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CHM 1025C & CHM 1032C Labs
Spectroscopy: Electron Energy Levels-----The Bohr Atom
OBJECTIVES

To distinguish between a continuous spectrum and a line spectrum.

To understand the relationship between spectral lines and electron energy levels.

To identify the unknown element in a fluorescent light by its “atomic fingerprint.”

To compare the observed wavelengths of the lines in the hydrogen spectrum to
the calculated wavelengths.

To become proficient in using a hand spectroscope.
DISCUSSION
On December 14, 1900, a revolutionary concept was born. The concept came from the mind
of Max Planck, a German professor of physics. The concept was quite simple: since matter
comes in lumps, perhaps energy also comes in lumps. We call a lump of matter an atom;
Planck called a lump of radiant energy a quantum. The concept that light energy comes in
discrete packets was revolutionary because previously light had been viewed as a continuous
wave of energy.
Light is radiant energy whose wavelength () is the distance traveled in order to
complete one cycle. The frequency of light refers to the number of cycles in one second.
Low-energy light has a long wavelength and a low frequency. High-energy light has a short
wavelength and a high frequency.
Figure 6.1 The wave nature of light
Light is a form of energy that travels with wavelike motion at a velocity of 300,000,000
meters per second. When we observe white light, we are actually seeing the effect of a
combination of several colors of light having different wavelengths. When white light is
passed through a prism, it separates into the six primary colors: red, orange, yellow, green,
blue, and violet.
Figure 6.2 The six component colors of white light
A rainbow is a natural phenomenon created when sunlight passes through raindrops.
Individual drops of rain act as miniature prisms to separate sunlight into various bands of
color. The wavelength of light can be expressed in nanometers, where a nanometer (nm) is
one-billionth of a meter. The range of visible light, violet to red, is usually considered 400-700
nm. However, in this experiment, you will probably observe visible colors from about 450-650
nm.
Visible light is only a small portion of the entire spectrum of radiant energy. Notice in
Figure 6.3 that visible light is a small window in a vast spectrum of radiant energy. This
spectrum includes X ray, ultraviolet, visible, infrared, and microwave radiation. Our eyes can
only detect light in the visible spectrum and not in other regions. That is, the wavelength of
ultraviolet light is too short to be visible and wavelength of infrared light is too long to be seen
by the human eye.
Figure 6.3
The continuous range of light energy from gamma rays to radio waves is called
the radiant energy spectrum, or sometimes the electromagnetic spectrum.
The Bohr Model of the Atom
In 1911 Ernest Rutherford and his fellow researchers were investigating the scattering
of high-energy alpha particles by a thin gold foil. Much to their amazement a few particles
were deflected at severe angles and a very few actually bounced off the gold foil. This
startling result revealed that the atom contains a dense positively charged nucleus
surrounded by electrons. Rutherford suggested that the electrons revolve about the nucleus
as the planets revolve around the sun. This became known as the planetary model of the
atom.
A few months later the Danish physicist Niels Bohr joined Rutherford in England. Bohr
adopted the planetary model of the atom but went further and speculated that electrons travel
in circular orbits at a fixed distance from the nucleus (figure 6.4). Since the orbit distance is
fixed, the electron possesses a definite energy. Moreover, Bohr proposed that the electron
could change energy by jumping from level to level.
Figure 6.4
In the Bohr model of the atom, the electron must occupy a discrete orbit of fixed
energy levels.
Electron Energy Levels
The Bohr model was a beautiful mental picture of electrons in atoms. It was consistent
with Planck’s quantum principle, but nobody knew whether the model was right or wrong.
There simply was no experimental evidence to support the theory. In 1913 Bohr received a
research paper on the emission of light from electrically excited hydrogen gas. Bohr noticed
that hydrogen emitted only discrete wavelengths of light and not a continuous spectrum. The
three most prominent emission lines were violet, blue-green and red.
We can describe the experiment as follows. First, hydrogen gas is sealed in a glass
tube. Then, an electrical voltage is applied to energize the hydrogen gas. An instant later the
excited hydrogen atoms release energy in the form of light. When this light passes through a
prism, it separates into narrow bands of light having a specific wavelength. Figure 6.5
illustrates the emission spectrum of hydrogen.
Figure 6.5
In the emission spectrum of hydrogen the light from the gas discharge tube
appears reddish-purple. After the light passes through a prism the reddishpurple splits into three lines which are violet, blue-green, and red.
As Bohr reflected on the emission spectrum of hydrogen, he realized that he had
powerful experimental for his model of the atom. His concept of energy levels was supported
