The Photon Model
Electromagnetic radiation travels through space as a continuous wave, with properties such as diffraction and interference providing evidence for this model. However, when electromagnetic radiation interacts with matter, it interacts as discrete energy quanta called photons.
The energy, E, of photon is directly proportional to the frequency, f, of electromagnetic radiation
E = hf = hc/λ
Where h is Planck constant 6.63 × 10-34.
The energy of a photon is very small when measured in joules, so the Electronvolt (eV) is a more appropriate unit of energy to use for photons. 1 Electronvolt is defined as the energy transferred when an electron travels through a potential difference of 1 volt.
The photoelectric effect
When electromagnetic radiation is shone on the metal, electron are released from the surface of the metal. This is known as photoelectric effect.
The photo electric effect provides evidence for a particulate nature of electromagnetic radiation.
Einstein’s photoelectric equation
During the photon-electron interaction, energy must be conserved. Einstein equated the energy of the incident photon with the energy required to release the electron, to produce the photoelectric equation
hf = Ø + KEmax
Where Ø is the work function of metal and KEmax is the maximum kinetic energy of the released electron.
We can explain this equation;
When a photon of energy hf hits the metal plate then it is absorbed by an electron. Some of the energy is used in escaping form the metal and the rest remains as kinetic energy of the electron.
A single photon can only interact with single electron.
If the photon is absorbed by an electron that is lower in the energy well, the electron will have less K.E. than K.Emax.
If the incident radiation has a frequency equal to the threshold frequency, f0, then the K.E. of the electrons is zero.
Hf0 = Ø
A line spectra is a display of the wavelength/frequencies emitted from light source.
The line spectra that shows the composition of light emitted by hot gases are called emission line spectra.
The line spectra observable when white light passed through cool gases are called absorption line spectra.
Atoms at different level has different line spectra as they have different spacing between their energy levels. When an electron charges its energy from one level E1 to another E2, it either emits or absorbs a single photon; the energy equals;
Photon energy = ΔE, hf = E1 – E2
Or, hc/λ = E1 – E2
Frequency is calculated by;
F = E/h
The wave length is calculated by; λ = c/f
Duality of light
- Light interacts with matter as a particle- the photon. The evidence for this is photoelectric effect.
- Light travels through space as a wave. The evidence for this is diffraction and interference of light using slits.
De Broglie Wavelength
De Broglie imagined that the light travel through the space as wave. He purposed that the wave like property can be explained by its wavelength.
Which is given by;
Or, λ = h/mv
Where h is Planck constant and p is momentum.
Diffraction is a property of wave. In an electron diffraction tube, the electrons from the heated filament are accelerated to high speeds by the large p.d. between cathode and anode. A beam of electrons passes through the polycrystalline graphite. The electron passes through it produce diffraction rings. This experiment shows that electron travels as wave.