1. About these slides
These slides are used as part of my lessons and shouldn’t be considered comprehensive
There’s no excuse for not turning up to lessons!
These slides use material from elsewhere on the assumption of fair/educational use
If you own the copyright to any of this material and want it credited/removed please contact me
These slides may contain errors
Use at your own risk!

3. Wave-particle duality
You should be familiar with the idea that light can be thought of as a wave or a particle
The particle is called a __________
The energy of this particle is given by the equation
E=hf
Where h is ________ constant and f is the frequency of the light
Rewrite the equation in terms of wavelength, l

4. Einstein

5. Evidence for wave-particle duality
One piece of evidence that light can behave as a wave or a particle is the photoelectric effect
This was discovered by Hertz as a side effect of his work on radio waves
He noticed that metals emit electrons when electromagnetic radiation of a certain frequency is directed at a metal

6. The photoelectric effect in action
Incident Radiation
electrode
gold leaf
zinc plate
Image from tap.iop.org

7. Photoelectric effect
The photoelectric effect gives rise to the following observations:
Emission of electrons only takes place above a certain threshold frequency of incident electromagnetic radiation. This minimum frequency is dependent on the metal.
If light was a wave then electrons would be emitted at any frequency, as electrons would gradually gather energy from the waves regardless of their frequency

8. Photoelectric effect continued
The photoelectric effect gives rise to the following observations:
Electrons are emitted as soon as the source of electromagnetic radiation is switched on, no matter what the intensity of the radiation.
If light was a wave then electrons would gather energy more quickly, and be emitted sooner, by high intensity light sources.

9. Photoelectric effect continued
The photoelectric effect gives rise to the following observations:
The number of electrons emitted per second is proportional to the intensity of the incident radiation, unless its frequency is less than the threshold frequency, in which case emission isn’t observed

10. Particles as waves

11. Electron diffraction
Image from

12. Electron diffraction
If electrons were acting as particles we would see them either pass straight through the crystal, or bounce off
Instead we see an interference pattern
Exactly the same as if electrons are acting as waves
It is possible to do the Young’s slits experiment and see an interference pattern even if the electrons are fired one at a time

13. de Broglie
In 1923 de Broglie was the first to suggest that matter could be a wave
He said that the de Broglie wavelength, l, of a particle is related to its momentum, p, by the equation
We know that momentum = mass x velocity so

14. Question Calculate the de Broglie wavelength of
An electron moving at 2.0 x 107 ms-1
A proton moving at the same speed
I weigh 85kg and can run at 6 ms-1 what would my de Broglie wavelength be?

15. Question Calculate the momentum and speed of
An electron that has a de Broglie wavelength of 500nm
A proton that has the same de Broglie wavelength

16. ✔

17. The photoelectric effect
We saw this last lesson
As long as light is above a certain frequency it can eject electrons from a metal surface
This can be explained as the photon having a certain energy, E = hf
It therefore follows that there is a minimum energy needed to eject an electron from a metal surface at zero potential
This is the work function, f

18. Explaining the photoelectric effect
In order to explain photoelectricity Einstein said that:
Electrons must be absorbing a single photon in order to escape from the metal
This photon transfers energy given by E=hf
If the photon has less energy than the work function, f, of the metal the electron cannot escape
The work function is the minimum energy required for an electron to escape the metal surface

19. Photoelectric effect
We can calculate the maximum kinetic energy of an electron ejected by a photon with energy hf
Ekmax = hf – f
So emission will take place as long as hf > f
Which means there is a threshold frequency above which an electron is emitted:

20. Plotting Ekmax against frequency
Since EKmax = hf – f we can plot a graph of the form y = mx + c
So if we plot EKmax against f we get a straight line
EKmax /J
What is the gradient?
What is the intercept on the x axis?
What would the intercept on the y axis be?
f / Hz

21. Questions
Why does photoelectric emission only take place above a certain frequency of incident radiation?
Calculate the frequency and energy of a photon of wavelength
450nm
1500nm

