Module 8: Nature of Light

Table of Contents

Mod 8: From the Universe to the Atom

Origins of the Elements

The Big Bang Theory

  • Proposes that 13.7 billion years ago, the Universe started as an extremely hot and dense point called a singularity, which produced an enormous amount of energy, expanding outwards and cooling down

  • The first particles formed were fundamental particles: leptons, neutrinos and quarks, and zero mass particles such as gluons and photons

  • As the temperature continues to fall, quarks combined to form hadrons e.g. protons and neutrons

  • The radiation dominates the Universe and more hydrogen and helium forms as temp falls

  • Temperature eventually falls low enough for hydrogen fusion to start, and matter starts to form

Transformation of radiation into matter

  • Subatomic particles condensed from radiation shortly after the universe began, according to Einstein’s mass-energy relationship – followed by period of nuclear synthesis when hydrogen, helium and some lithium nuclei were formed

  • For unknown reasons, slightly more matter than antimatter was formed, and this imbalance led to the matter found in the Universe today

  • As the Universe expanded & cooled, electrons and nuclei combined to forma toms, and these atoms joined to form the first stars

  • The Universe now consists of a vast number of galaxies and the space between them continues to expand at an increasing rate

Evidence leading to discovery of Universe’s expansion by Hubble

  • At beginning of 20th century, scientists believed the universe existed in a steady state, remaining static rather than evolving

  • When Einstein published his special theory of relativity in 1905, he predicted a model of the universe that was either expanding or contracting, but he didn’t believe it so introduced the cosmological constant to overcome this idea and support the steady state model

  • In 1922, Alexander Freidmann applied Einstein’s equations of general relativity, and showed that the equations predicted an expanding universe rather than the static one

  • This was supported by Edwin Hubble in 1923 who was studying the Andromeda nebulae. He noticed a pulsating star, and calculated its distance ushe ing inverse-square law from Earth to be 800 000 LY. He showed that Andromeda and other galaxies he discovered to be separate from our galaxy

  • His observations were supported by Slipher, showed in 1925, that the redshift of galaxies like Andromeda were much greater than any other star in the Milky Way

  • Hubble followed up this work by examining the redshift from 46 galaxies, and showed there was a linear relationship between the distance to a galaxy and the amount its light is redshifted – known as Hubble’s Law

Einstein’s mass-energy equivalence and nuclear synthesis in stars

  • The extremely high temperature and pressure produced by gravity in the core of stars enables them to convert matter to energy through fusion reactions. These reactions result in the conversion of mass to energy in accordance with Einstein’s mass-energy equivalence $E=mc^{2}$

Emission, absorption, & continuous black-body spectrum

  • Black-body radiation produces a continuous spectrum containing all wavelengths. As a black-body is heated, the wavelength at which most radiation is emitted decreases and the power radiated increases

  • A continuous spectrum is produced when incandescent light and sunlight is refracted through a prism. All the colours of the rainbow are present

  • Emission spectra form when atoms are exited by heating them in a vacuum tube, and the resultant light produces bright, coloured lines.

  • EM radiation is emitted as excited electrons fall back to lower energy levels and produce emission lines, which represent the energy values of the particular electron transfers for that element

  • Absorption spectra form when passing continuous spectra through an unexcited elemental gas, producing black lines against a continuous background.

  • Atoms absorb photons of specific energies. The atom absorbing the photon could be initially in the neutral ground state or it could be in an excited state. The energy values absorbed are represented by the black lines

Key features of stellar spectra & classifying stars

  • Many stars have different absorption lines due to their temperature difference

  • The current classification system based on the star’s temperature is called the Morgan-Kennan (MK) system, so the original alphabetical order scheme is re-arranged for temp

  • Stars are classified into 7 spectral classes labelled OBAFGKM, where O stars are the hottest

  • The system is subdivided further using numbers from 0-9, where 9 represents the coolest star

  • Astronomers call the mass of the Sun, a ‘solar mass’ and use it to specify the mass of other stars

  • The lines in the stellar absorption spectra reflect the density of the atmosphere of the star. The coolest stars are not hot enough for collisions to break apart molecules and hence show molecular lines

  • Hotter stars have collisions in the atmosphere energetic enough to singly ionise metals, and hence do not show molecular lines

  • Helium has a very high ionisation energy and hence the absorption lines of ionised helium are present only in very hot stars

  • Hydrogen lines are weaker in cooler stars since the first energy level is very high and very few hydrogen atoms reach this level in collisions at low temperatures

  • The colour of each spectral class is explained by recalling that the peak emission wavelength of the black-body radiation emitted by the star in inversely proportional to the surface temp of the star.

