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<!DOCTYPE html>
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<head>
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<title>Physics notes</title>
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<body><div class="container"><h1 id="physics-notes">Physics notes</h1>


<h2 id="particles-quantum-phenomena-and-electricity">Particles, Quantum Phenomena and Electricity</h2>


<h3 id="the-nuclear-model">The Nuclear Model</h3>

<p>Rutherford’s experiment showed that the structure of an atom consists of positively charged protons and neutral neutrons situated in the nucleus. This is surrounded by negatively charged electrons.</p>

<table>
<thead>
<tr>
  <th>Particle</th>
  <th>Charge (C)</th>
  <th>Mass (kg)</th>
</tr>
</thead>
<tbody><tr>
  <td>Proton</td>
  <td>1.6x10<sup>-19</sup></td>
  <td>1.673x10<sup>-27</sup></td>
</tr>
<tr>
  <td>Neutron</td>
  <td>0</td>
  <td>1.675x10<sup>-27</sup></td>
</tr>
<tr>
  <td>Electron</td>
  <td>-1.6x10<sup>-19</sup></td>
  <td>9.1x10<sup>-31</sup></td>
</tr>
</tbody></table>


<p>An atom can be represented by writing the nucleon number as super script, representing the sum of the protons and neutrons in the element, and the proton number as subscript.  <br>
In an uncharged atom the number of electrons orbiting the nucleus is equal to the number of protons.</p>


<h3 id="isotopes">Isotopes</h3>

<p>Isotopes are different forms of an element. They always have the same number of protons, but have a different number of neutrons. As they have the same number of protons and electrons they behave in the same way chemically.</p>


<h4 id="chlorine">Chlorine</h4>

<p>Chlorine is displayed as having a nucleon number of 35.5, and 17 protons. It doesn’t have 18.5 neutrons. <br>
There are two stable isotopes of Chlorine, <sup>35</sup>Cl<sub>17</sub> accounting for ~75% and <sup>37</sup>Cl<sub>17</sub> accounting for ~25%, giving an average of <sup>35.5</sup>Cl<sub>17</sub>.</p>


<h3 id="specific-charge">Specific Charge</h3>

<p>Specific charge is the charge-mass ratio. This is a measurement of the charge per unit mass.</p>


<h3 id="ions">Ions</h3>

<p>An atom may gain or lose electrons. The atoms becomes positively or negatively charged and is called an ion. <br>
If the atom gains an electron there are more negative charges, so the atom becomes a negative ion. <br>
Otherwise the atom becomes a positive ion.</p>


<h3 id="antimatter">Antimatter</h3>

<p>Every particle has its own antiparticle. An antiparticle has the same mass as the particle but has opposite charge. An antiproton has a negative charge, an antielectron has a positive charge, but an antineutron is also uncharged.</p>


<h3 id="annihilation">Annihilation</h3>

<p>Whenever a particle and its antiparticle meet they annihilate each other. Annihilation is the process by which mass is converted into energy, particle and antiparticle are transformed into two photons of energy.</p>


<h4 id="photon">Photon</h4>

<p>Light can be released in packets of energy. Einstein named these wave-packets photons. The energy carried by a photon is given by the equation.</p>


<p><script type="math/tex; mode=display" id="MathJax-Element-1587"> E = hf \\ As\ c = fλ\ we\ can\ also\ write\quad  E = \frac{hc}{λ} </script></p>


<h4 id="imbalance">Imbalance</h4>

<p>There is an imbalance in the amount of matter and antimatter, annihilating the antimatter and leaving matter to form.</p>


<h3 id="pair-production">Pair production</h3>

<p>Pair production is the opposite process to annihilation, energy is converted into mass. <br>
A single photon of energy is converted into a particle-antiparticle pair. (Obeying conservation laws) <br>
This can only happen if the photon has enough mass-energy to ‘pay for the mass’.</p>

<p>If pair production occurs in a magnetic field, the particle and antiparticle will move in circles of opposite direction, but only if they are charged.</p>

<p>Pair production can occur spontaneously but most occur near a nucleus which recoils to conserve momentum.  <br>
<script type="math/tex; mode=display" id="MathJax-Element-1588"> p + p \rightarrow p + p + p + \overline{p} \\ p + p \rightarrow p + p + π^{+} + π^{-} \\p + p \rightarrow p + p + n + \overline{n}</script></p>

<p>In each of the above reactions, the conservation laws have been obeyed.</p>


<h2 id="quarks">Quarks</h2>


<h3 id="rutherford-scattering-experiment">Rutherford scattering experiment</h3>

<p>Rutherford fire a beam of alpha particles at a thin gold foil. If the atom had no inner structure the alpha particles would only be deflected by very small angles. Some of the alpha particles were scatted at large angles by the nuclei of the atoms. From this Rutherford  deduced that the atom was mostly empty space with the majority of the mass situated at the centre.</p>


