# Experiment 12_ Atomic spectra by hcj

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```									                           Experiment 11: Atomic spectra
Last week, we used a laser to produce light with a sharply defined wavelength. The
laser was able to do this by taking advantage of very specific transitions between energy
levels in the atoms in the laser cavity (helium and neon). It turns out that very small
systems (atoms for example) do not obey the laws of classical mechanics but instead are
governed by more complicated laws of quantum mechanics. A fundamental result of
quantum mechanics is that electrons that are bound to nuclei of atoms can only occupy
discrete states with discrete energy levels. This is in stark contrast with classical
mechanics in which an electron orbiting a proton can orbit at any radius and therefore
have any energy. This means that light absorbed or emitted by an atom must be exactly
the right energy to match the allowed energy levels of the electron.
Another important modification to our classical picture is the behavior of light itself.
If we were to take a light source and turn the intensity down to a very low level, we
would find that light was being emitted in discrete packets called photons. Observation
of the emitted light (on a very sensitive screen for example) would show that the light
was arriving at definite times with discrete units of energy. The situation is analogous to
what happens when a steady stream of water from a faucet is reduced to a drip. In the
case of the photons, there is a direct relationship between their frequency (or wavelength)
hc
and their energy given by E  h          , where c  2.998  108 m / s is the speed of light,

and h = 6.626 x 10-34 Js is Planck’s constant.
Part 1: Qualitative examination of emission lines

When the transitions in atoms produce photons in the visible spectrum they can be
seen by the naked eye. Place a hydrogen-filled spectrum tube in the spectrum tube
power supply. Turn on the power and observe the color emitted by the gas. To see the
distinct lines, hold the diffraction grating close to your eye and look through the grating
at the tube. Describe what you are see, keeping in mind that for a diffraction grating, the
bright spots are located at d sin   m , where d is the separation between the slits.
Sketch a rough picture of the lines you see and indicate their color and values of m on a
sheet of paper. This will give you an idea of where the lines are when you use the
spectroscope in the next section of the lab to measure the wavelength of these lines.
Try looking at the spectra of some of the other tubes, helium, argon, etc… through the
diffraction grating. Note that the lines are different due to the different electron states
involved.

Part 2: Analysis of the spectrum of Hydrogen

In this section of the lab, we will measure the energies of photons that are emitted by
Hydrogen atoms. Hydrogen consists of a single proton and a single electron, the simplest
of atoms. In quantum mechanics, the states of the electron in a Hydrogen atom can be
calculated very accurately. These discrete states are found to have energies of
E1
En  2 ,
n
2m 2 e 2 2
where E1              (      ) = - 13.60 eV is a constant in terms of fundamental
h 2 4 0
parameters, and n is a positive integer. The fundamental parameters that are needed here
are the electron mass, m  9.109  10 31 kg , the charge of an electron, e  1.602  1019 C ,
Planck’s constant, h  6.626  1034 Js , and the permittivity of space,
 0  8.854  10 12 C 2 / Jm . More complex atoms require elaborate approximation
methods to find the states, but they are still quantized in an analogous way.
Transitions between states emit photons with energy equal to the energy lost by the
electron in the transition. Use the above formulas to calculate the wavelength emitted by
Hydrogen in the n  2 to n  1 transition. Are the transitions to the n  1 level (called the
Lyman series) in the visible part of the spectrum? Repeat your calculation for transitions
to the n  2 level (Balmer series). See the figure below for the general picture.

1. Read the introduction in the spectrometer instruction manual to understand how it
works. Proceed to setup the apparatus as described in the equipment setup
section. (You can skip the leveling of the spectrometer).
2. Study the section describing how to read the vernier scale on the spectroscope.
(Note that 1 minute is 1/60 of a degree)
3. Continue on with the instructions, making sure the diffraction grating is aligned
properly.
4. Measure the diffraction angles and compute the wavelengths for the lines that you
can see. Get the most accurate measurement you can achieve by averaging the
angles of diffraction on both sides of the centerline. You can also look at the
higher order ( m  1) diffraction peaks to get more data. If done carefully, the
experiment should yield errors around the 1- 2 % level.
5. Summarize your results with a comparison of measured values and theoretical
values for wavelengths in the Balmer series of Hydrogen.

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