  • Wien showed that the wavelength of maximum emission is related to the surface temp of the star

  • When looking at black-body emission curves for stars with different surface temps, note how the shift towards shorter wavelengths, as the temp of the star increases, changes the colour of the star

The Hertzsprung-Russell diagram

  • In 1911, Hertzsprung and Russell independently plotted the spectral class (temp) against luminosity for known stars. They discovered that the stars were grouped together in different regions on the graph. This graph is important for astrophysics since it shows that there are different types of stars, and that stars evolve in different ways depending on their initial mass
  • Masses of stars on the main sequence increase diagonally towards the upper left of the main sequence curve

  • The larger and hotter the stars, the less lifetime they have left before they supernova

  • The sizes of stars increase diagonally towards the upper right

  • The colour of stars moves from red (lower right) to blue (upper left)

  • The temperature of stars increases diagonally from bottom right to upper left

  • The luminosity of stars increases diagonally from lower right to upper left

  • Colour, luminosity, and temperature are directly related properties

Main sequence stars

  • Run diagonally from top left corner to bottom right corner

  • Over 90% of stars in our galaxy fall into this category including the Sun

  • Vary from large, hot, blue stars on the top left to small, red dwarf stars on the lower right

  • Produce energy by fusing hydrogen to helium in the core

  • Form when large clouds of gas are pulled together by gravity until the core temp becomes large enough for hydrogen fusion to begin

  • Larger stars must fuse hydrogen at a faster rate to balance the enormous inward pressure of gravity, hence why they are hotter (blue) and have shorter lifespans

  • Smaller MS stars (red dwarfs) have a slower fusion rate and longer lifespan

Giant Stars

  • a star that as finished fusing hydrogen in the core and is now fusing hydrogen in a shell around the core; a giant star can also fuse helium in the core

  • Most common are red giants – they are cool but quite luminous, occupying upper right of HR diagram

  • Given their low temp, their size must be huge to produce high luminosity

  • Produce energy by hydrogen fusion to form helium in outer core – aka. shell burning

  • All red giants are in a late stage of evolution, having fused all the hydrogen in their core to helium

White dwarf stars

  • The hot leftover core of a star that has ceased to fuse elements

  • Represent final phase of evolution of MS stars

  • When MS sequence stars run out of fuel, they blow away their outer layers to form a planetary nebula, and the core that remains collapses to form a white dwarf

  • White dwarfs have a similar mass to the Sun, but are about the size of Earth

  • They slowly radiate their remaining heat into space over a billion years, becoming duller, and eventually a black dwarf – however, the Universe is not old enough to produce a black dwarf yet

Supergiant stars

  • A very large star that has finished fusing hydrogen in the core; the largest of these can fuse heavier elements in shells around the core until they produce iron in the core

  • Formed from very large MS sequence stars that have ceased fusing hydrogen and helium in their core, and are now fusing carbon and heavier elements, while lighter elements fuse in shells around the core

  • They are the largest stars in the Universe

The Evolution of Stars

  • The lifecycle of a star is largely determined by its initial mass. The more massive and hotter stars burn hydrogen faster and evolve from MS sooner

  • Stars are born out of the gravitational collapse of cool, dense molecular clouds. As the cloud collapses, it fragments into smaller regions, which themselves contract to form stellar cores. These protostars rotate faster and increase in temperature as they condense, and are surrounded by a protoplanetary disk out of which planets may later form.

  • The central temperature of the contracting protostar increases to the point where nuclear reactions begin. At this point, hydrogen is converted into helium in the core and the star is born onto the main sequence. For about 90% of its life, the star will continue to burn hydrogen into helium and will remain a main sequence star.

  • Once the hydrogen in the core has all been burned to helium, energy generation stops and the core begins to contract. This raises the internal temperature of the star and ignites a shell of hydrogen burning around the inert core. Meanwhile, the helium core continues to contract and increase in temperature, which leads to an increased energy generation rate in the hydrogen shell. This causes the star to expand enormously and increase in luminosity – the star becomes a red giant.

