1. PHYS 420-SPRING 2006
Dennis Papadopoulos
LECTURE 12
BOHR’S ATOM

2. Evolution of our views of the atom
positive charge is concentrated at the center of the atom in an area ~1/1000th the size of the atom
the mass of the electron is very small compared to the mass of the atom (one thousand times less than the hydrogen atom

3. The Atom According to Bohr,
who was (mostly) right

4. The Planetary Model What’s wrong with this picture?
The attractive Coulomb force between the positive nucleus and the orbiting electron could provide the attractive force which keeps the electron in it’s orbit, much as the planets orbit the sun with gravity providing the centripetal force.
What’s wrong with this picture?
Accelerating charges radiate. Could this electromagnetic radiation be the source of the spectral lines?
No. This radiation must come at the expense of the kinetic energy of the orbiting electron!
It will eventually spiral into the nucleus. The atom would be unstable!

6. Kirchhoff and Bunsen: where there is emission, there can be absorption

7. The "Numerology" of emmission lines
It also turns out that C1=C2=C3…
But what does all of this mean??

8. The Bohr Atom
Classical electromagnetism does not hold for atom sized systems.
Used Planck’s energy quantization ideas to postulate that electrons orbit in fixed, stable, nonradiating states, given by
Used Einstein’s concept of a photon to define the frequency of radiation emitted when an electron jumps from one state to another. The photon energy is just the energy difference between states, i.e.,
Used classical mechanics to calculate the orbit of the electron.

9. Coulomb force keeps electrons in orbit:
But we know that the allowed values of the angular momentum are:
(Are you wondering why these are the allowed values? You should be.)
For n=1, this gives the “Bohr radius”:
which was in good agreement with experimental values.
For other values of n:

10. This also agreed with experiment.
energy quantization therefore follows from angular momentum conservation.
therefore the ionization energy is 13.6 eV. It takes 13.6 eV to liberate an electron in the ground state. At n=infinity, it is removed.
This also agreed with experiment.
Independent of the orbital angular momentum of the electron, the frequency of a photon emitted is:

11. How a laser works 3. Some of these atoms emit photons.
2. The flash tube fires and injects light into the ruby rod. The light excites atoms in the ruby.
3. Some of these atoms emit photons.
1. The laser in its non-lasing state
4. Some of these photons run in a direction parallel to the ruby's axis, so they bounce back and forth off the mirrors. As they pass through the crystal, they stimulate emission in other atoms.
5. Monochromatic, single-phase, columnated light leaves the ruby through the half-silvered mirror -- laser light!

12. That's exactly right; as n gets larger, 1 over n squared gets smaller, so there's less and less difference between the consecutive lines. You can see that the series has a limit-- that is, as n gets larger and larger, the wavelength gets closer and closer to one particular value. If n is infinity, then 1 over n squared is 0, and if you work out the numbers, you'll find that the wavelength is about 365 nm. That's just what experimentalists saw; around 365 nm, the lines became too close together to distinguish.

13. Correspondence principle
Note that the difference in energies of allowed orbits becomes smaller as n becomes larger.
In the limit of large quantum numbers, the frequencies and the intensities of radiation calculated from classical theory must agree with quantum theory.

15. At the beginning of class, I said that Bohr was mostly right…so where did he go wrong?
Failed to account for why some spectral lines are stronger than others. (To determine transition probabilities, you need QUANTUM MECHANICS!) Auugh!
Treats an electron like a miniature planet…but is an electron a particle…or a wave?