AP Physics Laboratory #22
Emission Spectra
DISCUSSION:
According to classical physics, as a wave light is characterized by its frequency (f) in Hertz (Hz)
and its wavelength (λ), both of which are related to the speed of light (c):
c  f
When solids are heated, they emit light. The light produced this way is called black-body radiation. As the
temperature increases the color distribution shifts to higher frequency.
In 1900 Max Planck proposed that the vibrating atoms in a heated solid could absorb or emit
electromagnetic energy only in certain discrete amounts. Planck introduced an equation that relates the
frequency of light to its energy. Planck’s equation is:
E  hf
h is Planck's constant, 6.626 x 10–34 J • s. Planck hypothesized that energy can only be absorbed or
emitted as positive whole number multiples of hf. That is, an energy change is allowed to be hf, 2hf, 3hf,
and so on, but is not allowed to be a fraction of hf. Planck’s quantum theory introduced the idea that
energy is quantized. Bohr derived an expression of energy levels specifically for the hydrogen atom:
E n  2.179 x10 18
1
n2
Albert Einstein extended Planck’s theory to successfully explain the photoelectron effect. Einstein
suggested that light could be described not only as having wave-like properties but also as having
particle-like properties. He proposed that particles of light called photons are tiny packets of energy and
that the energy of a photon of light with frequency f is given by Planck’s equation.
E photon  hf
As a result of Einstein’s work we now view light as both a particle and a wave.
The electric current applied to a cathode ray tube causes electrons to flow from the cathode to the anode.
These electrons collide with the gas atoms in the tube causing electrons in the gas atom to jump from low
energy levels to higher energy levels. When this happens, the atom is no longer in its ground state; it is in
a higher energy excited state. Electrons have a natural tendency to return to the ground state by losing
energy. This excess energy is lost through the emission of light. The energy of the emitted photon (light)
corresponds to the energy lost by the electron as it moves from the higher energy level to a lower energy
level. When an electron loses energy by undergoing a transition from a higher to a lower energy level in
an atom the amount of energy lost will be ΔE:
E  E final  Einitial
where Efinal is the energy of the final state and Einitial is the energy of the initial state. When the energy is
lost due to the emission of a photon of light by the atom, the frequency and wavelength of the light is
related to ΔE as follows:
E  E photon  hf 
hc

THE EXPERIMENT:
1. Using your spectroscope look at the light being emitted by the hydrogen lamp. Use the colored
pencils to record the emission spectrum that you see on the scale below. Write down the wavelengths
of the emission lines that you observe below each line.
2. Carefully replace the hydrogen lamp with the mercury lamp. Using your spectroscope look at the
light being emitted by the mercury lamp. Use the colored pencils to record the emission spectrum that
you see on the scale below. Write down the wavelengths of the emission lines that you observe below
each line.
3. Carefully replace the mercury lamp with the helium lamp. Using your spectroscope look at the light
being emitted by the helium lamp. Use the colored pencils to record the emission spectrum that you
see on the scale below. Write down the wavelengths of the emission lines that you observe below
each line.
ANALYSIS:
In addition to any necessary measurements or calculations from the experiment itself, include the
following in your lab report.
4. Using Bohr’s equation for the allowed electron energy levels of the hydrogen atom calculate the
energy for the first six electron energy levels. The energies for n = 1 and n = 2 are already done for
you. It is useful to write all of the energies to the same power of ten (use 10–19 as indicated).
Value of n
Energy in J
6
5
4
3
2
5.448 x 10–19
1
21.79 x 10–19
5. Complete the table given below by calculating the photon energy in joules and wavelength in
nanometers for each electron transition of hydrogen indicated. The energies should all be reported to
the same power of ten (use 10–19 as indicated). The ninital = 2 to nfinal = 1 transition is already done for
you.
Transition
ninitial  nfinal
62
61
54
53
52
51
43
42
41
32
31
21
Energy
( x 10-19 J)
Wavelength
(nm)
16.34
121.6
6. Referring to the table you already completed and your data for the emission spectrum of hydrogen
identify which transitions correspond to the emission lines that you observed for hydrogen.
Wavelength Observed
(nm)
Transition
ninitial  nfinal
7. Construct an energy level diagram to scale for the allowed energies of the electron in the hydrogen
atom. A sketch of what the diagram will look like is given below:
8. On the energy level diagram:
a. Draw and label the n = 1 to n = 6 energy levels. Give the value of n and the energy for each level.
Do not forget to label your energy units!
b. Indicate which energy level is the ground state.
c. Indicate which transitions correspond to the emission lines you observed for hydrogen.
d. Using colored pencils to indicate the color of the associated energy transition, draw the transitions
as down arrows in your diagram. Label each transition with the wavelength that you observed.
9. Based on your results, what is nfinal for all of the visible emission lines of the hydrogen atom?
10. Consider a hydrogen atom with its electron in the n = 5 excited state. Which transition from this state
will result in the emission of the lowest frequency of light? Explain your reasoning.