Chapter 7 Atomic, nuclear and particle physics

Photons and energy states

All electromagnetic radiation, including light, travels in small packets called photons. We call quantum to smallest possible quantity of anything: They are discrete (can't be split, the opposite of continuous) Intensity of radiation = density of photons in an fixed area Frequency of radiation = Size of photon Energy of radiation = frequency of radiation --> E = h * f, where E is energy, h is plank's constant and f is frequency In wave theory, the speed of electromagnetic waves (radiation e.g. light) is defined as c = f * λ, where c is speed of light, f is frequency and λ is wavelength. Therefore, λ = hc/E

Photons are produced by atoms. However, an emission of a photon means that the energy within an atom has decreased. As the emission spectra of atoms is in forms of separate lines tells us that energy can only be emitted in discrete amounts. This means that the energy it transmits it is fixed and exact. We can state that that the emission of each photon occurs when an atom changes from one precise energy level to lower one; an atom can also absorb one photon to increase to a higher energy level as long it has the precise amount of energy. For example, here are the energy states of hydrogen:

The lowest energy state is the ground state. When comparing two states, the one with more energy is called the excited state. In order too see the energy required in order to increase an atom to from a energy state (E_1) to an excited energy state (E_2), the atom must be hit with a photon with the energy E_2 - E_1. The atom will remain in that state briefly, and then release the exact same photon with the same amount of energy.All the photon's energies required for that a particular atom to move from ground state to all excited states is the absorption spectrum. All the photons released when the atom returns to ground state is the emission spectrum. As it can be seen, the lines get closer as frequency increases, or wavelength decreases

Atomic structure

Structure Nucleus: formed by nucleons (Protons and neutrons) Shells: formed by electrons

Characteristics of atoms: Most of the mass is found in the center of the atom, in the nucleus. The sheels, in the other hand, occupies most of the space. Atomic number, or proton number: Nº of protons Nucleon number: Protons + Neutrons Total charge: Protons - Neutrons Isotopes are atoms with same proton number but different nucleon number Nuclides are atoms with both same proton and nucleon number. Protons and neutrons weight about 1 amu (atomic mass unit). Electrons we consider them weightless, since they weight 1/1840 amu Electrons have a negative charge and protons a positive charge. This charge is called the elementary charge (e) Exact mass of protons, neutrons and electrons, value of 1 amu, value of the elementary charge and 1 eV are given in the databooklet

The current nuclear model of the atom was established by the Geiser-Marsden experiment.Prior to this experiment, they believed that the matter inside the atom was distributed equally all through out the atom.In order to disprove this, the experiment consisted of shooting alpha particles to a gold foil. With the old model, they predicted that the alpha particles where able to pass through the foil without a problem, however, onece the experiment took place, a small number of particles deviated slightly (10º) of their course and some reaching angles of 90º.With the results, scientist theorized the nuclear model of the atom, where most of the mass, the one with positive charge, was located in the center. Since the nucleus is charged, it deviated the alpha particles that were about to collide with it. But since the nucleus is so small relative to the size of the entire atom, the number of deviated particles was very small.

Radioactivity

As it can be seen, atoms needed a specific proportion to nucleus in order to be stable. If not, they will release nuclear or ionizing radiation, in form of particle or gamma (energy) rays that ionize nearby particles. Radioactivity is the emission of ionizing radiation caused by changes in the nuclei of unstable atoms. The process by which atoms change into other elements is known as radioactive decay.The day of an unstable nucleus is spontaneous, random, unpredictable and uncontrollable. We can't determine when a specific unstable nucleus is going to decay. However, if we have a sample of identical radioactive nuclei. There are several types of decay

Alpha radiationRadiation that consists in emitting an alpha particle. An alpha particle is made up of 2 neutrons and 2 protons, therefore they have a relative mass of 4 amu and a charge of 2e (e is the elementary charge). Alpha radiation in atoms that are too massive. As such, atoms release alpha radiation at high speeds, not only reducing its size, but also transforming part of the extra nuclear potential energy into kinetic energy. Due to the alpha particle and relative slow speed (compared to the other particles emitted through radiation), it has low penetration. However, it has a high ionizing power.They can be represented through a molecular. It can be represented in a molecular formula:

Beta radiationRadiation that consists in a neutron transforming into a proton, releasing an beta-negative particle (an electron) and an electron anti-neutrino in the process. The electron is released of the atom at high speeds. This occurs in unstable atoms where there's too many neutrons for protons. Electrons released have medium ionization power and medium velocity.

Beta-positive radiationRadiation that consists in a proton transforming into a neutron, releasing an beta-positive particle (an positron) and an electron neutrino in the process. This occurs in unstable atoms where there's too many neutrons for protons. Electrons released have medium ionization power and medium velocity. A positron is the anti-particle of the electron, so it will have similar characteristics except that it has a positive charge instead of a negative one, and when it interacts with an electron they annihilate (they destroy each other and release energy in the process) The positron is released of at high speeds.

Gamma radiationGamma radiation occurs when unstable atoms release nuclear potential energy though gamma rays. Gamma rays are also emitted as a side product in other types of radiation. These are energy rays, so they don't have a charge, and therefore low ionization power, although they are the fastest than alpha and beta particles.

Properties of radioactive decay

Background radiationRadioactive isotope occur naturally in nature. This creates a small amount of radiation we can't avoid, although our body is naturally prepared to combat it.Half of this radiation comes from radom in the air and uranium isotopes found in granite.

Penetration Alpha particles: low penetration, can be blocked by thick paper Beta particles: medium penetration, can be blocked with a 3mm aluminium sheet Gamma rays: high penetration, can be blocked with 3 cm of lead.