22. Questions The work function of a metal plate is 1.1 x 10-19J
Calculate:
The threshold frequency
The maximum kinetic energy of electrons emitted from this plate when light of wavelength 520nm is directed at the metal surface

23. Electron volts We’ve already encountered the electron volt
It is defined as the unit of energy equivalent to the work done when an electron is moved through a potential difference of 1 volt and is equal to 1.6 x 10-19J

24. Ionisation An ion is a charged atom
Ionisation is the process of making an ion by adding or removing electrons
The energy to do this can be provided by electricity, heat, light or by collisions between alpha, beta or gamma radiation and an atom

25. Energy levels in atoms
Electrons surrounding atoms are like standing waves
They have certain allowed energy levels
It is the movement between these levels that happens during excitation
The lowest energy state of an atom is its ground state
If an electron moves into a higher energy level the atom is in an excited state

26. Excitation
In excitation an electron can be moved from an inner shell to an outer shell
This only happens at specific excitation energies which are dependent on the atom and correspond to its excited states
This is excitation by collision – one electron hits another and promotes it to a higher energy level

27. Excitation continued
The excitation energy will always be less than the ionisation energy
There are a number of excitation energies for each atom
These correspond to the difference between different shells
Electrons can also ‘jump’ more than one shell at a time

28. Energy Levels Example: Mercury
Ionised 0.00 eV
-1.59 ev
-1.60 eV
-2.51 eV
-2.71 eV
-3.74 eV
-4.98 eV
-5.55 eV
-5.77 eV eV
This is excitation by absorption of a photon. If it has exactly the right frequency it promotes the electron to a higher energy level

29. De-excitation The excited states of an atom are unstable
They have a gap in a low energy electron shell
Electrons from a higher shell can drop into this lower level, emitting a photon in the process

30. De-excitation Example: Mercury
Ionised 0.00 eV
-1.59 ev
-1.60 eV
-2.51 eV
-2.71 eV
-3.74 eV
-4.98 eV
-5.55 eV
-5.77 eV eV
This is fluorescence
An atom in an excited state can de-excite by emitting photons of the same or lesser energy than the one that excited it
In this case the photons have energies of 0.79 eV and 4.67 eV

31. Calculating the frequency of photons
Since the photon emitted comes from the transition between two energy levels it will have an energy, E given by:
E = E1 – E2
Where E1 is the energy of the higher level and E2 the energy of the lower
We also know that E = hf, so we can calculate the frequency of the emitted photon

32. Fluorescent Tubes
Fluorescent tubes contain mercury vapour and have a fluorescent coating on the inner surface
Filament Electrodes
Mercury Vapour

33. Fluorescent Tubes When a tube is turned on:
Ionisation and excitation of mercury atoms occurs as they collide with each other and with electrons
Photons are emitted at UV and visible frequencies
UV photons are absorbed by atoms in the fluorescent coating
Coating atoms de-excite and emit visible photons
A range of coatings is used to give a ‘white’ light

34. Questions
Ionised 0.00 eV
-1.59 ev
-1.60 eV
-2.51 eV
-2.71 eV
-3.74 eV
-4.98 eV
-5.55 eV
-5.77 eV eV
How much energy is needed, in Joules, to excite the atom to its highest excitation level?
How many different energies could photons released by a mercury atom in the 5.46 eV excited state have?

35. Question
An atom absorbs a photon of energy 3.8 eV and subsequently emits photons of energy 0.6 eV and 3.2 eV
Sketch an energy level diagram to represent these changes
Describe what is happening to the electrons in the atom during this process
What is the frequency of the photons emitted?

36. Answer

37. Spectral Lines
Since each element has different energy levels, and therefore transitions between levels, each element will emit different frequencies (wavelengths) of electromagnetic radiation
This means the photons emitted are characteristic of that element

38. Mercury
Image from:

39. Hydrogen
Images from

40. Question
A mercury atom de-excites from its 4.9 eV energy level to the ground state
Calculate the wavelength of the photon released
c = 3.0 x 108 ms-1, e = 1.6 x C, h = 6.63 x Js