  • Eventually, the core reaches temperatures high enough to burn helium into carbon. If the mass of the star is less than about 2.2 solar masses, the entire core ignites suddenly in a helium core flash. If the star is more massive than this, the ignition of the core is more gentle. At the same time, the star continues to burn hydrogen in a shell around the core.

  • The star burns helium into carbon in its core for a much shorter time than it burned hydrogen. Once the helium has all been converted, the inert carbon core begins to contract and increase in temperature. This ignites a helium burning shell just above the core, which in turn is surrounded by a hydrogen burning shell.

  • What happens next depends on the mass of the star:

    • In stars less than 8 solar masses, the inert carbon core continues to contract but never reaches temperatures sufficient to initiate carbon burning. However, the existence of two burning shells leads to a thermally unstable situation in which hydrogen and helium burning occur out of phase with each other. This thermal pulsing is characteristic of asymptotic giant branch stars.
    • The carbon core continues to contract until it is supported by electron degeneracy pressure. No further contraction is possible (the core is now supported by the pressure of electrons, not gas pressure), and the core has formed a white dwarf. Meanwhile, each thermal pulse causes the outer layers of the star to expand, resulting in a period of mass loss. Eventually, the outer layers of the star are ejected completely and ionised by the white dwarf to form a planetary nebula.
  • In stars greater than 8 solar masses, the contracting core will reach the temperature for carbon ignition, and begin to burn to neon. This process of core burning followed by core contraction and shell burning, is repeated in a series of nuclear reactions producing successively heavier elements until iron is formed in the core.

    • Iron cannot be burned to heavier elements as this reaction does not generate energy – it requires an input of energy to proceed. The star has therefore finally run out of fuel and collapses under its own gravity.

    • The mass of the core of the star dictates what happens next. If the core has a mass less than about 3 times that of our Sun, the collapse of the core may be halted by the pressure of neutrons. In this case, the core becomes a neutron star. The sudden halt in the contraction of the core produces a shock wave which propagates back out through the outer layers of the star, blowing it apart in a core-collapse supernova explosion. If the core has a mass greater than about 3 solar masses, even neutron pressure is not sufficient to withstand gravity, and it will collapse further into a stellar black hole.

    • The ejected gas expands into the interstellar medium, enriching it with all the elements synthesised during the star’s lifetime and in the explosion itself. These supernova remnants are the chemical distribution centres of the Universe.

$$\newcommand{HNucleus}{\ce{^{1}_{1}H}}\newcommand{HeNucleus}{\ce{^{4}_{2}He}}\newcommand{positron}{\ce{e+}}$$

Nucleosynthesis reactions in stars

There are 2 principle reactions that enable stars to produce energy by fusing hydrogen to helium:

  • The Proton-Proton chain (PP chain) involves 3 reactions that enable 4 protons to fuse to helium in the core of MS stars around the mass of the Sun or less:
  1. Collide 2 hydrogen atoms together forming deuterium (positron + electron neutrino+ mass-2 isotope of hydrogen)

  2. Deuterium combines with hydrogen forming helium-3 and a gamma ray

  3. 2 helium-3 isotopes combine forming helium-4 nucleus plus 2 protons

  • The CNO cycle – carbon-nitrogen-oxygen - is cyclic process involving carbon isotopes being changed to nitrogen and oxygen and back to carbon in a catalytical process that enables 4 protons to fuse to helium in the cores of much larger and hotter stars (>1.3 solar masses)

  • Each time the cycle is repeated, 4 protons $(\HNucleus)$ are converted to a helium nuclei $(\HeNucleus)$ plus 3 gamma rays $(\gamma)$, 2 positrons $(\positron)$, and 2 electron neutrinos $(v_e)$

  1. A carbon-12 nucleus captures a proton and emits a gamma ray, producing nitrogen-13.
  2. Nitrogen-13 is unstable and emits a beta particle, decaying to carbon-13.
  3. Carbon-13 captures a proton and becomes nitrogen-14 via emission of a gamma-ray.
  4. Nitrogen-14 captures another proton and becomes oxygen-15 by emitting a gamma-ray.
  5. Oxygen-15 becomes nitrogen-15 via beta decay.
  6. Nitrogen-15 captures a proton and produces a helium nucleus (alpha particle) and carbon-12, which is where the cycle started.