<h3 id="smaller-scattering">Smaller scattering</h3>

<p>In 1968 Physicists conducted a similar experiment to Rutherford’s but they fired a beam of high energy electrons at nucleons. The results obtained were very similar to Rutherford’s. The results showed that protons and electrons were made of three smaller particles, each with a fractional charge.</p>


<h3 id="quarks-1">Quarks</h3>

<p>These smaller particles were named quarks and are thought to be fundamental particles. <br>
There are six different quarks, each of which has its own antiparticle.</p>

<table>
<thead>
<tr>
  <th>Quark</th>
  <th>Charge (Q)</th>
  <th>Baryon number (B)</th>
  <th>Strangeness</th>
</tr>
</thead>
<tbody><tr>
  <td>d</td>
  <td>-1/3</td>
  <td><ul>
1/3
</ul></td>
  <td>0</td>
</tr>
<tr>
  <td>u</td>
  <td><ul>
2/3
</ul></td>
  <td><ul>
1/3
</ul></td>
  <td>0</td>
</tr>
<tr>
  <td>s</td>
  <td>-1/3</td>
  <td><ul>
1/3
</ul></td>
  <td>-1</td>
</tr>
</tbody></table>


<table>
<thead>
<tr>
  <th>Anti-Quark</th>
  <th>Charge (Q)</th>
  <th>Baryon number (B)</th>
  <th>Strangeness</th>
</tr>
</thead>
<tbody><tr>
  <td><script type="math/tex; mode=display" id="MathJax-Element-1589">\overline{d}</script></td>
  <td>+1/3</td>
  <td>-1/3</td>
  <td>0</td>
</tr>
<tr>
  <td><script type="math/tex; mode=display" id="MathJax-Element-1590">\overline{u}</script></td>
  <td>-2/3</td>
  <td>-1/3</td>
  <td>0</td>
</tr>
<tr>
  <td><script type="math/tex; mode=display" id="MathJax-Element-1591">\overline{s}</script></td>
  <td>+1/3</td>
  <td>+1/3</td>
  <td>+1</td>
</tr>
</tbody></table>


<h4 id="lone-quarks">Lone quarks</h4>

<p>Quarks never appear on their own. The energy required to separate two quarks is enough to make two new particles.  <br>
A particle called a neutral pion is made from an up quark and and an anti-upquark.  <br>
Moving these apart  creates another up quark and an anti-upquark. We now have two pairs quarks.</p>


<h3 id="particle-classification">Particle classification</h3>

<p>Knowing that quarks are the base particles, we can separate all other particles into two groups, those made from quarks and those which are not.</p>

<p>Hadrons- Heavy and made from smaller particles</p>

<p>Leptons- Light and not made from smaller particles</p>


<h3 id="hadrons">Hadrons</h3>

<p>The properties of Hadrons are due to the combined properties of the quarks that make them. <br>
There are two categories of Hadrons: Baryons and Mesons.</p>


<h4 id="baryons">Baryons</h4>

<p>Made from three up quarks.</p>

<p>Protons and neutrons are Baryons.</p>

<p>The proton is the only stable Baryon, all others eventually decay into a proton.</p>


<h4 id="mesons">Mesons</h4>

<p>Made from a quark and an antiquark</p>


<h3 id="anti-hadrons">Anti Hadrons</h3>

<p>Anti hadrons are made from the opposite quarks as their hadron counterparts, for example a proton is made from the quark combination uud and an antiproton is made from the anti quark of each.</p>


<h3 id="leptons">Leptons</h3>

<p>Leptons are a family of particles that are much lighter than Baryons and Mesons and are not subject to the strong interaction. There are six leptons in total, three of which are charged and the rest of which are not. <br>
 The charged particles are electrons, muons and tauons. <br>
 The muon and tauon are similar to the electron but bigger, the muon being 200 times larger and the tauon 3500 times. <br>
 Each of the charged leptons has its own neutrino. If a decay involves a neutrino and a muon, it will be a muon neutrino, not a tauon or electron neutrino.</p>

<p>The neutrino is a chargeless, almost massless particle. It isn’t affected by the strong interaction or EM force and barely by gravity, making it almost impossible to detect.</p>

<table>
<thead>
<tr>
  <th>Lepton</th>
  <th>Charge (Q)</th>
  <th>Lepton number</th>
</tr>
</thead>
<tbody><tr>
  <td>Electron</td>
  <td>e<sup>-</sup> | -1</td>
  <td>+1</td>
</tr>
<tr>
  <td>Electron neutrino</td>
  <td>v<sub>e</sub> | 0</td>
  <td>+1</td>
</tr>
<tr>
  <td>Muon</td>
  <td>μ<sup>-</sup> | -1</td>
  <td>+1</td>
</tr>
<tr>
  <td>Muon neutrino</td>
  <td>v<sub>μ</sub> | 0</td>
  <td>+1</td>
</tr>
<tr>
  <td>Tauon</td>
  <td>τ<sup>-</sup> | -1</td>
  <td>+1</td>
</tr>
<tr>
  <td>Tauon neutrino</td>
  <td>v<sub>τ</sub> |0</td>
  <td>+1</td>
</tr>
</tbody></table>


<p>For each of the above, the respective anti-lepton has opposite charge and a lepton number of -1.</p>


<h4 id="conservation-laws">Conservation laws</h4>

<p>For particle interactions to occur the following laws must be obeyed</p>

<ul>
<li>Charge must be conserved. The total charge prior to the interaction must be the same as that afterward</li>
<li>Baryon number must be conserved</li>
<li>Lepton number must be conserved</li>
<li>Strangeness must be conserved in EM and strong interaction, but not in weak interaction</li>
</ul>


<h2 id="forces-and-exchange-particles">Forces and exchange particles</h2>


<h3 id="the-four-interactions">The Four Interactions</h3>

<ul>
<li>The electromagnetic interaction causes an attractive or repulsive force between charges</li>
<li>The gravitational interaction causes an attractive force between masses</li>
<li>The strong nuclear interaction causes an attractive (or repulsive) force between quarks (and so hadrons)</li>
<li>The weak nuclear interaction does not cause a physical force, it makes particles decay. ‘Weak’ means that there is a low probability that it will happen</li>
</ul>

<table>
<thead>
<tr>
  <th>Interaction/Force</th>
  <th>Range</th>
  <th>Relative  Strength</th>
</tr>
</thead>
<tbody><tr>
  <td>Strong nuclear</td>
  <td>~10<sup>-15</sup> m</td>
  <td>1</td>
</tr>
<tr>
  <td>Electromagnetic</td>
  <td>∞</td>
  <td>~ 10<sup>-2</sup></td>
</tr>
<tr>
  <td>Weak nuclear</td>
  <td>~10<sup>-18</sup></td>
  <td>~10<sup>-7</sup></td>
</tr>
<tr>
  <td>Gravitational</td>
  <td>∞</td>
  <td>~10<sup>-36</sup></td>
</tr>
</tbody></table>


<h3 id="exchange-particles">Exchange particles</h3>

<p>In 1935 the idea that interactions/forces between two particles were caused by ‘virtual particles’ being exchanged between the two particles. <br>
The general term for exchange particles is bosons and they are fundamental particles like quarks and leptons.</p>

<table>
<thead>
<tr>
  <th>Interaction/Force</th>
  <th>Exchange particle</th>
  <th>What it acts upon</th>
</tr>
</thead>
<tbody><tr>
  <td>Strong nuclear</td>
  <td>Gluons between quarks or Pions between Baryons</td>
  <td>Nucleons (Hadrons)</td>
</tr>
<tr>
  <td>Electromagnetic</td>
  <td>Virtual photon</td>
  <td>Charged particles</td>
</tr>
<tr>
  <td>Weak nuclear</td>
  <td>W<sup>+</sup> W<sup>-</sup> Z<sup>0</sup></td>
  <td>All particles</td>
</tr>
<tr>
  <td>Gravitational</td>
  <td>Graviton</td>
  <td>Particles with masses</td>
</tr>
</tbody></table>


<h4 id="borrowing-energy-to-make-particles">Borrowing energy to make particles</h4>

<p>The exchange particles are made from ‘borrowed’ energy, borrowed from nowhere. <br>
The Heisenberg uncertainty principle can be used to show that-</p>


<p><script type="math/tex; mode=display" id="MathJax-Element-1592">A\ particle\ of\ mass\ energy\ ΔE\ could\ exist\ for\ Δt\ as\ long\ as\ ΔEΔt <= h\ where\ h\ is\ Plank's\  constant </script></p>

<p>This means that a heavy particle can only exist for a short time, while a lighter particle may exist for longer.</p>


<h2 id="the-strong-interaction">The Strong Interaction</h2>

<p>The strong nuclear force acts between quarks. Since Hadrons are the only particles made of quarks only they experience the strong nuclear force. <br>
In both Baryons and Mesons the quarks are attracted to each other by exchanging virtual particles called ‘gluons’.</p>

<p>On a larger scale the strong nuclear force acts between the Hadrons themselves, keeping them together. A pi-meson or pion is exchanged between the hadrons. This is called the residual strong nuclear force.</p>


<h3 id="force-graphs">Force graphs</h3>


<h4 id="neutron-neutron-or-neutron-proton">Neutron-Neutron or Neutron-Proton</h4></div></body>
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