Matter Waves and Atomic Spectra
Name_____________ Partner ______________ Partner ______________
In 1913, Niels Bohr, using fundamental physics principles such as Newton’s 2nd Law,
Conservation of Energy, electrostatic attraction, and the new ideas of quantization of
angular momentum and photon energy, developed a model which predicted the energy
levels an electron could have as it orbited the nucleus of a hydrogen atom. His model
allowed the electron to be at a number of discrete distances (or radii) from the proton
nucleus and to have corresponding discrete levels of energy. The closer the negatively
charged electron, the more tightly it was held by electrostatic attraction to the positively
charged proton and the greater its binding energy (assigned a negative number because
you have to add energy to the electron to break it free from the nucleus).
Bohr’s model assumed the hydrogen electron could move in discrete shells from the
nucleus, as shown on the next page (not to scale). The shells were numbered moving
outward: n = 1; n = 2; n = 3; etc. Bohr’s model predicted the following energy levels:
1
E n  13.6 eV n 2
where eV stands for electron volts, a measure of energy (1 eV = 1.60 x 10-19 J), the
potential energy an electron gains when “falling” through an electrical potential of 1 volt.

The energies are negative
because energy must be added to separate the electron from the
atom.
Louis deBroglie explained Bohr’s result as follows:
The electron is a wave which forms a standing wave around the nucleus. This can only
happen if the circumference of the path of wave propagation equals an integer number of
wavelengths. Combining this condition with the known attraction due to the electric
force, deBroglie derived Bohr’s energy levels.
Let’s build a table of the energy levels of the hydrogen electron using Bohr’s formula:
n=
Energy level (eV)
1
2
3
4
5
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Matter Waves and Atomic Spectra
n=1
n=2
n=3
n=4
n=5
Electrons normally like to stay in the n = 1 state (also called the ground state). They can
be moved to a “higher” or excited level by absorbing light energy or energy from another
electron. In the diagram above, there are a series of electron transitions from n = 2, 3, 4,
and 5 to the n = 1 state on the left side, and transitions from higher energy levels to the
n = 2 state on the right side. Bohr explained the discrete glowing colors of hydrogen gas
by saying that when an electron moved back to a lower level, it did so by giving off
energy in the form of a light pulse or photon. The photon energy was exactly the energy
difference between the energy level the electron was at, and the energy level it went to.
So when an electron in the n = 2 level moves to the n = 1 level, Bohr predicted it would
give off an energy difference of 13.6 eV – 3.40 eV or 10.2 eV. What is the energy of the
photon given off when an n = 3 electron transitions to n = 2?
__________ eV
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Matter Waves and Atomic Spectra
The energy of a light photon is related to its wavelength (w) by
E = hc /w
where h is Planck’s constant (6.63 x 10-34 Js), c is the speed of light (3.00 x 108 m/s), and
w is the photon wavelength in meters. We conveniently measure light wavelengths in
nanometers (nm). Converting E = hc/w into units of eV’s and nm’s:
E = (1240 eVnm) / w
(w in nm)
Then, turning the equation around so we can solve for wavelength and find out what
wavelength of light is being emitted in our n = 2 to n = 1 transition:
w = (1240 eVnm)/E
w = (1240 eVnm)/10.2 eV = 122 nm
Wavelength corresponds to the color of light and 122 nm corresponds to an
ultraviolet colored photon. Because different elements have different nuclear charge,
each one produces its own characteristic spectrum of frequencies, called “spectral lines”.
Let’s look at the light of several glowing gases and see if we can identify them by
their unique colored line signature.
Your instructor will show you four different glowing gas tubes, energized by the flow
of electricity, like a neon light. Look at the glowing tubes with a diffraction grating (the
transparent film in a small plastic frame) and the light will be separated into its
component colors, like the rainbow from a prism. You’ll have to look well off to the side
to see the spectrum, which will be a series of discrete, different colored lines on a black
background. On the next page, draw a pencil line representing each of the main color
lines for Gas Tube A. Repeat for Gas Tubes B, C, and D. Then identify gases A, B, C,
and D from the line spectra depictions for the four elements on the following page.
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Matter Waves and Atomic Spectra
Sample A
_______________
Sample B
_______________
Sample C
_______________
Sample D
_______________
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Matter Waves and Atomic Spectra
Hydrogen
Helium
Neon
Krypton
Does your team agree on the identifications? Yes / No?
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Matter Waves and Atomic Spectra
These line spectra are the unique “fingerprints” of the elements and compounds. We can
identify the composition of stars and glowing gases from their color spectrum.
Now, go back to your hydrogen spectra and copy down the wavelengths in nm for the
main lines you see. These will be pretty approximate, but estimate as well as you can.
Reddest Line
Middle Line
Most Violet Line
__________
__________
__________
These visible lines are given off when electrons transition from higher shells to the
n = 2 shell (the Balmer series). Photons given off in transitions from higher shells to the
n = 1 shell are higher energy (because of the greater energy difference), in the ultraviolet
(UV) part of the electromagnetic spectrum, and we can’t see them. Photons given off in
transitions from the higher shells to the n = 3, n = 4, and higher shells are lower energy,
in the infrared (IR) part of the electromagnetic spectrum, and we can’t see them either.
Now, let’s see how well these observed lines (and their energy levels) agree with the
Bohr Model predictions. Go back to the table on page one and compute the following
energy differences (just the magnitudes, don’t worry about signs):
Color
Energy transition
Red
Blue-green
Violet
n = 3 to n = 2
n = 4 to n = 2
n = 5 to n = 2
Energy
difference
(eV)
Predicted
Wavelength
(nm)
Observed
Wavelength
(nm)
From the energy difference, predict the wavelength using: w = (1240 eVnm)/E
Finally, write in your observed wavelengths in the last row.
Are they reasonably close? Yes / No
(keep in mind this is an “eyeball” measurement)
From experiments such as this, we developed an understanding of the electronic structure
of the atom, upon which all chemistry is based.
Questions
1. According to de Broglie’s standing wave model of electron configurations, why are
energy levels quantized (only certain values possible)?
2. When an electron drops to a lower energy level in an atom, a packet of light (photon)
is emitted. What atomic property (or properties) determines the amount of energy
carried by the photon?
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