Structure of the Atom

The Electron

Cathode ray early experiments

  • Early cathode ray experiments by Crooke (1870), found that if a high voltage was placed across electrodes in a vacuum inside a glass tube, then current continues to flow and rays emitted from cathode make the glass near anode glow green

  • Experiments showed the rays travelled in straight lines, cast a shadow, could turn a paddle wheel (had mass), and were deflected by magnetic fields

Evidence supporting wave model Evidence supporting particle model
- Rays expose photographic plate, like light - Rays pass through thin metal foils - Rays aren’t deflected by electric fields (later shown to be wrong) - Travel in straight lines and cast shadow - Turn a paddle wheel and hence have momentum - Deflected by magnetic fields - Emitted at right angle to cathode surface rather than in all directions like a wave

Thomson’s charge-to-mass experiment

  • Cathode ray debate settled by JJ Thomson (1897)
  • Confirmed cathode rays were deflected by magnetic and electric fields
  • Accelerated electrons from cathode to anode
  • He constructed a vacuum tube with electric and magnetic fields at right angles to each other
  • By adjusting both fields, he found the velocity of the rays

$$\begin{gather*}qE=qvB\\ v=\frac{E}{B}\end{gather*}$$

  • He measured the radius of curvature of the rays in a magnetic field and found the charge-to-mass ratio of the particles

$$\begin{gather*}qvB=\frac{mv^{2}}{r} \\ \frac{q}{m}=\frac{v}{Br} \end{gather*}$$

Millikan’s Oil Drop experiment

  • After Thomson found the charge-to-mass ratio of the electron, there were still 2 unknowns; the mass and charge if the electron was a quantum of charge, Millikan figured an ionised object would have a charge that would be an integer multiple of the charge on the electron. To find the charge, he used an electric field to levitate droplets of known mass when the charge is at rest, the forces must sum to 0,

$$\begin{gather*}mg=qE=\frac{qV}{d} \\ q=\frac{mgd}{V} \end{gather*}$$

  • ‘m’ is mass of sphere; d is separation between charged plates
  • The charge on the sphere is not the charge on the electron but an integer multiple of the electron charge. To find the charge, the experiment was repeated many times and a common denominator was found.

The Nuclear Model of the Atom

Geiger & Marsden (1909)

  • Under Rutherford’s guidance, they conducted a series of experiments to investigate the scattering of alpha particles by the atoms in a thin gold foil sheet
  • At the time, the atom was thought to be a mass of uniform density that contained electrons (Plum Pudding model)
  • They expected the alpha particles to be deflected by only small angles
  • They expectantly found most alpha particles passes straight through with little or no deflection
  • Surprisingly, some alpha particles were scattered by more than 900. This could not be explained by Thomson’s model.

Rutherford’s Atomic Model

  • To explain the above results, he proposed a nuclear model
  • Suggested almost all the mass of the atom was concentrated in a tiny positively charged nucleus with electrons orbiting around held by electrostatic attraction
  • He proposed that most of the atom was empty space
  • He proposed the electrostatic attraction between -ve electrons and +ve nucleus would provide centripetal force to hold the electrons in orbit
  • His model was classically unstable, since an orbiting electron would be accelerating and emit EM radiation
  • This radiation would cause the electron to rapidly lose KE and spiral into the nucleus
  • He also couldn’t explain atomic emission and absorption spectra.

Chadwick’s discovery of the neutron

  • in 1930, Bothe & Becker reported when they bombarded a beryllium target with alpha rays, an intense neutral radiation was produced. It was very penetrating but not ionising, so it was thought to be gamma radiation

  • in 1931, Joliot & Curie found the radiation emitted from beryllium could eject protons from paraffin but also thought it was gamma radiation

  • in 1932, he conducted a series of experiments where he measured the recoil velocity of atoms such as hydrogen after they were bombarded with radiation

  • he applied laws of conservation of momentum and KE, and showed the radiation was made up of neutral particles with the mass of a proton

Quantum Mechanical Nature of the Atom

The Spectrum of Hydrogen

  • has 4 visible lines; red, blue-green, and 2 violet
  • in 1885, Balmer wrote an equation that could be used to calculate these lines:

$\frac{1}{\lambda}=R\left(\frac{1}{4}-\frac{1}{n^{2}}\right)$

  • n could take on values $\geq$3

  • describes a series of lines that get closer together and approach a limiting wavelength of 364nm as n→∞

Bohr’s model of the atom

  • Rutherford’s planetary model had 2 major limitations:

    • Unstable model since orbiting electrons would emit EM radiation, lose energy, and spiral into nucleus
    • Couldn’t explain atomic emission and absorption spectra
  • Bohr tried to find ways to overcome these limitations

  • In 1913, he proposed a new model of the atom that used quantised electron orbits to explain the specific wavelengths of light emitted and absorbed by these atoms

  • 3 postulates:

    • Electrons can only orbit in specific quantised orbits, which he called stationary states. They did not emit EM radiation
    • An electron can move between orbitals by emitting or absorbing a photon of radiation with an energy equal to the energy difference between orbitals

$\Delta E=E_f =E_i =hf=\frac{hc}{\lambda}$

  • The orbitals can only have an angular momentum given by:

$mvr=\frac{nh}{2\pi}$

  • He overcame Rutherford’s limitations through 2 postulates:

    • His 1st postulate overcomes Rutherford’s stability problem
    • His 2nd postulate explains atomic emission and absorption spectra by saying each line in the spectra corresponds to specific photon energy related to an electron moving between orbitals. Photons are absorbed when electron moves to higher level, and photons emitted when moving to lower level
  • Limitations of Bohr’s model

    • Not possible to calculate wavelengths of spectral lines of all other atoms
    • Works well for atoms with one electron in outer shell but not for others
    • Couldn’t explain the Zeeman effect or the hyperfine splitting of spectral lines
    • His model is a mixture of classical and quantum physics, ignored laws of electromagnetism

Rydberg’s equation

  • Generalised Balmer’s equation and could calculate wavelength of the photon emitted or absorbed for any transition of an electron

$\frac{1}{\lambda}=R\left(\frac{1}{n_f^2}-\frac{1}{n_i^{2}}\right)$

De Broglie’s matter-waves

  • in 1924, proposed that particles would have wave properties and an associated wavelength given by equating Einstein’s mass-energy equivalence with the energy of a photon

$$\begin{gather*}\frac{hc}{\lambda}=hf=mc^2 \\ \text{Since particles with mass cannot travel at c, let c=v:} \\ mv^2 =\frac{hv}{\lambda} \\ \lambda =\frac{h}{mv} =\frac{h}{p} \end{gather*}$$

  • he proposed the quantisation of stationary states corresponded to standing electron waves

  • standing electron waves only exist in orbitals with a circumference equal to the whole number of electron wavelengths

$$\begin{gather*} 2πr=n\lambda \\ \text{sub }\lambda=\frac{h}{mv} \\ mvr=\frac{nh}{2π}\end{gather*}$$

  • each period of the standing wave is one wavelength

Schrodinger’s model of the atom

  • produced the first full quantum model

  • generated a mathematical model for the distribution of electrons in an atom: the electron cloud model, representing the probability of electron’s location around the nucleus

  • combined equations for behaviour of waves from de Broglie

  • overcame most limitations of Bohr’s model and forms basis of current model

Properties of the Nucleus

Radioactive Decay

  • unstable nuclei spontaneously emit particles and radiation until stable

  • spontaneous decay is accompanied by a loss of mass (mass defect) since some mass in converted into energy of the emitted particle according to Einstein’s mass-energy equivalence

  • a nucleus is unstable if proton-neutron ratio is not correct or if nucleus is too large (atomic number > 82)

  • 3 types of radioactive decay

    • Alpha
    • Beta (plus and minus)
    • Gamma
  • Alpha and beta decay are spontaneous transmutations that change the radioactive isotope into a different element

  • Nucleons: neutrons and protons (hadrons in the nucleus)

Alpha Beta Gamma
Made of Helium nucleus $\left(\HeNucleus\right)$ Electrons/Positrons High frequency photons
Charge & Ionisation Positive charge, highly ionising Negative charge, highly ionising No charge, poorly ionising
Penetration Power Low penetration Moderate penetration High penetration

