Particles and Nuclides
01. Models in Physics
In science, and in physics in particular, we rely on models to explain how the Universe around us works.
Models make complex, often invisible things or processes easier to visualise. Models take many forms. Some,
like the models of atoms and nuclei used in this chapter. The Rutherford-Bohr model and model of gas
molecules are very good models. JJ Thomson was the first person to create a model of the structure of the
atom, which he called the plum pudding model. The nucleus of the atom was discovered by Rutherford,
Geiger and Marsden in 1909.
2. The Rutherford-Bohr atom
The Rutherford-Bohr model of the atom consists of a tiny, central, positively charged nucleus, containing protons and neutrons, surrounded by orbiting negatively charged electrons. it can be used to explain much of the chemical behavior of atoms.
2.1 Rutherford’s Gold Foil Experiment (1911)
Experiments carried out by Ernest Rutherford and his research assistants Hans Geiger and Ernest
Marsden.
Experimental Setup
- Alpha particles (helium nuclei) were directed at a
thin gold foil. - A detecting screen coated with zinc sulphide
surrounded the foil to observe scattering.
Observations
- Most alpha particles passed through the foil with little or no deflection.
- Some were deflected at small angles.
- A few (about 1 in 8000) were deflected at very large angles, some even back towards the source.
Conclusions
- Atom is mostly empty space: Most alpha particles passed through.
- Nucleus: A small, dense, positively charged center caused significant deflections.
- Electrons: Surround the nucleus, making up most of the atom’s volume.
03. Charges, masses and specific charges
The charges and masses of the proton, neutron and electron are shown in the Table below:
The specific charge of a particle is defined as the charge per unit mass, and its units are Ckg−1.
The specific charge is calculated using the formula:
The specific charge of a particle = charge of the particle/mass of the particle = Q/m
Specific charge of a proton = +1.60 × 10−19 / 1.673 × 10−27 = 9.56 × 107 Ckg−1
The specific charge of the neutron is 0 and the electron is −1.76 × 1011 Ckg−1
04. Describing Nuclei and Isotopes
Proton Number, (Z): The number of protons in any given nucleus.
Nucleon Number, (A): The total number of protons and neutrons in the nucleus.
The two nuclear numbers and the chemical symbol are used together as a shorthand way of describing any nucleus.
This is called the AZX notation.
(A, is always written as a superscripted prefix and Z, is a subscripted prefix)
Isotopes: The same element having the same proton number, Z, but different nucleon numbers, A.
The isotopes of hydrogen
05. Stable and Unstable Nuclei
Aspect | Stable Nuclei | Unstable Nuclei |
Radioactive Decay | Does not undergo radioactive | Undergoes radioactive decay |
Proton-Neutron Ratio | Balanced ratio of protons to | Imbalanced ratio of protons to neutrons. |
Energy State | Energetically favourable and | Energetically unfavourable and unstable. |
Examples | Carbon-12, Oxygen-16 | Uranium-238, Carbon-14 |
5.1 Alpha and Beta Radioactive Decay
Not all nuclei are stable. In fact, the vast majority of known isotopes are unstable. Unstable nuclei can
become more stable by the process of radioactive nuclear decay. Although there are many different decay
mechanisms, three types are far more common than all the others. These are alpha, beta and gamma decay.
Aspect | Alpha Decay | Beta Decay | Gamma Emission |
Definition | Emission of an alpha | Transformation of a neutron into a | Emission of gamma radiation |
Particle Emitted | Alpha particle | Beta particle (electron in beta | Gamma photon |
Change in Nucleus | Nucleus loses 2 | Nucleus changes one neutron to a | Nucleus drops to a lower energy |
Effect on Atomic | Decreases by 2. | Increases by 1 (beta-minus) or | No change. |
Effect on Mass | Decreases by 4. | Remains the same. | No change. |
Penetrating Power | Low (stopped by | Moderate (stopped by plastic or a | High (requires thick lead or |
Example | Uranium-238 to | Carbon-14 to Nitrogen-14 | Cobalt-60 emitting gamma |
6. Detecting Nuclear Radiation
6.1 The cloud chamber
The cloud chamber is a device used to visualize the paths of ionizing particles. It contains a supersaturated vapor of water or alcohol. When a charged particle passes through, it ionizes the vapor along its path. The ions act as condensation nuclei, causing the vapor to condense into tiny droplets, which form visible tracks that can be observed and photographed. The cloud chamber was instrumental in the early discovery and study of subatomic particles.
