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What Makes an Atom
What Makes an Atom
The General Structure of an Atom
The General Structure of an Atom
To begin our discussion on how the elements formed, we should probably go over what an atom is first. An atom is the basic building block of everything around us and their structure is unique to each element in the periodic table. There are two main regions which are important to an atom: the nucleus and the electron cloud. The stuff in the nucleus are generally referred to as nucleons, namely protons (positively-charged particles) and neutrons (neutrally-charged particles) and are about 1000 times heavier than electrons (negatively-charged particles). Despite having very different mass, electrons and protons have equal and opposite charge. If the number of electrons do not match the number of protons in an atom, it is said to be ionized, or that it has a total charge that is not zero.
We can see a picture on the right showing this structure for a neutral Helium atom.
It's the number of protons in the nucleus which defines an element. Some of the common elements you may know are Hydrogen (1 proton), Helium (2 protons), and Iron (26 protons). Nuclei are pretty amenable to adding neutrons, with some configurations being more stable than others. Atoms that have a number of neutrons different from its most stable configuration are called isotopes. The most stable configuration of Hydrogen has no neutrons while that of Helium has 2 neutrons. Common isotopes considered in this unit are Deuterium (Hydrogen with 1 neutron), Tritium (Hydrogen with 2 neutrons), and Helium-3/'light' Helium (Helium with 1 neutron).
When it comes to electrons, they're kind of special. Because they're so fast and light, we physicists say they live somewhere in a cloud surrounding the nucleus. More importantly, when they are bound to a nucleus, they can only exist at certain energy levels with no more than two electrons having the same energy in an atom. Each of these energy levels are set based on the number of protons in the nucleus. Electrons can go to a higher energy level if they get energy from somewhere to do so and can go to a lower energy level if they release some of that energy. The energy that drives this change usually comes in the form of a massless but energetic photon or, as we commonly know it, light.
An Analogy for Electron Energy Levels
An Analogy for Electron Energy Levels
Imagine you're riding a roller coaster. The number of people that can be in each cart has a maximum that can ride the roller coaster, say two people. Since we care about our safety, each person is strapped into their seat for the duration of the ride in a safety harness. In order for one person to move from one cart into another or to leave the cart, the ride operator needs to come along, take off the safety harness, and escort them to a free seat. In this analogy, the carts are the energy levels, the people are the electrons, and the ride operator represents a photon's energy either emitted or absorbed by the electron which allows it to change energy levels.
What is Anti-Matter?
What is Anti-Matter?
You have probably heard of the particles we're talking about at some point. But what about anti-particles? Similar to how Superman and Bizzaro share the same powers but have different levels of righteousness, anti-particles share many of the same characteristics as their particle counter-parts with some main key differences:
Anti-particles have the same mass as their counterparts.
Anti-particles have the opposite charge of their counterparts.
If the particle is a lepton, the anti-particle has the opposite lepton number.
If the particle is a lepton, the anti-particle has the same flavor.
When a particle and its anti-particle collide, they annihilate into two photons or particles with the same lepton number and flavor.
When a particle is created, so is its anti-particle.
There are other properties here that aren't listed that differ between particles and anti-particles, like spin, but this detail isn't critical to our understanding in the course at this time. What is important, though, is a particle's lepton number and flavor. Remember how I said that electrons are special? Their anti-particle is, too, and it's so famous that it has its own name: the positron. They belong to a certain class of particles called leptons. Other leptons include tau and muon particles. The flavor of a particle corresponds to the type of lepton it is (e.g. an electron). The lepton number represents the number of these (anti-)particles that enter/exit an interaction. The Standard Model of Particle Physics demands that this number and flavor be the same before and after any interaction, which ties into points 5 and 6.
We can describe particle - anti-particle annihilation with a simple formula. We'll focus on electrons and positrons annihilating one another in this example. Looking at point 5, we see that we expect a collision of matter and anti-matter to produce either light or other particles with the same lepton number and flavor. If they annihilate into photons, there must be at least two photons emitted from the collision to conserve the electron and positron's energy and momentum. Electrons and positrons are leptons with the electron flavor, they can annihilate to become an electron neutrino and electron anti-neutrino. But what is a neutrino? Let's go to the next section and find out!