Half-Life

  • Time for half the nuclei to decay

$$N_t =N_0 e^{-\lambda t}$$

$$\lambda=\frac{ln(2)}{t_{\frac{1}{2}}}$$

Nuclear Fission

  • When a large nucleus splits into 2 smaller nuclei, the products are smaller than the parent nuclei and hence energy is released in accordance with Einstein’s mass-energy equivalence

  • Can be initiated in some large isotopes by the nucleus absorbing a neutron – additional neutron makes nucleus unstable and split into 2 smaller nuclei

  • Fission accompanied by the release of neutrons, which can be used to trigger further fissions in surrounding nuclei and produce a chain reaction

  • Fission triggered by neutron absorption is an example of artificial transmutation

  • Changing the one chemical element into another by artificial methods

  • Some isotopes of uranium (uranium-235 and 233) undergo fission and release neutrons and energy when they absorb a neutron

  • Studies show that slow neutrons are more likely to be absorbed by nuclei than fast neutrons – led to concept of neutron moderation and critical mass

  • Neutron moderation: using material containing small nuclei that doesn’t absorb neutrons – slows neutrons down

  • Critical mass: minimum mass required to sustain a fission chain reaction in a solid sphere of fissionable material

Release of energy in the process

  • Due to Einstein’s mass-energy equivalence, the mass defect between the resultant fission products and the heavy nucleus, produces energy

  • This energy appears in different forms: kinetic energy of the neutrons, gamma radiation – all these forms of energy are converted to heat by absorption in with the surrounding coolant and moderator

Calculating binding energy

  • Calculate mass defect – difference in mass between the nucleons and the atom (e.g. $\HeNucleus$)

  • mass of nucleons = 4.0026 u

  • mass of helium atom = 4.0331 u

  • mass defect = 4.0331 u – 4.0026 u = 0.0305 u

  • Calculate the nuclear binding energy using $E=mc^{2}$ (1 amu = 1.6605 x 10-27 kg)

  • 0.0305 x 1.6605 x 10-27 x (3 x 108)2 = 4.55 x 10-12 Joules

  • An uncontrolled fission chain reaction occurs at an increasing exponential rate – each fission initiates more than one fission and the number of fission reactions increases – WW2 bombs

  • Controlled fission reactions occur at a constant rate – each fission initiates one more fission – used in nuclear power stations

  • All nuclear power reactors contain the following elements:

Fuel Generally, this is slightly enriched uranium in the form of uranium oxide rods
Moderator Usually water (heavy or ordinary water) is used around the fuel to slow/moderate the neutrons in order to increase the probability they are captured by a nucleus
Coolant Water is circulated to remove heat from the reactor core
Control rods These are boron or cadmium rods that absorb neutrons. These rods are lowered int- the reactor to control the rate of reaction
Shielding Concrete and lead is used to surround the reactor core to protect the operators and environment from radioactive material escaping
Waste Since uranium is a very heavy atom, it has a high neutron-to-proton ratio. The neutron-rich daughter products of fission are very radioactive. 1/3 of spent fuel rods must be removed from the reactor core every year and stored for thousands of years before their radioactivity is at safe levels

Nuclear Stability & Nuclear reactions

  • Nucleons are held in the nucleus by the strong nuclear force, which acts between all nucleons and is significantly stronger than the electrostatic force, which tries to push protons apart in the nucleus

  • Strong nuclear force has a very short range, nuclei with more than 82 protons are unstable and radioactive

  • The strong force causes the individual nucleons to combine to form a nucleus. When a stable nucleus is formed, mass is lost and energy is released – called the mass defect and the energy released when the nucleus is formed is called the binding energy of the nucleus

  • Binding energy per nucleon is a measure of how tightly the average nucleon is bound to the nucleus and hence it is also a measure of the stability of the nucleus

  • The plot below is the binding energy per nucleon against mass number

  • The stability of the nucleus increases with mass number up to iron (Fe) and then decreases. This is why fusion of light elements and fission of heavy elements both release energy

  • If 2 light elements fuse together, they produce a more stable nucleus with a greater mass defect – hence, mass is lost when fusion occurs and energy is released

  • If a heavy nucleus split in half, the products would be more stable than the parent nucleus – this means they have a greater binding energy per nucleon, and mass would be lost and energy released during the reaction