Magnetic Fields: Alpha particles: highest charge and slow speed, but their big mass makes field slightly vary their direction Beta particles: elementary charge, medium speed and small mass, fields heavily change their direction Gamma rays: no charge and high speed, they are unaffected by a field

Patterns of radioactive decayAlthough is imposible to tell when a specific unstable atom is going to decay, we know that each radioactive isotope has a half-life, the time it takes for half of any sample of unstable nuclei to decay. We can find it using a graph plotting the number of undecayed nuclei (y-axis) over time (x-axis)

Decay seriesA decay series is the process where a highly unstable nuclei goes through different types of radiation several times.

Matter and Energy

Einstein theorized that mass and energy are essentially nearly the same thing. The relationship between energy and mass is the famous equation:

It is important to remember that 1 amu = 931.5 eV One important property of matter is that the sum of the mass of the components (electrons, protons and neutrons) is bigger than the amount of mass the molecule itself has. The difference between this two is called mass defect. Is believed that the remaining mass converted in energy and released. This energy is called the binding energy. Is also important to know that the biding energy is the energy required to separate all the nucleons in an atom.The graph of binding energies per number of nucleons is important to know. Note that after Nickel, with 62 nucleons, the bingin energy starts to decrease.

From this, we can extract energy using either Fission or Fusion:

Nuclear fissionNuclear fission is the splitting of a heavy nucleus intro two lighter nuclei. A fission of a larger nucleus increases the size of a binding energy per nucleon and releases energy. It can be represented as a molecular equation

Nuclear fusionNuclear fusion is the combination of two light nuclei to produce a heavier nucleus. The new nuclei is more stable as it has a larger binding energy. This can also be represented as a molecular equation:

Calculating energyWe can calculate the amount of energy given off by alpha radiation, nuclear fission and nuclear fusion by following these steps: Calculate the mass in both sides and find the mass difference We transform the mass difference into energy (using E=mc^2, explained later) If we want to calculate the amount of energy given per nuclei, we don't have to do anymore. However, if we calculate the amount of energy given per mole, we multiply the energy given of by Avogrado's number.

The standard model

The standard model tries to cover all the types of sub-atomic particles and elementary particles they exist. Elementary particles are particles that can't be split into its components. The opposite are composite particles.The three main categories are: Quarks Leptons Exchange particles(gauge bosons) Quarks and leptons are fermions, while exchange particles plus the Higgs boson are bosons.

Before continuing. Is important to note that for each sub-atomic particle there is an anti-particle, that has the same mass as the particle, but the opposite charge and quantum numbers (baryon number and lepton number; seen later).When an anti-particles meets with its particle counterpart, they annihilate: both the particle and the anti-particle become pure energy, emitting to gamma rays. The reverse process is pair production, that occurs when to gamma rays collide, creating a particle and its anti-particle counterpart.This is also produces the concept of supersymmetry, the idea that there's an equal amount of particles and anti-particles in the universe.

QuarksThere are 6 types of quarks, or flavours. The most common of them are up and down quarks. All quarks have a baryon number of 1/3, and they either have a charge of 2/3 of the elementary charge or -1/3 of the elementary charge. Also, the strange quark has a strange number of -1, unique in this property.Quarks hace a property called quarks confinement, which is that quarks are unable to be found in nature by its own. As so thy must form groups of quarks, or hadrons. There are two types of hadrons Baryons: combinations of 3 quarks. Common examples are protons (2 up quarks and 1 down quark) and neutrons (2 down quarks and 1 up quark) Mesons: combination of 1 quark and 1 antiquark. Common examples are positive pions (up quark and down anti-quark) and neutral pions (up quark and up anti-quark)

LeptonThere are 6 types of leptons, electron, muons and tau and their neutrino version. All of them have a lepton number of 1. The neutrino versions don't have charge, the others have a charge of -1. They can appear in nature, but only the electron is stable enough, so all of them end up decaying into them.

Exchange particlesExchange particles explain the forces at a fundamental level. When there's two particles interacting with each other, there's an exchange of a exchange particle between them. These particles are very fast and not observable. Because of this, exchange particles are described as virtual particles. These are Photons W bosons Z boson Gravitons Gluons

Fundamental forces (in order of strength)

Strong nuclear force:In a nucleus of an atom, the electromagnetic force pulling the protons apart is stronger than the gravitational force pulling the protons together. The strong force keeps the balance. It affects gluons and photons. Its exhange particle is the gluon. Its range is limited by the nucleus

Electromagnetic forceBinds electrons to protons. It also allows atoms to each other and form bigger structures. It attracts matter of opposite charges and repels matter of equal charge. Affects all charged particles Its range is infinite, although it decays with the inverse square law Its exchange particle is photons

Weak nuclear forceBeta decay Limited to the nucleus It affects quarks and leptons It is exhange particles are W and Z bosons

Gravitational forceIt attracts all mass together It affects all mass It is exchange particles are gravitons, altohugh it hasn't been proved. Its range is infinite, although it decays with the inverse square law

Interactions between subatomic particles

Sub atomic particles can interact each other, just as molecules do with other. However, the Quantum numbers must be conserved at each side of a reaction. These are Baryon number Lepton number Overall charge Strangeness (only in strong force and electromagnetic force interactions)

In order to represent this interactions we also use Feynam diagrams: here is an example and some rules so you understand

The area to the left of the vertex it represents the particles before the interactions, the area to the right it represent particles after interactions Observable particles are represented by straight lines. If the arrows are pointing right, the particle is normal, if the arrow is to left, it's an anti-particle. It doesn't represent the motion of the particles in practice The curved lines represent virtual particles The change in orientation of a line means that the motion of the particle changed. Here are several examples: