material particles, like protons or neutrons in case of α-particles or electrons in case of β-particles.
The γ-particles are photons that have no mass and are just lumps of energy.

So, to emit this energy, a nucleus should be in some kind of excited state and, emitting the γ-rays, the nucleus transforms into a stable state.

In simple terms this process of emitting γ-radiation can be explained as follows.
When α- or β-decay occurs, the balance of mass and energy between original atom and all the components of the decay changes. The total original mass and energy of the atom is now distributed among the resulting atom and the products of the decay.
Mass defect will now play a significant role, but some extra energy might still be left in the nucleus of the original atom.
This extra energy puts a nucleus in an excited state that causes emitting γ-radiation as pure lumps of energy (high frequency photons), thus transforming an atom into a stable state.

Because of the high penetrating properties of γ-radiation it can be used for some purposes. For example, in radiotherapy to treat cancer, to detect oil and gas deep under the surface of the Earth, even to change the inner structure of materials by exposing them to γ-radiation.

Friday, March 24, 2023

Mass Defect: UNIZOR.COM - Physics4Teens - Atoms - Fission

Notes to a video lecture on

Mass Defect

We will discuss a concept and measurement of mass, as related to elementary particles and atoms.

The mass of elementary particles is often measured in atomic mass units (abbreviated as amu or simply u, or Da after John Dalton).
The definition of this unit is related to a notion of having a mass of a proton or a neutron to be close to 1 unit.
Physicists measured a mass of an atom of carbon 12C6 that has 6 protons and six neutrons and decided that 1/12 of this mass is a good unit of mass, so protons and neutrons will have their mass close to 1 unit.

After many experiments the mass of three main elementary particles (proton, neutron and electron) was calculated.
In terms of the atomic mass units (amu) they are:
Proton - 1.0072766 amu
Neutron - 1.0086649 amu
Electron - 0.0005486 amu

Consider now an atom of Deuterium that has 1 proton, 1 neutron and 1 electron 2H1.
Experiments show that its mass is 2.014102 amu.
The sum of masses of its components is
1.0072766 + 1.0086649 +
+ 0.0005486 = 2.0164901

It appears that the mass of an atom of Deuterium is less than the sum of masses of its components.
Where did the matter go?

Just to be sure, let's do a similar calculation for an atom of Uranium 238U92 that has 92 protons, 146 neutrons and 92 electrons.
Experiments show that its mass is 238.02891 amu.
The sum of masses of its components is
+ 92·0.0005486 = 239.9849938

As in the case of Deuterium, the mass of an atom of Uranium is less than the sum of masses of its components.

The answer to this discrepancy is in the most famous formula of the Theory of Relativity
E = m·c²

This formula (that we are using without a proof) connects mass m, energy E stored in it and speed of light in vacuum c.
It states that any object has inner energy needed to keep this object in its state, to preserve it.
Atom contains elementary particles that must stay together to assure the atom's integrity. It requires . Therefore, the energy must be taken from the mass of components to put the atom together.

The difference between the mass of an atom and a sum of masses of its components, so called mass defect, is the source of the energy that maintains the atom's integrity.

In case of Deuterium 2H1 the mass defect is
2.0164901 − 2.014102 =
= 0.002388

In case of Uranium 238U92 the mass defect is
239.9849938 − 238.02891 =
= 1.95608

Thursday, March 2, 2023

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

Notes to a video lecture on


Electron is one of the three main particles present in every atom - protons and neutrons make up a nucleus, and electrons are rotating around a nucleus.

According to current view, electron is an elementary particle. Physicists have not identified any smaller particles that compose an electron.
There are some theories about some smaller particles inside an electron, but so far they have not been generally supported.

This leaves us to discuss the properties and characteristics of electrons, not their inner structure, like in the case of a proton or neutron with quarks and gluons they are composed of.

The first characteristic of an electron is its electric charge. When discussing subatomic particles, the electric charge of an electron is a unit of measurement. Therefore, its electric charge has absolute value of 1.
The electric field has two types of charge - positive and negative. An electron has a type negative, while a proton has type positive. Hence, we say that electric charge of an electron is −1, while a proton's electric charge is +1.

The usual symbol for an electron is e.

Another important characteristic of an electron is its mass.
The experiments show that its mass is very small relatively to a mass of a proton or a neutron. In fact, it's almost 2000 times less than the mass of a proton.

We discussed the structure of an electron configuration of an atom in a lecture "UNIZOR.COM - Physics 4 Teens - Atoms - Electronic Structure of Atoms - Electrons and Shells" of this course. Let's continue this topic and get deeper into an electron configuration.

We know that electrons occupy shells around a nucleus, sequentially numbered 1, 2, 3 etc.
Every shell has certain number of subshells, and the number of subshells within each shell equals to a shell number:
shell #1 - 1 subshell s
shell #2 - 2 subshells s, p
shell #3 - 3 subshells s, p, d
shell #4 - 4 subshells s, p, d, f
Electrons within the same subshell have the same energy level.