  • Another aspect of stability is the neutron-to-proton ratio

  • The number of neutrons = number of protons, in small nuclei – but as size of nucleus increases, more neutrons are needed to maintain the stability of the nucleus – this is because adding neutrons adds to the strong nuclear attraction but not to the electrostatic repulsion

  • If an isotope falls off the line of stability, it will undergo a series of radioactive decays/transmutations until it returns to the line of stability as a stable isotope

  • If an isotope falls to the left of the line of stability, it would have too many neutrons to be stable and would emit beta particles to return to the line of stability

  • If an isotope falls to the right of the line, it would have too many protons and emit beta plus particles and/or alpha particles to move closer to the line of stability

Nuclear Fusion

  • A nuclear reaction in which 2 or more small nuclei combine to form a large nucleus

  • Requires some energy to start the process since electrostatic repulsion between nuclei must be overcome to bring them close enough together for the strong nuclear force to bind the nucleons together

  • This can be achieved by using very high temperatures e.g. at the core of the Sun, hydrogen nuclei are moving so fast that some head-on collisions result in the nucleons fusing together

  • Fusion would be a better reaction to use to produce nuclear power on Earth than fission, because fusion would have more readily available fuel (hydrogen) and doesn’t produce radioactive waste

  • However, maintaining high temperatures would provide technological difficulties

Artificial and Spontaneous nuclear reactions
  • A spontaneous transmutation occurs when an unstable nucleus (more than 83 protons or atomic mass > 209) emits an alpha or beta particle

  • An artificial transmutation is one that is artificially initiated – by bombarding the nucleus with a high-speed proton or a slow neutron

  • Rutherford fired alpha particles into nitrogen gas and detected a highly energetic particle that he identified to be a proton

  • If energy is to be released during a spontaneous or artificial nuclear reaction, the products must be less massive than the reactants – mass must be lost to provide the energy released in accordance to Einstein’s mass-energy equivalence

  • When calculating energy released:

    • Find the mass defect

    • Then use Einstein’s equation to determine the mass released in joules

    • Alternatively; if masses are given in atomic mass units (amu), multiply the mass defect by 931.5 MeV to obtain the energy released in MeV

Deep Inside the Atom

Subatomic Particles

  • A fundamental particle is a particle not made up of other particles

  • The atom was not as simple as scientists previously thought, protons and neutrons were found to be made up of quarks, and were not fundamental particles

  • Quarks are elementary particles that are the building blocks of hadrons; have a fractional charge, interact with strong force, obey Pauli exclusion principle

  • Evidence that protons & neutrons were not fundamental particles:

    • Beta-minus decay involved a neutron being transformed into a proton and beta-plus decay involved a proton changing into a neutron. Since electrons/positrons were emitted, these changes indicated an internal structure

    • Measurements of the magnetic moment of nuclei showed that the neutron had an associated magnetic field, suggesting that some moving charge(s) existed within the neutron

    • Inelastic scattering experiments between electrons and protons in 1969, conducted using high-energy particle accelerators, indicated there were tiny, scattering centres inside protons

Existence of other subatomic particles

  • In 1932, a positive electron (positron) was observed after a cosmic ray collision in a cloud chamber

  • Cosmic rays are high energy, charged particles that are produced in the Sun and other stars. They continually bombard the Earth’s atmosphere. In these collisions, energy is sometimes converted into mass in accordance with Einstein’s equation, and new particles are formed

  • In the 1930s and 40s, cosmic ray experiments led to the discovery of several new subatomic particles – the muon, kaon, and lambda – they were short-lived and had large masses

  • Large subatomic particles called hadrons to distinguish them from leptons (electrons and neutrinos)

  • Hadrons: heavy composite particles made up of quarks that are affected by the strong nuclear force

  • Leptons: elementary particles that aren’t affected by the strong nuclear force

The Standard Model of particle physics

Fundamental Forces

  • 4 fundamental forces in the Universe (from weakest to strongest)
  1. Force of gravity

  2. Electromagnetic force

  3. Weak nuclear force

  4. Strong nuclear force

  • Gravity has an infinite range and is an attractive force. The particle responsible is called the graviton, but it hasn’t been discovered yet. Gravity holds planets in their orbits, and the stars in their galaxies

  • EM force acts between charged particles – electrostatic force between nucleons. It has an infinite range, but is much stronger. The particle responsible for this force is the photon

