Light

q go back

Hey Bros - Dr Ormande Waters, 5th June 2024

You can bring out your torches and stab vampires and Frankenstein and other monsters with the other peasants - Dr Ormande Waters, 5th June 2024

Galileo Galilei

We know where the Titanic is....imagine in 500 years, the Titanic is a legend. The Titanic doesn't exist, it's a myth. - Dr Ormande Waters, 5th June 2024

Before you submit reports, no you cannot use chat gtp - waters

• Ole Rümer: proposed using Jupiter’s moons to find c

Light

• It acts as a particle and a wave
• Newton: Light is corpuscular (particles) - no experiment
• Huygen - wavelike (no experiment) - pretty good

1801 Thomas Young: Double Slit Experiment

One at a time, dear boy - Dr Ormande Waters, 5th June 2024

• diffraction/interference occurs
• thus it is a wave
• proof beyond doubt that light is wavelike

“i’m gonna shoot you” “smile when i shoot you”

I KNEW IT DR WATERS DISPROVED THE VACUUM THING

Black Body Radiation

• An object which perfectly absorbs all radiation incident upon it, is a black body
• There is no reflection of transmission of the incident radiation
• NB: this is not saying that no energy being emitted by the object, as all objects above 0 K emit energy
• All objects emit energy across the entire spectrum of the EMR spectrum
• However there is a peak wavelength which they will emit at
• As the temperature of an object increases, the peak wavelength of emission waves towards shorter wavelength
• On a $\lambda$ vs $I$ graph, ${\lambda }_{peak}$ moves to left as $I$ increases
• $I$ at all $\lambda$ increases as spectral lines do not cross
• Ultraviolet catastrophe - so called because classical physics modelling light as wave-like model could not explain why the ${\lambda }_{peak}$ of energy emitted by hot objects did not progress significantly in the UV portion of the EMR spectrum (or x-rays or gamma rays)
• Cavity radiation as a model of a black body
• Planck: modelled cavity radiation as being whole number multiples of a very small, discrete, amount of energy (what we now call quantum)
• Plank did not believe that energy was quantised and believed his constant was an heuristic device which would eventually be explained away

$\text{Plank’s Constant: }6.63\times 10^{-34}\text{ J s}$

“they’re not as black as we used to think” - dr ormande waters, 10 june 2024

Some Equations

$E=hf$

• $E$ is energy
• $f$ is frequency
• $h$ is Plank’s constant $6.63\times 10^{-}34\text{ J s}$

$v=c=\lambda f$

• wave equation

$\therefore E=\frac{hc}{\lambda }$

$1\text{ eV}=1.6\times 10^{-}19\text{ J}$

Photoelectric Effect

• Used to prove light is a particle
• It is observed that high frequency results results in the ejection of electrons from a polished metal surface
• Initially agrees perfectly with wave model of light, i.e. energy, as a wave, is transferred to metal and electrons have sufficient energy gained to leave the metal
• However, it was found that if the intensity of the light increased, then number of electrons ejected increased
• If you reduce the frequency of light, then less electrons for same intensity
• If you reduce the frequency too much, then there are no electrons ejected
• DIdn’t matter what the intensity was, or the time of incident, no electrons were produced beneath the threshold of frequency, and this value was different for different metals
• Photoelectric effect is as much about how it cannot be explained by wave model of light as how it can be explained by light being quantised, i.e. particle light in its nature
• From E = hf, it is possible to determine the minimum energy (and frequency of light) required to eject electrons from any given metal
• Once you are at or above threshold frequency, greater intensity = more electrons ejected because the number of photons is greater at a greater intensity
• Electrons are ejected with a range of energies
• Since there is a minimum amount of energy required to remove electrons from a metal and work is done on the electrons then each metal has a work function, W, which is the minimum energy required to release electrons from that metal
• Any energy above W, is converted to the kinetic energy of the electron
• Since a there is a range of energies of electron ejected for a given metal and frequency, there is a characteristic maximum kinetic energy (and thus maximum intensity of light) associated with from a given metal at a given frequency
• $E_{k_{max}}=hf-W$
• Metals consist of a cationic lattice in a sea of delocalised electrons
  • Electrons are localised with a range of energies of bonds
• From the least bound electron at the surface of a metal, to more tightly bound electrons further in, to very strongly bound electrons in the energy levels (electron shells) of the cations

Einstein Solved the problem

• Proposed that energy is quantised and that each electron had a minimum amount of energy required to release it from a metal
• Thus, light of a given minimum quantity of energy was required to do so (remove those electrons

17th June 2024 quotes

• “don’t be bohr-ing”
• “einstein is a lazy dog”

Photoelectric cell:

• Electrons also known as photoelectrons
• A photoelectric current is a current resulting from the motion of photoelectrons
• Stopping voltage refers to the voltage required to prevent the most energetic photoelectron released by light of a given frequency from reaching the cathode
• Gradient of electron energy vs light frequency is equal to Plank’s constant

Spectra

• White light passed through prism gives a continuous spectrum
• When analysing the spectrum of light from the sun, a large number of dark lines were observed
• Fraunhofer lines - if you heat up a cold gas of an element, then a spectral analysis of the gas will show the production of coloured lines, which always occur in the same position in the spectrum, and are different for different elements (and are diagnostic for the presence of particular elements)
• If white light is passed through the cold gas of an element, then dark lines are observed in the same positions as the colours produced when the gas is heated
• Absorption spectrum - produced by passing white light through a cold gas - gives a coloured spectrum with dark lines (line spectrum) or bonds (bond spectrum)
• Emission spectrum - produced by heating up the gas of an element - gives a dark background with coloured lines/bands
• Continuous spectrum - produced by white light (all colours)
• bands are thicker than lines
• it was noted for hydrogen that the portion of dark lines in the absorption spectrum were exactly the same as the portions of the coloured lines in the emission spectrum

Bohr’s Model of the Atom

• Electrons are in circular orbit in electron shells around the nucleus of an atom
• Atoms have several electrons shells, which are situated at different radii from the nucleus, and the radii of the shells are different for different atoms
• Electrons can only be in an allocated shell (no clouds)
• Electrons are held in circular motion by the centripetal force exerted by the nucleus
• But they cannot fall into the nucleus or lose energy due to centripetal force
• Electrons can transition between shells (or be ionised) but cannot be “between shells”
• Atoms will be in their “ground state”, i.e. all electrons are as close to the nucleus (are filling the shells closest to the nucleus)

“put your fingers in the hole, ladies and gentlemen” - dr waters 20 june 2024

de Broylie

$mc=\frac{h}{\lambda }$ $\therefore m=\frac{h}{\lambda c}$

• Beta decay uses 0.9c for value