Quantum phenomena

Student revision notes

Change of quark character:

  • B- decay: d quark into a u quark

  • B+ decay: u quark into a d quark

  • Energy and momentum are conserved in interactions

Photoelectric effect

  • Photon energy = hf or hc/λ

  • One photon interacts with one electron

  • Work function (ϕ) is defined as the minimum energy needed to release an electron from the surface of a metal

  • Electron is released if hf≥ϕ

  • Remaining energy is the maximum kinetic energy of electron

  • Threshold frequency is where photons have just enough energy to provide the work function energy (f0) = minimum f required to eject photoelectron. So hf0=ϕ => f0=ϕ/h

Photoelectric equation

  • hf=ϕ+KEmax

  • Stopping potential - the potential difference needed to stop the fastest moving electrons

  • Work done to p.d. in stopping fastest electrons = the energy they were carrying

  • eVs = KEmax

  • (e=1.6×10^-19 and Vs=stopping potential)

  • Electronvolt - energy gained by an electron moved through a potential difference of 1V.

  • Ionised - an electron is removed from the atom

  • Excitation - electron gains energy and is promoted up to a higher energy level

Fluorescent tubes

  • High voltage applied to tube accelerates fast moving electrons that ionise some mercury atoms, producing more free electrons.

  • Free electrons collide with electrons in other mercury atoms

  • Mercury atoms gain energy through electron impact, exciting electrons to higher energy levels

  • Mercury atoms emit UV photons through de-excitation

  • Coating on inside of tube absorbs UV photons, exciting its electrons to higher energy levels

  • When these electrons de-excite they move down energy levels and emit lower energy photons to form visible light

Line spectra and energy levels

  • Electrons in an atom can only exist in certain well-defined energy levels

  • When electrons de-excite they move down energy levels and emit photons

  • Since these transitions are between definite energy levels, only certain energy changes allowed

  • So the energy of each photon emitted can only take a certain allowed value, which corresponds to a specific wavelength

  • Light with this specific wavelength is a line on a spectrum

  • hf=hc/λ=ΔE=E2-E1

  • Different transitions produce different photons/λ

  • Smaller ΔE = longer wavelength, smaller frequency

Why there is KEmax + range

  • Photon energy is constant

  • Photon loses all its energy in one interaction (one photon interacts with one electron)

  • Max obtained from hf-ϕ

  • Electrons beneath surface must do work (use energy) to reach surface then ϕ is required —> leaves less energy for KE once it is released - hence range

Wave particle duality

  • EM radiation - wave diffraction and interference patterns but particle photoelectric effect

  • Electrons - wave electron diffraction but particle deflection in magnetic/electric fields

  • de Broglie wavelength - λ = h/mv with m being momentum

  • Momentum increases, de Broglie wavelength decreases so the angle of diffraction in an electron diffraction pattern gets smaller

  • Only get diffraction if a particle interacts with an object of about the same size as its de Broglie wavelength

Knowledge and understanding changes over time

  • First hypothesised to explain observations

  • Other scientists evaluate de Broglie's theory (process known as peer review) before publication

  • Tested with experiments

  • Once enough evidence was found to back it up, theory was accepted as validated by scientific community

  • Photon energy is constant

  • If photons have less energy than ϕ, they cannot provide sufficient energy to release electrons

  • Electrons are easier to obtain and accelerate than protons

  • Wave theory predicts photoelectrons will be emitted with any frequency

Intensity increase

  • KE not changed - energy of photon not dependant on intensity so electron does not gain extra energy

  • Intensity increase, number of photons per second increase

  • One photon interacts with one electron so more interactions —> number of electrons released per second increases

  • Current = rate of flow of charge

  • Light below f0 do not release electrons because photons carry quanta of energy

Mercury low pressure

  • Keeps mercury as vapour

  • Allows electrons to accelerate without being impeded/absorbed by nitrogen or oxygen

  • Must be large distance between collisions to allow electrons to gain enough energy

Facts and definitions

  • Work functions units - J

  • The electron volt (eV) - the energy gained by an electron moved across a potential difference of 1V

  • Ionisation energy - energy required to completely remove an electron from an atom in its ground state

  • Ground state - the lowest energy state of an atom

  • Fluorescence - high energy (UV) photons are absorbed and lower energy photons (longer λ) are emitted in the visible part of the spectrum

  • Wave particle duality - particles (e.g. electrons, light) behave sometimes as particles and sometimes as waves

  • Experiment showing waves behaving as particles - photoelectric effect

  • Experiment showing particles behaving as waves - electron diffraction

  • Momentum (p) - mass x velocity (p=mv)

  • Units of momentum - kgms^-1

  • Stopping potential - the potential difference needed to stop the fastest moving photoelectrons travelling with kinetic energy KEmax in the photoelectron effect

  • Particle diffraction effects - a particle (e.g. an electron) will diffract when the size of the de Broglie wavelength is roughly the same size as the object causing the diffraction