Neutrons, (Anti-) Neutrinos, and Particle Stability
Neutrons, (Anti-) Neutrinos, and Particle Stability
Neutrons are another kind of special particle, as they are made of other particles. The neutron is composed of a proton and an electron, which cancel in charge, and a new kind of particle called an anti-neutrino. The anti-neutrino has the opposite lepton number as the electron and a neutrino has the same lepton number and flavor as an electron, so we dub these electron (anti-)neutrinos. In order to keep the lepton number the same before and after the creation of a neutron, a neutrino-anti-neutrino pair is produced from the collision of a proton and an electron, where the anti-neutrino remains in the structure of the neutron and the neutrino exits as a by-product of the interaction. To the right, we have a picture explaining exactly what this looks like. You will also see that a photon can leave the interaction, too. If the proton and the electron collide with more energy than is necessary to bind together and form a neutron, that energy will be transferred into the kinetic energy of the neutron and the neutrino and any excess in the form of a photon. When particles collide to form a new set of particles, this processes is called fusion.
However, neutrons on their own (i.e. not in an atom) are not stable! Unstable particles are described by their lifetime, or the amount of time we expect the particle to stick around before exponentially decaying into its composite particles. The neutron's lifetime is about 878.4 seconds. For example, if we had a sack of 1000 neutrons and measured how many neutrons were there 878.4 seconds later, we'd see that the number has exponentially decreased to only 368 neutrons. If we waited again for another neutron lifetime and looked inside the sack, we'd only see 135 neutrons! This also means that there are 865 protons, electrons, and anti-neutrinos in the sack, too, since these are the particles that make up a neutron. To calculate these values, we follow the formula on the right where the number of remaining neutrons, N(t), at some time, t, depend on the initial number of neutrons you have, N(0), and the neutron lifetime, \tau. Since neutrons are stable only for a relatively short amount of time, this will be important later when we try to form Helium in the early universe. The process of neutrons decaying into their composite particles is called beta decay.
Keeping the Nucleus Together: The Binding Energy
Keeping the Nucleus Together: The Binding Energy
In principle, we can have as many nucleons in an atom's nucleus as we'd like. However, only certain combinations of protons and neutrons make a nucleus stable. The amount of energy that is released when fusing neutrons and protons together is called the binding energy. When atoms form through fusion, its total mass will actually be lower than if you added up all the masses of the nucleons. Particles that are fused together to a stable state exist in a state of low potential energy. Kind of like a ball stuck in a valley between two mountains, it will take a massive amount of energy to get it out and over the mountains. This binding energy is released during fusion; since mass is energy, the higher the binding energy, the lower the mass of the atom. While there is no exact formula to calculate the binding energy of a nucleus, they have been well-measured and we can look at a chart of binding energies for common isotopes. We can then see whether any possible decay products have less energy, making a decay possible. Keep in mind, neutrons in the nucleus can still decay...
Let's investigate!
First, let's see if Light Helium is stable. To calculate the total mass of the nucleus, we add up all the masses of the nucleons and subtract the total binding energy (that energy is devoted to keeping the nucleus together). Note that the values in the chart are in terms of binding energy per nucleon. For the example of Light Helium, we find the total mass is 2806.414 MeV. If this nucleus were to break apart, it would have decay into Deuterium and a proton. Calculating these masses, we see that they are 1874.626 MeV and 937.28 MeV, respectively. These particles have more energy than Light Helium, meaning that this decay mode is impossible.
Let's turn our attention now to Tritium. Using the same formula, we see the total mass is 2807.939 MeV. If one of the neutrons in its nucleus undergoes beta decay, the resulting particle will be Light Helium, an electron, and an anti-neutrino: a total mass of 2806.925 MeV, less than that of Tritium. This means that Tritium is not a stable isotope of Hydrogen! Measurements confirm this and find its lifetime to be about 12.5 years.
Calculate the Total Mass!
Calculate the Total Mass!
In the above example, we presented the total mass of some particles without showing our work. Following the procedure written out in the above paragraph, calculate these masses for yourself! Double-check your calculations with the answers.
A Guide to Particle Properties
A Guide to Particle Properties
When it comes to atoms, there's a lot of moving pieces with a lot of unique properties. We provide a quick-reference chart here detailing the important properties to consider going forward, as well as the pictures and symbols we will use in this unit to represent each particle. Take some time to review this chart before continuing the unit. Keep in mind that the masses are listed as energies, so this value is really mc2.
An important caveat to this picture is the neutrino mass. Neutrinos are predicted to be massless particles by the Standard Model of Particle physics. Additionally, Earth-based and cosmological experiments have confirmed that they can change their flavor if they're given enough time. Hence, we keep the values for neutrinos in this chart as an open question mark.
We've now covered many of the important aspects surrounding the formation of atoms. Let's apply what we've learned to the formation of atoms in the early universe in the next page: Making Helium.
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