Physics 104
Atomic Spectra
Objectives
Part 1: Identify and describe hydrogen energy levels, quantization of energy, electron
excitation and decay, and energy transfer between a photon and an electron in a hydrogen
atom.
Part 2: Virtually determine the unique spectra of elements in a spectral tube using a
recording spectrometer.
Part 3: Use a diffraction grating spectrope to determine the wavelength and energy of
hydrogen spectral lines.
Materials and Equipment
PhET Simulation: Models of Hydrogen Atom PhET Simulation: Discharge Lamps
Hydrogen emission tube Emission tube transformer
Diffraction grating spectrometer
Background
During the first quarter of the 20th century, physicists developed models of the atom. The Bohr
model is widely used by physicists and chemists because it accurately describes and predicts the
ways atoms absorb and emit energy. A fundamental feature of atoms described by the Bohr model is
quantized energy, which is a natural phenomenon that allows each electron in an atom to only
occupy an orbit with a discrete, or specific amount of energy. Electrons may absorb energy from
incoming photons of light, and may release energy gained from collisions with photons of light, but
only in these specific, or quantized, amounts.
When atoms orbiting a nucleus are
bombarded with high energy photons
of light, they move to energy levels, or
orbits, further from the nucleus and
are said to be in an excited state.
When these electrons fall back toward
the nucleus, they release the exact
amount of energy they absorbed as
new photons of light. Electrons at the
lowest energy level are said to be at
their ground state. The newly
released photons carry energies in
combinations that are unique for that
type of atom. To the right is a
representation of a hydrogen atom
with its unique energy levels.
Ionization occurs when enough
energy is transferred from an incoming
photon to an orbiting electron to force
the electron to leave the atom entirely,
making the atom and positive ion.
The Lyman and Balmer series are
common patterns for an electron to
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take while falling back to the ground state.
Energy levels are also graphically displayed in charts, like this one for
Hydrogen. The chart attempts to scale each level and describe the
energy required to move a ground state electron to that level.
Emission tubes, commonly referred to as Neon lights or fluorescent
lights, are common in everyday life. These devices take advantage of
the energy released by electrons falling to ground. The tubes are
filled with atoms of a gas and a high voltage is applied between the
ends of the tube. As current, in the form of free electrons, flows
through the tube, the electrons strike the electrons that orbit the
nuclei of the gas atoms. Energy is transferred to the orbiting
electrons causing them to become excited. As they fall to ground, they
release this energy as photons of light, and the tube glows. Specific
selection of the gas in the tube, special coatings on the inside of the
tubes, and careful adjustment of the voltage and current applied can
create specific colors of light.
Spectroscopy is a powerful tool used in physics, astronomy, and chemistry to determine the
elemental composition of glowing gasses. By using a diffraction grating, which is a collection of
very tiny, parallel slits in an opaque barrier, light can be dispersed into its constituent
wavelengths. Astronomers use this technique to determine what elements are found in the sun and
other stars. In the laboratory, a diffraction grating spectrometer uses a diffraction grating to
disperse light and allow the determination of the individual wavelengths of photons that are
emitted as electrons in the observed gas fall to ground state.
Relevant Equations
The energy carried by a photon of light can be calculated using the following formula where E is the
energy in Joules or Electronvolts, h is Planck’s Constant (also in J or eV), f is the frequency of the
light in Hz, and c is the speed of light in a vacuum, c=3x108m/s, h=6.626x10-34 J· s = 4.1357x10-15 eV·
s.
ℎ𝑐
𝐸 = ℎ𝑓 = (1)
𝜆
The wavelength, λ, of a spectral line seen through a spectrometer can be determined using formula 2,
where d is the distance between the grating slits, θ is the angle between the spectral line and the
center line (the path light would have taken if the grating was not present), and m is the order of
the series of spectral lines. The order of lines closest to m=0, or the center, is the first order, m=1.
𝑑𝑠𝑖𝑛𝜃 = 𝑚𝜆 (2)
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Part 1: Procedure
After you complete a step (or answer a question), place a check mark in the box () next to that step.
Set Up
1. Open the Models of the Hydrogen
Atom Simulation.
2. Toggle the simulation to Prediction
mode.
3. Turn on the White light source.
4. Click on the spectrometer and
energy level diagram.
5. Select the Bohr model of the atom.
Collect Data
6. Slow the simulation to its lowest speed. Watch the electron and record the color of
the emitted photon for at least three energy level transitions.
Excited State Energy Level Transition Energy Level Color of Emitted Photon
n= n=
n= n=
n= n=
7. Draw each of the three transitions you observed on the energy level diagrams.
6 6 6
5 5 5
4 4 4
3 3 3
2 2 2
1 1 1
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8. Put the simulation into its fastest speed and watch the spectrometer. Sketch the
spectral lines.
Analyze Data
10. Calculate the energy carried by the photons for three spectral lines. The horizontal
axis is showing wavelength of the photons in nanometers.
Color of Emitted Photon Wavelength Energy
λ1= E1 =
λ2= E2 =
λ3= E3 =
Analysis Questions
1. In the simulation, what do the flying colored balls represent? What do the different
colors signify?
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2. How many of the spectral lines would be visible to the naked eye?
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3. Which spectral lines that are visible to the naked eye would be easiest to see with a
diffraction grating spectrometer? Which would be harder to see?
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4. Using the Bohr model, write a paragraph that describes what is happening to the
electron that is orbiting the nucleus. Include a description of energy levels, energy
absorption, and energy emission.
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5. Describe why each element has a unique spectra.