There is another very important characteristic of an electron we have not discussed yet. It's called a spin.
An important property of an electron is that in the magnetic field it behaves like a little magnet similarly to a behavior of a electrically charged object spinning around an axis.

By analogy, physicists called this property of an electron a spin and, consequently, considered an orientation of the axis of this spin as an important characteristic of an electron.

A famous physicist Wolfgang Pauli suggested so called Pauli exclusion principle, according to which no more than two electrons can share a single trajectory (called orbital) within a subshell, and, if two of them do, they must have opposite orientation of the axis of their spins.

The number of orbitals inside a subshell depends on the subshell number. The first subshell s can have 1 orbital, the second subshell p has 3 orbitals, the third subshell d has 5 orbitals, etc. going along odd numbers, so subshell #X has 2X−1 orbitals.

(a) electrons are moving within shells (#1, #2, #3 etc.)
(b) that are subdivided into subshells (a shell #N has N subshells with letters substituting the subshell numbers, like s for subshell #1, p for subshell #2, d for subshell #3 etc.)
(c) with 2M−1 orbitals inside a subshell #M
(d) where each orbital capable to hold no more than 2 electrons, which must have opposite spin.

We can represent this structure as the following table:
ShellSubshellOrbits# of e

Simple calculations can prove that the number of orbits per shell #N equals to and, consequently, the maximum number of electrons that shell #N can hold is 2·N². This is exactly the formula obtained in the lecture "Electrons and Shells" referenced above.

Double Slit Experiment

There are many articles and videos about double slit experiment on the Web.
In particular, there is a lecture by Richard Feynman about it (almost an hour long).
More recently, Jim Al-Khlili did it in a more theatrical way in about 9 minutes, that I like a lot.
You can find both on the Web.

Below is yet another presentation of this topic, we do it for completeness of our story about electrons.

Imagine a box with two parallel slits at the bottom filled with sand. As sand goes down through slits it accumulates at the tray underneath a box forming two parallel hills, corresponding to two slits above the tray.

This is a clear example of how particles (in this case, sand) independently go through slits without interfering.

Consider an experiment with monochromatic light going through two slits. In this case the slits should be really close to each other and very narrow.
On a screen opposite to slits you will see the bright and dark lines - the result of interference between two rays coming through two slits.
Picture below reflects the intensity of light on a screen - a red curve with oscillating amplitude, maximum in the middle and diminishing to both ends.
Flat wave front of monochromatic light are split into two coherent rays. The bright and dark lines on a screen appear because these two rays come to a corresponding point on a screen in phase or out of phase. In the first case the interference between these rays is positive and enhance the brightness, in the second case rays work against each other and the spot is dark.
The lecture "UNIZOR.COM - Physics 4 Teens - Waves - Phenomena of Light - Interference" explains this process of interference in details.

This is an example of how waves (in this case, waves of electromagnetic field) interfere with each other when going through two slits, making a completely different picture on a screen than if we dealt with particles, like sand above.

In these two experiments, we see two different behaviors of particles and waves going through two slits.
Particles going through different slits do not interfere with each other, while waves do.

Let's see how electrons behave in a similar setting.

Instead of flat wave front of monochromatic light we direct a bunch of electrons. Those that go through two slits will hit a screen with some sensitive to electron material, like the one used in old CRT computer screens.
What will we see on this screen?

Strangely enough, contrary to our perception that electrons are just small particles, the picture is as if electrons are waves that, going through two slits, interfere with each other.

Well, maybe, when a lot of electrons are going through slits, there are some forces among them that distribute them in such a pattern that resembles the interference.
Let's change the experiment and randomly send electrons one by one with sufficient time interval between them, so some will go through the first slit and some - through the second. This way they will not interfere with each other.
What will be a picture on a screen?
In the beginning we will see only individual dots randomly positioned on a screen. After sufficiently large number of electrons fall onto a screen, the pattern will be obvious, and it will be identical to the above pattern of interference.

Common sense tells us that, since electrons are sent to slits one at a time and they randomly go through one or another slit, there should be no information transfer from one electron to another and, therefore, no interference. We should just see two parallel lines on a screen, each across a corresponding slit, similarly to how sand goes through two slits. Yet, the picture was obviously like an interference.

Let's try to analyze which slit each electron goes through. Maybe, this will clarify the situation.
We put a detector near one slit that detects the electron passing by, and repeat the experiment with sending electrons to slits one at a time.
Indeed, about have the times our detector reacted on a passing by electron, as we would expect, considering the randomness of shooting electrons.
But to our surprise the picture on a screen now will be exactly as if individual particles hit slits and accumulate exactly opposite to slits on a screen. Indeed, a particle-like behavior.

That is strange. Do electrons see our detection device and change the behavior?
Let's fool the electrons. Since our detector of electrons requires some electricity to work, we will retain it in place, but unplug it from the wall.
Surprisingly, we will see the interference picture again.

Go figure.

That completes this pseudo-detective story about behavior of electrons going through a two slits configuration.