by the line spectrum of hydrogen. He reasoned as follows: When a voltage is applied to a
hydrogen gas discharge tube, electrons jump to a higher energy level. For example, the
electron may jump from the first level to the second, third, fourth, or fifth level. The electron is
excited in a higher level and can lose energy by dropping to any one of the lower levels
closer to the nucleus.
When the electron drops to a lower energy level, it loses a specific amount of
energy that corresponds to one quantum of light. That is, the quantum of light possesses the
same amount of energy as that lost by the electron as it drops from a higher to lower energy
level. This experimental evidence supported Bohr’s model of the atom perfectly. However, it
was Planck’s idea that light comes in lumps that allowed for Bohr’s penetrating insight.
Figure 6.6 shows the correlation between Bohr’s energy levels and observed lines in the
hydrogen spectrum.
Figure 6.6
The relationship between quantum levels and hydrogen spectral lines is shown.
The violet is emitted when electrons drop from the 5th to the 2nd orbit. The bluegreen line corresponds to the transition from the 4th to 2nd; the red line when
electrons drop from the 3rd to 2nd quantum level.
Further study of emission spectra revealed that each element produces a different set
of spectral lines. Thus, the energy difference between energy levels is unique for atoms of
each element. For this reason, the line spectrum of a given element is unique and is
sometimes referred to as an “atomic fingerprint.”
The Balmer Formula
Jakob Balmer, a Swiss mathematician and physicist, did not publish his first paper until he
was sixty years old. In 1885, Balmer published a mathematical formula that accounted for
the visible lines emitted from excited hydrogen gas. The Balmer formula shows that the
wavelength () of light for each hydrogen spectral line is related to a small whole number (n)
in the following way:
When Balmer set n = 3, the calculated wavelength was equal to the wavelength of the red
line in the hydrogen spectrum. Substituting n = 4 and n = 5 gave values for the blue-green
and violet lines observed in the spectrum of hydrogen. When Niels Bohr read Balmer’s
paper, he realized that the n value could represent an energy level and that the 2 in the
formula corresponded to the second energy level.
The following sample calculation uses the Balmer formula to find the wavelength of a
spectral line in the Hydrogen spectrum.
Example Exercise 6.1
Calculate the wavelength of visible light corresponding to the energy released when the
electron drops from n = 6 to n = 2 in a hydrogen atom.
Solution: We can use the Balmer formula to calculate the wavelength of this visible spectral
line as follows:
A spectral line of this wavelength is in the violet portion of the spectrum. Although this line is
not intense, if you look very carefully at the emission spectrum of hydrogen, you may see a
faint violet line at 410 nm.
The Rydberg Equation
Several years after Balmer had introduced his formula, the Swedish physicist Johannes
Rydberg derived a more general formula for calculating the wavelengths of spectral lines. The
Rydberg equation accounts for an electron dropping from any higher energy level (nH) to any
lower level (nL). The general form of the equation is:
The Balmer formula is adequate to explain the visible lines in the spectrum of hydrogen
because they correspond to excited electrons dropping to n = 2. However, the Rydberg
equation also accounts for spectral lines in the ultraviolet and infrared portions of the
spectrum. When the electron drops to n = 1, the spectral lines are in the ultraviolet region of
the spectrum and therefore not visible to the eye. Similarly, when the electron falls to n = 3,
the spectral lines are in the infrared region of the spectrum and not visible.
The Quantum Mechanical Atom
In the mid-1920s an entirely new model of the atom began to emerge. The behavior of
electrons in atoms could no longer be adequately explained using the Bohr model of the atom.
The German physicist Werner Heisenberg proposed that it was impossible to determine
accurately both the position and energy of an electron. Heisenberg stated that it is impossible
to precisely measure both the location and momentum of a small particle simultaneously. In
fact, the more accurately the position of an electron in an atom is known, the less precisely its
energy can be calculated. Heisenberg’s statement came to be known as the uncertainty
principle.
Gradually, the deeper nature of the atom came into focus. The new model retained the
idea of energy levels but incorporated the concept of uncertainty. The new model that
emerged became known as the quantum mechanical atom. In the Bohr model, the energy of
an electron is defined in terms of a stationary orbit about the nucleus. In the quantum
mechanical model, the energy of an electron is described in terms of its probability of being
found within a prescribed volume of space surrounding the nucleus. This region of high
probability for finding an electron of given energy is called an orbital. In the quantum
mechanical model, an orbital describes the energy state of the electron.
EQUIPMENT AND CHEMICALS