6.2 The spark counter
The spark counter is a radiation detector that uses an electric field to detect ionizing particles. It consists of a wire mesh or series of wires placed above a metal plate with a small gap in between. When a charged particle passes through the gap, it ionizes the air, creating a conductive path. A high voltage applied across the gap causes a spark to jump, which can be counted and recorded. Spark counters are useful for detecting and measuring high-energy particles.
6.3 The Geiger-Muller counter
The Geiger-Muller counter is a widely used radiation detector that measures ionizing radiation. It consists of a Geiger-Muller tube filled with an inert gas like helium, neon, or argon at low pressure. When radiation enters the tube, it ionizes the gas, producing a pulse of electric current. This pulse is amplified and counted, providing a measure of the radiation intensity. Geiger-Muller counters are popular due to their simplicity, reliability, and ability to detect a wide range of radiation types, including alpha, beta, and gamma radiation.
7. Nuclear Equations
The AZX notation can be used to describe the nuclear reactions that take place during radioactive decay.
During alpha, beta and gamma radioactive decay, two simple conservation rules come into play:
- nucleon number, A, is always conserved
- proton number, Z, is always conserved
In practice this means that the total (addition) value for A before the decay is equal to the total (addition) value of A after the decay (and, similarly, the totals for Z remain the same before and after the decay).
Look at the following two examples:
7.1 Alfa Decay
In alpha decay, an unstable nucleus emits an alpha particle (consisting of 2 protons and 2 neutrons), resulting in a new element with a lower atomic number and mass number.
Example: Radium-226 → Radon-222 + α
Decay of Radium
7.2 Beta Decay
In beta decay, a neutron is converted into a proton, emitting an electron (beta particle).
The atomic number increases by 1 while the mass number remains unchanged.
Example: Carbon-14 → Nitrogen-14 + e−
08. The Photon Model of Electromagnetic Radiation
Planck developed the concept of a fundamental unit of energy, which became known as a quantum. He proposed that atoms absorb and emit radiation in multiples of discrete amounts that are given by the Planck equation:
where:
- f is the frequency of the radiation absorbed or emitted, and
- h is a constant, now called the Planck constant. (h = 6.63 × 10−34Js) It was Planck who called these discrete units of energy ‘quanta’ and
the small ‘packets’ of electromagnetic radiation making up these quanta became known as photons.
the small ‘packets’ of electromagnetic radiation making up these quanta became known as photons.
09. Antiparticles
In 1928, Paul Dirac proposed the existence of the positron, the antiparticle of the electron. He
suggested that the positron had the same mass as an electron, but that most of its other physical properties
(such as its charge) were the opposite to that of the electron. Dirac thought that positrons were positively
charged electrons.
9.1 Rest mass-energy
The amount of energy released by converting all of the mass of a particle at rest into energy using
Einstein’s famous mass-energy equation: E = mc2
where m is the rest mass of the particle and c is the speed of light.
- The positron is one of the few antiparticles that has its own different name
- The other more common antiparticles are the antiproton, the antineutron and the antineutrino.
- Antiparticles are not common. The Universe appears to be overwhelmingly dominated by matter.
9.2 Particle–antiparticle interactions
- Annihilate: When a particle meets its corresponding antiparticle, other. This means that the total
mass of the particle pair is converted into energy, in the form of two gamma ray photons.
mass of the particle pair is converted into energy, in the form of two gamma ray photons.
- Two gamma photons are always produced during particle – antiparticle annihilation in order to
conserve momentum.
- The total energy of the gamma photons is equal to the total rest energies of the particle – antiparticle
pair, in order to conserve energy.
conserve momentum.
pair, in order to conserve energy.
9.3 Pair production:
- The opposite process to annihilation is called pair production.
- In this process, a photon with enough energy can interact with a large nucleus and be converted
directly into a particle-antiparticle pair.
- The rest energy of an electron (and therefore a positron) is 0.51 MeV or 8.2 × 10−14J.
- In order to create this particle-antiparticle pair, the photon must have enough energy to create both
particles.
- The wavelength of the photon needed to do this can be calculated by:
directly into a particle-antiparticle pair.
particles.
