THE HYDROGEN ATOM
Introduction:
In the early 1900s, Ernest Rutherford devised an experiment which revised the
model of the atom. His gold foil experiment showed that most of the mass (including the
protons) is found in the nucleus and that the electrons were in a region about that nucleus.
Line spectra for elements would later be used to refine the model of the atom.
The main question to be answered was why atoms emitted light of only certain
frequencies instead of a continuous spectrum like that of an incandescent light bulb.
Niels Bohr answered this question and introduced the ideas of quantization and energy
levels.
In this experiment, you will use the equations developed by Balmer, Rydberg and
Bohr to predict the wavelengths and energies of light emitted for transitions in the
hydrogen atom. These values will be compared with your experimental values and the
accepted values found in your text.
Purpose:
The purpose of this experiment is to measure the wavelengths and calculate the
energies of the lines in the Balmer series of the hydrogen atom. These values will be
compared with the values predicted from the equations.
Equipment/Materials:
hydrogen discharge tube
spectroscope
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Safety:

This experiment poses no unusual safety hazards. Do not touch the discharge
tubes because they can become quite hot.
Procedure:
1. Measure and record the wavelengths of the four lines in the Balmer series of the
hydrogen atom.
2. Using the Rydberg equation, calculate the wavelength that would be predicted for
each transition in the Balmer series. All transition are from higher energy levels to
the n = 2 energy level.
1 
 1
= R 2  2  n > 2

n 
2
1
R = 1.097 X 107 m-1
3. a. Using the wavelengths measured, calculate the energy per atom for each line in the
Balmer series.
b. Using the equation below, calculate the energy expected for each line in the Balmer
series.
 1
1 
 Rhc  2  2 
 nf ni 
R = Rydberg Constant
h = Planck’s Constant
c = speed of light
c. Find the energy for each transition from the diagram in your text.
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4. Construct an energy level diagram showing the energies and colors of light observed
in the Balmer series.
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THE HYDROGEN SPECTRA
Data:
Part I.
Observed Wavelengths:
Line 1 _______________ nm
Line 2 _______________ nm
Line 3 _______________ nm
Line 4 _______________ nm
Predicted Wavelengths:
n = 6 to n = 2
n = 5 to n = 2
n = 4 to n = 2
n = 3 to n = 2
Accepted Values for Wavelengths:
Line 1 _______________ nm
Line 2 _______________ nm
Line 3 _______________ nm
Line 4 _______________ nm
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Part II
Observed Energies:
Line 1 _______________ J
Line 2 _______________ J
Line 3 _______________ J
Line 4 _______________ J
Predicted Energies:
n = 6 to n = 2
n = 5 to n = 2
n = 4 to n = 2
n = 3 to n = 2
Accepted Values for Energies:
Line 1 _______________ J
Line 2 _______________ J
Line 3 _______________ J
Line 4 _______________ J
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Questions:
1. The Paschen series lines in the atomic spectrum of hydrogen result from transitions
from n > 3 to n = 3. Calculate the wavelength in nm of a line in this series resulting from
an n = 6 to n = 3 transition. Where would this line be found in the electromagnetic
spectrum?
2. Calculate the wavelength of light emitted when an electron changes from n = 3
to n = 1 in the hydrogen atom. In what region of the spectrum is this radiation found?
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THE HYDROGEN SPECTRA
TEACHER NOTES
Standards Met:
3.7.12.B – Evaluate appropriate instruments and apparatus to accurately measure
materials and processes.
 Apply and evaluate the use of appropriate instruments to accurately measure
scientific and technologic phenomena within the error limits of the equipment.
3.1.12.C – Assess and apply patterns in science and technology.
 Assess patterns in nature using mathematical formulas.
 Assess and apply recurring patterns in natural and technological systems.
3.4.10.A – Apply concepts about the structure and properties of matter.
 Know that atoms are composed of even smaller sub-atomic structures whose
properties are measurable.
Observed Wavelengths:
Typical Student Data
Line 1 ____390________ nm
Line 2 ____410________ nm
Line 3 ____480________ nm
Line 4 ____680________ nm
Predicted Wavelengths:
n = 6 to n = 2
410 nm
n = 5 to n = 2
434 nm
n = 4 to n = 2
486 nm
n = 3 to n = 2
656 nm
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Accepted Values for Wavelengths:
Line 1 ____410.2______ nm
Line 2 ____434.1______ nm
Line 3 ____486.1______ nm
Line 4 ____656.3______ nm
Part II
Observed Energies:
Typical Student Data
Line 1 ___5.10 X 10-19__ J
Line 2 ___4.85 X 10-19__ J
Line 3 ___4.14 X 10-19__ J
Line 4 ___2.92 X 10-19__ J
Predicted Energies:
n = 6 to n = 2
-4.85 X 10-19 J
n = 5 to n = 2
-4.58 X 10-19 J
n = 4 to n = 2
-4.09 X 10-19 J
n = 3 to n = 2
-3.03 X 10-19
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Accepted Values for Energies:
Line 1 __4.84 X 10-19___ J
Line 2 __4.58 X 10-19___ J
Line 3 __4.09 X 10-19___ J
Line 4 __3.03 X 10-19___ J
Answers to Questions:
1. The Paschen series lines in the atomic spectrum of hydrogen result from transitions
from n > 3 to n = 3. Calculate the wavelength in nm of a line in this series resulting from
an n = 6 to n = 3 transition. Where would this line be found in the electromagnetic
spectrum?
1090 nm
Infrared region
2. Calculate the wavelength of light emitted when an electron changes from n = 3
to n = 1 in the hydrogen atom. In what region of the spectrum is this radiation found?
103 nm
Ultraviolet region
Last updated 11-02
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