Photoelectric effect

diffraction of electrons

• a narrow beam of electrons in a vacuum tube is directed at a target material (e.g graphite) which acts as a diffraction grating - as the electrons move in between the layers they spread out

• the electrons are diffracted in certain directions only

• they form a pattern of rings on a fluorescent screen at the end of the tube

• bright rings of maximum intensity occur where interfere constructively

• beam produced by attracting electrons from a heated filament to a positively charged metal plate which has a hole

• speed of electrons increased by increasing potential difference - this decreases the diffraction rings as the de broglie wavelength decreases - less diffraction because shorter wavelength compared to spacing in graphite layers

line spectra

• the energy levels of an atom are discrete and specific to that atom

• the energy level transitions are discrete

• photons emitted with discrete energies that are specific to that atom

• the wavelengths of the line spectrum are characteristic of that element

energy levels

• ground state - the lowest energy level an electron can occupy

• ionisation level - electron is just free / released from atom

why energy levels are negative

• the ionisation level is 0 energy reference - for the electrons to become free / reach 0 energy, energy must be supplied

• absorbing a photon can cause excitation if the energy of the photon is equal to the energy level difference between the final and the initial level of an energy level transition

ionisation

atomic electron gains sufficient energy needed to leave the atom

ionisation energy

the minimum energy required to remove an electron from an atom in ground state

excitation

atomic electron gains energy and moves to a higher energy level

how excitation / ionisation occur

• caused by atom absorbing a photon or by an atom colliding with a free electron, both transferring energy

dexcitation

atomic electron loses gained energy and moves down back to a lower energy level, emitting a photon in each transition - with energy equal to the energy difference between the levels the electron moves between

• this may be indirectly back to its original energy level if there are intermediate energy levels

• directly if there are no intermediate energy levels

• indirect produces photons with a range of lower frequencies / energies / longer wavelengths than what was initially absorbed

photons must have exact energy to cause excitation

• absorbed by atom in a one to one interaction

• must transfer their whole energy in this single interaction

• energy levels discrete and energy level transitions require exact energies

fluorescent tube

• a beam of free electrons passing through tube collide with electrons in the mercury atom - each free electron transfers some of its kinetic energy to one atomic electron in one atom - this is sufficient enough to excite it to a higher energy level

• each excited electron moves back down to ground state, emitting a photon on energy equal to the difference between the two levels it moves between in each transition - UV emitted

• each coating atoms absorbs a UV photon, causing excitation

• each atomic electrons of coating move indirectly back down to previous lower level in de-excitation, each emitting lower a energy photon, some in the visible part of the spectrum

why there is low pressure and high pd in fluorescent tube

• low pressure to allow for sufficient distance between collisions for the electrons to gain enough kinetic energy for the required excitations to occur

• high pd to accelerate the electrons more to sufficient speeds so that they are at suffient energies to cause UV emission upon de-excitation

photoelectric effect on metal plate given a negative charge.

• EM radiation is incident - the emission of electrons from the surface of the metal occurs

• a minimum energy of photon is required to cause electrons to be removed from the metal surface - the work function - this depends on the metal

• a photon must provide at least this energy to one electron in one interaction

• the emission of a photoelectron occurs without delay

• excess energy gained by the electron becomes the kinetic energy of the photoelectron - emitted with a range of KE up to a maximum value, depending on the incident photon energy

• photon energy is directly proportional to the photon frequency $E = hf$

• so work function corresponds to a minimum frequency - threshold frequency

• $$Ephoton=\phi+Ek\max$$

• surplus electrons remaining on the the plate decrease with time as emitted photoelectrons carry away negative charge

• intensity = photon energy x number of incident photons / area x time

• increasing intensity at the same frequency means that number of photons incident per second increases

• each photon causes emission of one electron so intensity is also proportional to the number of released photoelectrons per second, provided frequency exceeds threshold

• more electrons released from plate every second so loses charge more rapidly.

why kinetic energy of photoelectrons can range up to a maximum value

• at surface, only work function is required to remove electron from metal - have max ke

• deeper electrons require greater energy than work function to get to surface and be removed from metal - have less than max ke

• for fixed photon energy

photoelectric current and stopping potential

I = e x number of photoelectrons released / time

• constant photoelectric current reached when all photoelectrons released each second reach anode due to anode pd

• when the direction of the potential difference is reversed and it is sufficient enough, electrons released from the metal can be attracted back

• at the stopping potential, Vs, photoelectrons with the maximum kinetic energy can be stopped - all of its kinetic energy, equal to eVs would be lost in doing work against pd

• as V approaches stopping potential, photoelectrons lose kinetic energy in crossing to anode - fewer of the photoelectrons released per second have sufficient initial kinetic energy to reach anode - photoelectric current decreases

em radiation incident on positively charged plate

• photoelectric effect involves the emission of electrons which are negatively charged

• losing any electrons would mean losing negative charge, therefore gaining positive charge instead of losing charge

wave particle duality of light

• wave behaviour - diffraction

• wave behaviour - interference

• particle behaviour - photoelectric effect

matter waves and de Broglie wavelength

• beam of electrons deflected in a magnetic field - particle property

• beam of electrons diffracted and interfere - wave property

• only particle behaviour would produce a small spot or particles would scatter randomly

• de broglie wavelength = h / momentum

• de broglie wavelength inversely proportional to momentum

• fluorescence due to collision with an atomic electron is a particle behaviour

• acceleration is a particle behaviour