The Bohr Atom

Spectroscopy

• Kirchhoff/Bunsen – used spectroscope to identify emission spectra of elements

Emission Spectra

•Each element displays a unique combination and number of bright lines against a dark background (darkness is no light). •Measurements on these are in nanometers (commas are decimal points)•The sun spectrum at the top is the complete white light emission from the sun; the dark lines are called Fraunhofer lines. They are the result of absorption of light by upper layers of the sun and earth’s atmosphere.

• Just like emission spectra, but the opposite.

• Energy seems to be taken up by the cold gas rather than emitted like the hot gas.

Absorption Spectra

http://www.scienceinschool.org/repository/images/issue4spectrometer11_large.jpg

• Johann Balmer – discovers a numerical relationship between the wavelengths of the lines in the H emission spectrum and the counting numbers. He cannot explain this.

• Johannes Rydberg later expands the relationship to account for all the lines in hydrogen’s spectrum:

• This still cannot be explained, but it works.

Explanation of Emission Lines?

22

1

2

11

nRH

Black Bodies

• Objects that emit radiation at every wavelength

• They do not do this equally, nor with equal efficiency:

• The peak emission wavelength lowers with temperature

THEORY=FAIL•Blackbody emitters had been studied extensively, and their spectra were known.•The theory used to predict their emission was not consistent with the results:

•The theory works at lower temperatures, but at higher ones fails pretty epically.•Later, this would be dubbed the “ultraviolet catastrophe” (Paul Ehrenfest, 1911)

The Quantum Theory

• Max Planck, physicist, is bugged by the Rayleigh-Jeans equation

• Entropy is his big concern• Formulates the “principle of elementary

disorder”– (1899) Agrees with theory! Then it fails.– (11/1900) Reformulates! Then it fails.– (12/1900) Introduces “energy elements” (a

trick, he thinks, but it works)

The Photoelectric Effect

• Observed by Hertz (1887) – shining bright light on metals causes a current to flow.

• Explained by Lenard (1902) – electrons are being knocked loose by the incoming light. This disagrees with Maxwell’s wave description of light—waves shouldn’t do this.

Idea Datahttp://www.cem.msu.edu/~harrison/cem483/pelec.gif http://www.gravitywarpdrive.com/NGFT_Chapter_10.htm

The Planck Relationship

• Planck proposes (1900) that emission from blackbodies is quantized (energy elements): – E = hν (E=hf, where f = ν =

frequency)– h = Planck’s Constant (6.626 x 10-34 J·s)

• Einstein imagines this relationship would apply to light (“photon gas”) (1905)

More Photoelectric Effect

• Plotting E vs. f from photoelectric effect data shows that E=hf! (h is the slope)

• This work done by Millikan later

The Bohr Model

• Atoms don’t spiral into the nucleus. Why?

• Bohr (1913) suggests why: electrons can only orbit at certain distances.

• Why?

That’s Not Important Right Now

• Emission – an electron moves toward the nucleus• Absorption – an electron moves away from the nucleus• The energies seen in emission spectra are the energies

required to move an electron from one “orbit” to another.

•This theory agrees completely with the relationship suggested by Balmer and Rydberg!•The “n” values are the “Principal Quantum Number”, which signifies the orbit. n must be nonzero.

22

1

2

11

nRH

The invisible world…

• Balmer’s equation had a fixed 2– These lines were visible– Lines starting at 1, 3, 4, etc. were not– Once the lines were able to be detected, the

formula had to be generalized

• Bohr used this relationship to show the energies of the electrons as they moved from n to n.

• Unfortunately, Bohr was wrong.

2218 11

1018.2if nn

JxE

http://www.physchem.co.za/OB12-mat/Graphics/spectra1.gif