Science Kit Hand Spectroscope
[The SK spectroscope (WW16525M00, ~$9.00) is available from Science Kit, Inc.,
777 East Park Drive, Tonawanda, NY 14150 (800) 828-7777.]



spectrum tube power supply
gas discharge tubes: helium, neon, argon, krypton, xenon, mercury, hydrogen
colored pencils: violet, blue, green, yellow, orange, red (optional)
Figure: The Hand Spectroscope. Light enters the spectroscope through the slit and strikes
the diffraction grating. The grating is a thin piece of plastic etched with hundreds of parallel
grooves. The diffraction grating separates light into different wavelengths. The numbers on
the scale represent wavelengths from 400 nm to 700 nm. The digit 4 is read as 400nm, 5 as
500 nm and 6 as 600 nm. There are ten divisions between each number on the scale;
therefore each division is 10 nm. For example, the scale divisions between 4 and 5 are read
as: 410, 420, 430, 440, 450, 460, 470, 480, and 490 nm.
PROCEDURE
A. Continuous Spectrum vs. Line Spectrum
1.
With the hand spectroscope observe the emission spectrum from one or more of
the following: the sun, an ordinary light bulb, the light reflected off an overhead
projector screen. Color the observed spectrum onto the chart in the Data Table.
2.
Insert a helium gas discharge tube into a power supply and observe and record
the color of light produced. Carefully examine the emitted light from the
helium using the spectroscope. Mark the wavelength of the six most intense
lines in the Data Table.
Note: It is necessary to have room lights on in order read the scale
divisions in the spectroscope.
B. Identifying an Element by its “Atomic Fingerprint”
1.
Place a neon gas discharge tube into the power supply and describe and
record the observed color. Examine the emitted light through the
spectroscope and record in the Data the color all intense lines (V, B, G, Y, O, R).
Replace the neon tube with each of the following gas discharge tubes: argon,
krypton, xenon, and mercury. Record the observed color as well as the color
of the intense lines in each spectrum.
Note: The spectral lines are best viewed in the dark. Room lights can be
turned off since scale readings are not necessary. It may be
convenient to turn on an overhead projector light long enough to
record the data.
2.
Observe the line spectrum from a fluorescent light using the spectroscope.
Disregard the continuous background spectrum and draw the three most intense
lines in the Data Table. Compare the line spectrum from the fluorescent light to
the lines from the Ne, Ar, Kr, Xe, and Hg gas discharge tubes. Identify the
unknown element in the fluorescent light from its “atomic fingerprint.”
C. Hydrogen Emission Spectrum
1.
Closely observe the emission spectrum of hydrogen with a hand spectroscope.
Record the wavelengths of the three most intense lines in the Data Table.
(Room light is once again necessary to read the scale.)
2.
Using the Balmer formula, calculate the wavelength () of light produced when
an electron drops from the 3rd to 2nd energy level. (Round the answer to two
significant digits; for example, 433.3 nm rounds to 430 nm.)
3.
Repeat the wavelength calculation for the spectral lines produced when the
electron drops from the 4th to 2nd energy level; and from the 5th to 2nd energy
level.
4.
Record the observed and calculated wavelength values in the Data Table.
Calculate the error by finding the difference between the observed and
calculated wavelengths.
Spectroscopy: PRE-LABORATORY ASSIGNMENT
1.
In you own words, define the following terms:
“Atomic fingerprint”_____________________________________________________
Balmer formula________________________________________________________
continuous spectrum____________________________________________________
frequency_____________________________________________________________
light_________________________________________________________________
line spectrum__________________________________________________________
nanometer (nm)________________________________________________________
quantum______________________________________________________________
visible spectrum________________________________________________________
wavelength____________________________________________________________
2.
Name the six primary colors in the visible spectrum in order of:
(a)
decreasing wavelength_____________________________________________
(b)
decreasing frequency______________________________________________
(c)
decreasing energy_________________________________________________
3.
What wavelengths of light are indicated by the following scale readings observed
through a hand spectroscope?
4.
What are the colors of the three most intense lines in the emission spectrum of
hydrogen?
5.
A hydrogen gas discharge tube emits a faint violet line when electrons drop from the 7 th
to the 2nd energy level. Use the Balmer formula to calculate the wavelength for this
spectral line.
6.
How many quanta of light are emitted when 1 electron drops from the 7th to 2nd energy
level? When 10 electrons drop from the 5th to 2nd energy level?
7.
What safety precautions must be observed in this experiment?
Spectroscopy:
NAME ______________________
DATE ________________
SECTION ___________________
DATA TABLE
Spectroscope # ______________
A. Continuous Spectrum vs. Line Spectrum
1.
Continuous Emission Spectrum - White Light
2.
Line emission spectrum - Helium
B. Identifying an Element by its “Atomic Fingerprint”
1.
2.
Line Spectra from Gas Discharge Tubes
(a) Neon
Observed Color:
__________________________
Spectral Lines:
V
B
G
Y
O
R
(b) Argon
Observed Color:
Spectral Lines:
__________________________
V
B
G
Y
O
R
(c) Krypton
Observed Color:
Spectral Lines:
__________________________
V
B
G
Y
O
R
(d) Xenon
Observed Color:
Spectral Lines:
__________________________
V
B
G
Y
O
R
(e) Mercury Observed Color:
Spectral Lines:
__________________________
V
B
G
Y
O
R
Line Spectrum from a Fluorescent Light
The unknown element in the fluorescent light is _______________
C. Hydrogen Emission Spectrum
1.
Observed Wavelengths of Spectral Lines
2.
Calculated Wavelengths of Spectral Lines
(a) red line (electrons drop from 3rd level to 2nd level)
(b) blue-green line (electrons drop from 4th level to 2nd level)
(c) violet line (electrons drop from 5th level to 2nd level)
Spectral Line
Observed
Wavelength
Calculated
Wavelength
Difference in
Wavelengths
red line
____________nm
____________nm
____________nm
blue-green line
____________nm
____________nm
____________nm
violet line
____________nm
____________nm
____________nm