1. How do we know the structure of the atom?

2. The famous Geiger-Marsden Alpha scattering experiment
In 1909, Geiger and Marsden were studying how alpha particles are scattered by a thin gold foil.
Thin gold foil
Alpha source

3. Geiger-Marsden
As expected, most alpha particles were detected at very small scattering angles
Thin gold foil
Small-angle scattering
Alpha particles

4. Geiger-Marsden
To their great surprise, they found that some alpha particles (1 in ) had very large scattering angles
Thin gold foil
Small-angle scattering
Alpha particles
Large-angle scattering

5. Explaining Geiger and Marsdens’ results
The results suggested that the positive (repulsive) charge must be concentrated at the centre of the atom. Most alpha particles do not pass close to this so pass undisturbed, only alpha particles passing very close to this small nucleus get repelled backwards (the nucleus must also be very massive for this to happen).
nucleus

6. Rutherford did the calculations!
Rutherford (their supervisor) calculated theoretically the number of alpha particles that should be scattered at different angles. He found agreement with the experimental results if he assumed the atomic nucleus was confined to a diameter of about metres.

7. Try this problem
In a Geiger Marsden scattering experiment, a nucleus has a diameter of (m) 1.4 x The alpha particle has a mass of (kg) 6.64 x What is the kinetic energy of the alpha particle that has a de Broglie wavelength equal to the diameter of the nucleus? How fast is it traveling?
Lambda = h/p E = p2 /2m = h2 /(2 m lambda2 ) = 1.7 x J v = h/( m lambda) = 7.1 x 106 m/s

8. And this one
The same alpha particle is fired at a gold nucleus (Z=79) How close does the alpha particle get to the nucleus?
KE far away = PE close up KE = 1.7 x = k q Q/r r = 9 x 109 (2)(79)(1.6 x C)2/ 1.7 x = 2 x 10-13

9. Rutherford did the calculations!
That’s times smaller than the size of an atom (about metres).

10. Stadium as atom
If the nucleus of an atom was a ping-pong ball, the atom would be the size of a football stadium (and mostly full of nothing)!
The model has electrons orbiting like planets.
Nucleus (ping-pong ball

11. Limitations of this model?
According to the theory of electromagnetism, an accelerating charge (and the orbiting electrons ARE accelerating centripetally) should radiate energy and thus spiral into the nucleus.

12. Evidence for atomic energy levels

13. Evidence for atomic energy levels
When a gas is heated to a high temperature, or if an electric current is passed through the gas, it begins to glow.
cathode
anode
electric current
Light emitted
Low pressure gas

14. Emission spectrum
If we look at the light emitted (using a spectroscope) we see a series of sharp lines of different colours. This is called an emission spectrum.

15. Absorption Spectrum
Similarly, if light is shone through a cold gas, there are sharp dark lines in exactly the same place the bright lines appeared in the emission spectrum.
Light source
gas
Some wavelengths missing!

16. The Rydberg Equation
Balmer and Rydberg (this version) came up with a formula to show all these energies, but no explanation as to why: Where R is the Rydberg constant x 107 m-1 And the energy is E = hc/l

17. Answer this one:
What is the energy of a photon from the Rydberg Equation using n=3?

18. Why?
Scientists had known about these lines since the 19th century, and they had been used to identify elements (including helium in the sun), but scientists could not explain them.

19. At school they called me “Bohr the Bore”!
Niels Bohr
In 1913, a Danish physicist called Niels Bohr realised that the secret of atomic structure lay in its discreteness, that energy could only be absorbed or emitted at certain values.
At school they called me “Bohr the Bore”!

20. The Bohr Model
Bohr realised that the electrons could only be at specific energy levels (or states) around the atom.

21. The Bohr Model
We say that the energy of the electron (and thus the atom) can exist in a number of states n=1, n=2, n=3 etc. (Similar to the “shells” or electron orbitals that chemists talk about!)
n = 1
n = 2
n = 3

22. The Bohr Model
The energy level diagram of the hydrogen atom according to the Bohr model
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
High energy n levels are very close to each other
Energy eV
Electron can’t have less energy than this
-13.6

23. The Bohr Model
An electron in a higher state than the ground state is called an excited electron.
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
High energy n levels are very close to each other
electron

24. Atomic transitions
If a hydrogen atom is in an excited state, it can make a transition to a lower state. Thus an atom in state n = 2 can go to n = 1 (an electron jumps from orbit n = 2 to n = 1)
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
Wheeee!
electron

25. Atomic transitions
Every time an atom (electron in the atom) makes a transition, a single photon of light is emitted.
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
electron

26. Atomic transitions
The energy of the photon is equal to the difference in energy (ΔE) between the two states. It is equal to hf. ΔE = hf
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
electron
ΔE = hf

27. The Lyman Series
Transitions down to the n = 1 state give a series of spectral lines in the UV region called the Lyman series.
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
Lyman series of spectral lines (UV)

28. The Balmer Series
Transitions down to the n = 2 state give a series of spectral lines in the visible region called the Balmer series.
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
Balmer series of spectral lines (visible) UV

29. The Pashen Series
Transitions down to the n = 3 state give a series of spectral lines in the infra-red region called the Pashen series.
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
Pashen series (IR)
visible UV

30. Emission Spectrum of Hydrogen
The emission and absorption spectrum of hydrogen is thus predicted to contain a line spectrum at very specific wavelengths, a fact verified by experiment.
Which is the emission spectrum and which is the absorption spectrum?

31. Pattern of lines
Since the higher states are closer to one another, the wavelengths of the photons emitted tend to be close too. There is a “crowding” of wavelengths at the low wavelength part of the spectrum
n = 1 (the ground state)
n = 2
n = 3
n = 4
n = 5
-13.6
Energy eV
Spectrum produced

32. How do you excite an atom?
Heating to a high temperature
Bombarding with electrons
Having photons fall on the atom
I’m excited!

33. Limitations of the Bohr Model
Can only treat atoms or ions with one electron
Does not predict the intensities of the spectral lines
Inconsistent with the uncertainty principle (see later!)
Does not predict the observed splitting of the spectral lines