  • The weak nuclear force is the force responsible for beta decay, where it is instrumental in changing neutrons to protons and vice versa. It has a very short range

  • The strong nuclear force acts at a very short distance between nucleons that holds them together in the nucleus

Force Acts on Relative strength Gauge bosons Range (m)
Gravity Objects with mass $10^{-38}$ Graviton Infinite
EM Objects with charge $10^{-13}$ Photon Infinite
Weak nuclear Quarks and leptons $10^{-2}$ W and Z boson $10^{-16}$
Strong nuclear between quarks & between nucleons 1 Pions (between nucleons) Gluons (between quarks) $10^{-15}$

Elementary Particles

  • all observed matter in the Universe is made up from elementary particles – 6 quarks, 6 leptons, & 5 types of bosons

Hadrons

  • hadrons are composed of quarks

  • protons and neutrons are also composed of quarks

  • Proton – 2 up and 1 down quarks

  • Neutron – 2 down and 1 up quarks

  • experience the strong nuclear force

  • there are 6 different quarks and 6 anti-quarks – they have fractional charges

Generation Quark Flavour Charge
1st Up +2/3
Down -1/3
2nd Charm +2/3
Strange -1/3
3rd Top +2/3
Bottom -1/3

Leptons

  • not influenced by strong nuclear force
Generation Lepton
1st Electron & electron-neutrino
2nd Muon & muon-neutrino
3rd Tau & tau-neutrino

Bosons

  • Unlike quarks & leptons, bosons do not obey the Pauli exclusion principle

  • There are specific bosons for each fundamental force and one for the Higgs field that is responsible for giving elementary particles mass

The Standard Model

  • The theory that describes the elementary particles of nature and 3 of the forces (excluding gravity) that operate between them

  • Shows that pairs of quarks can combine in quark-antiquark pairs to form particles called mesons, and in groups of 3 to form baryons

  • Meson: a hadron made up of 2 quarks (a quark-antiquark pair)

  • Baryon: a hadron made up of 3 quarks with different colour charges

  • Protons and neutrons are baryons as they are made up of 3 quarks

  • All stable particles that make up atoms and matter are formed form the 1st generation

  • 2nd & 3rd generation of elementary particles make up all the short-lived particles that are created in particle accelerators

  • Protons and neutrons also contain gluons that bind quarks together

  • When a quark emits a W boson, the quark changes flavour – the W boson rapidly decays into a beta particle and antineutrino

Advantages Disadvantages
Successfully replicated experimental results such as the gluon, Higgs boson, W&Z bosons, and the 6 quarks All particles discovered can be explained by the Standard Model Assumes neutrinos have 0 mass Does not include gravitational force, dark matter, or dark energy

Particle Accelerators

  • Test predictions of the standard model by colliding particles together and studying the product particles that form

  • Use high voltages to accelerate charged particles to give them enough kinetic energy to initiate nuclear reactions

  • The largest particle accelerator is the Large hadron Collider at CERN

The Cyclotron

  • Charged particles travel in an evacuated space between 2 dees (d-shaped magnets) which forces them to travel in a circle
  • Accelerated by a high-voltage alternating electric field applied across the dees
  • Increasing speed causes the particles to spiral outwards until they reach the edge of the magnetic field, and are then deflected to their target
  • Relatively cheap but cannot be used to accelerate large particles

Linear Accelerator (LinAc)

  • Consist of a large number of evacuated, hollow metal cylinders to accelerate the charged particle as it moves between the cylinders

  • These drift tubes are given the same charge as the particle being accelerated while the particle in inside it

  • The next tube carries the opposite charge, to accelerate the particle towards it and across the gap

  • Inside the tubes, although charged, the net electric field is 0, so they only accelerate across the gaps between the tubes

  • Easier to construct than others, less expensive, do not need magnetic fields or large diameter for construction

  • Cannot be used to study large particles

Synchrotron

  • Uses a magnetic field to keep accelerating particles moving in a circle of constant radius

  • They have several linear accelerators with magnetic deflection sections at intersections to curve the speeding particles into the next straight section

  • A disadvantage is that is can only accelerate one packet of charged particles at a time

  • They can be used for large particles since they can produce very high energies which will provide better collisions

  • Energy losses are huge, very expensive to build, need expensive magnets and a large diameter space

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