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Part 2: Procedure
After you complete a step (or answer a question), place a check mark in the box () next to that step.
Set Up
1. Open the Models of the Neon Lights
Simulation.
Collect Data
2. In the One Atom setting, set the
voltage on the cell to 9V and fire
one electron.
3. What makes the electron fly from one plate to the other?
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4. Was the electron orbiting the nucleus of the Hydrogen atom (which the simulation
does not show) excited enough by the collision with the incoming electron to produce
an emission? Explain why or why not.
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5. Set the voltage on the cell to 24V and fire one electron.
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6. Was the electron orbiting the nucleus of the Hydrogen atom (which the simulation
does not show) excited enough by the collision with the incoming electron to produce
an emission? Explain why or why not.
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7. What color was the emitted photon? ______________________________
8. What voltage will allow two photons to be emitted, sometimes? ___________________
9. What colors are the photons? ______________________________
10. If the cell were set to 30V, how many photons could be emitted if the Hydrogen’s
excited state electron stops at each energy level on the way back to ground? _______
11. At the top of the simulation, choose Multiple Atoms, set the voltage to 30V, and
select ‘continuous’ electron production.
12. Slide the production slider to 100% and toggle on the spectrometer.
13. Sketch the spectral lines for different elements below. Use colored pencils.
Hydrogen Emission Spectra Mercury Emission Spectra
Sodium Emission Spectra Neon Emission Spectra
Analyze Data
14. Which element has the strongest yellow spectral lines? ___________________________
15. Which element has the most spectral lines? ____________________________
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Analysis Questions
1. Write a paragraph that describes the physics that allows ‘neon’ lights and fluorescent
lights to work. Include a description of what happens at the atomic level that causes the
production of photons of light.
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Synthesis Questions
Use available resources to help you answer the following questions.
1. If each of the elements was used to create a light bulb, which would be the least
energy efficient? Which would be the most energy efficient?
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2. One of the elements is often used to make street lights. Which one is it?
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3. Why would engineers pick this particular element to make street lights?
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Part 3: Procedure
After you complete a step (or answer a question), place a check mark in the box () next to that step.
Set Up
1. Set the Hydrogen emission lamp on a
textbook. Set the end of the spectrometer
about 10cm from the lamp.
2. Align the spectrometer to 180 degrees, such
that peering through the eyepiece shows an
image of the emission lamp, which should
look bright pink.
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3. Gently tighten the adjustment screw on the end of the spectrometer by rotating it
toward the lamp. Watch the bright pink line and tighten the screw until the line
gets wide enough to see clearly.
Collect Data
4. While peering through the eyepiece, slowly rotate the eyepiece section of the
spectrometer until more spectral lines are visible.
5. Hydrogen has four distinct spectral lines that our eyes can see. The first set, or first
order m=1, is the brightest and closest to the center, or m=0.
6. Measure the angle from m=0, or the center,
using the scale on the lower left of the
spectrometer platform. The magnitude of
angle, θ, is the absolute value of 180˚ minus
the reading on the Vernier scale. The
diagram on the right shows how to read a
Vernier scale.
7. Measure the angle for each of the spectral
lines and record the angles in the table.
Analyze Data
8. Assume the distance between diffraction grating slits is d=1.7x10-6m and the order is
m=1. Calculate the wavelength, % difference from accepted wavelength, and energy
of each spectral line.
Color and Order Distance θ Wavelength Wavelength Energy E (J
accepted λ between slits (radians) λ (m) %Difference or eV)
(nm)
Red (660nm) m=1 d=1.7x10-6m
Cyan (490nm) m=1 d=1.7x10-6m
Blue (440nm) m=1 d=1.7x10-6m
Purple (410nm) m=1 d=1.7x10-6m
Analysis Questions
1. Are the calculated wavelengths close to the accepted wavelengths for each color?
What could have caused any differences?
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2. Which spectral line was created by photons with the most energy? Which line was
created by photons with the least energy?
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3. How are the photons of light that make each spectral line relate to the Hydrogen
atoms inside the lamp?
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4. If a gas other than Hydrogen were inside the lamp, would the spectral lines be the
same? How might they differ?
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Synthesis Questions
1. For a lamp with an unknown gas, at what angle would we find a 520nm spectral line?
2. For a Hydrogen lamp, at what angle would we find the red spectral line in the second
order, m=2?
3. When comparing the strength of spectral lines, why do planet hunting astronomers
look for stars with Hydrogen and Helium lines with similar strengths to those found in
our own Sun?
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Multiple Choice Questions
Select the best answer or completion to each of the questions or incomplete statements below.
1. Perhaps to confuse a predator, some tropical gyrinid beetles (also called whirligig
beetles) are colored by optical interference that is due to scales whose alignment forms a
diffraction grating, which scatters light instead of transmitting it. When the incident
light rays are perpendicular to the grating, the angle between the first-order maxima,
m=1, and the zero order, m=0, is 26˚ in light with a wavelength of 550nm. What is the
grating spacing of the beetles scales?
A. 2.13x10-6m D. 1.254x10-6m
B. 1254.6m E. 7.21x10-7m
C. 721.26m
2. Green light at 520nm is diffracted by a grating with a slit spacing of 3x10 -6m. Through
what angle is the light diffracted in the fifth order, m=5?
A. 60.7˚ D. 53.3˚
B. 61.3˚ E. 64.3˚
C. 52.3˚
3. How much energy is carried by the photons making up the green light in the previous
question?
A. 3.825x10-6J D. 3.825x10-37J
B. 3.825x10-12J E. 3.825x10-19J
C. 3.825x10-28J
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