The Wave Model successfully predicts light will:
- travel in straight lines at constant speed.
- reflect of surfaces with the angle of incidence equal to the angle of reflection.
- have an intensity that follows and inverse square law with distance.
- have momentum and exert pressure on surfaces that it shines on.
- have kinetic energy which is transferred to heat when a substance absorbs the light.
- show partial transmission and reflection then it reaches a boundary between two substances. The
amount of reflection increases as angle of incidence increases is a correct prediction.
- change direction (refract) when it passes from one material to another and changes speed. The
ratio sin i/sin r is a constant.
- diffract when it passes around an object or through a gap.
- show constructive and destructive interference when light paths overlap.
- cause coloured effects and is due to a difference in the frequency of the waves.
- be able to be polarized.
The wave model has difficulty explaining:
- the increase in the angle of refraction when the frequency of the light increases.
Diffraction of Light
Diffraction is the change in the direction of light at passes by an edge or through a gap.
Diffraction is strong when the wavelength of the light/wave is greater than or equal to the size of the obstacle or opening.
The smaller the gap and the longer the wavelength, the greater the amount of diffraction.
2.
Young's experiment
When light with the same wavelength and phase passes through a double slit and falls on a screen, a series of noses and antinodes are seen.
The longer the wavelength, the closer the slits and the greater distance to the screen, the further apart are the nodes and antinodes.
Photoelectric Effect
When EM waves with a high enough frequency shines on a negatively charged metal that is sufficiently reactive, the light is absorbed and electrons are knocked from the metal.
The threshold frequency is the lowest frequency EM wave that will cause electrons to be ejected.
If the frequency is lower than the threshold, no electrons are ejected even if the intensity of the light is increased.
Einstein explained this behaviour by saying EM waves are not smooth and continuous but come in little packets called photons.
The energy needed to raise an electron to the surface of the metal is called the work function.
Each electron is ejected by only one photon. If the energy of the photon is less than the work function of the metal, the electron will not be ejected.
The energy of an ejected electron is equal to the energy of the photon absorbed minus the work function.
The energy of the photon is equal to Planck's constant times the frequency of the photon.
The momentum of a photon is equal to Planck's constant divided by its wavelength.
Matter Waves
The wave/particle duality says waves have particle like properties and particles have wavelike properties.
That particles could behave like waves was suggested by Louis de Broglie. He suggested correctly that the wavelength of a particle is equal to Plank's constant divided by its wavelength.
The wave like properties of EM waves is most apparent for radiowaves because a radiowave photon has a minute amount of energy and many are needed to transfer a worthwhile amount.
The particle like properties of EM waves are most apparent for gamma rays because the wavelength of gamma rays is very short and each gamma ray has a large amount of energy so the arrival of one is a sizeable event.
Electrons have wavelength of around 10-10 m. When electrons are aimed at crystals, the layers of atoms act as gaps for diffraction and the emerging electrons paint a diffraction pattern like light does.
Energy Levels of Electrons
Even though an orbiting electron is an accelerating charge and should give off EM waves, it doesn't when orbiting in one of the allowed energy levels.
When an orbiting electron drops from a higher energy orbit to a lower one, one photon is given off.
The energy of the photon is equal to the energy difference between the two orbits.
Orbiting electrons only accept the energy from a collision with another electron that will take it up to one of the allowed energy levels.
When an electron in a high energy level returns to the lowest level it may do so in one step or go temporarily to any of the intermediate energy levels giving off several photons on the way down.
The set of wavelengths given off from a substance is its emission spectrum
A photon gives up all of its energy or none of it to an orbiting electron. So the orbiting electron will only absorb a photon if it has just the right amount of energy that will send the orbiting electron to one of the higher energy levels.
3.
Shining the complete spectrum of light onto a sample of a substance will result in some of the photons absorbed and removed from the spectrum. This results in a dark line in the absorption spectrum.
One nanometre is equal to ten to the minus nine metres.
The energy of a photon in eV is equal to 1240 divided by its wavelength in nanometres.
Motion of charges in Electric fields
The electric field between two charged parallel plates is uniform is strength, directed from the positive plate to the negative plate and equal to the potential difference between the plates divided by the distance between the plates.
The electric force on a charged particle in an electric field is equal to the field strength times the size of its charge.
The charged particle, when moving between the plates has a constant acceleration at right angles to the plates and a constant velocity parallel to the plates.
The charged particle follows a parabolic path between the plates.
