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PC1144
Experiment
4Atomic Spectra GENTLE REMINDER!
Level 1 Physics Laboratory (S12‐04‐02) Page 1 of 10
1. Wear proper attire (long pants and shoes) when you come for your practical session.
2. Remember to print out your worksheet and laboratory manual and bring along when you come for your practical
session.
3. Before leaving the laboratory, make sure the demonstrator on duty initial on your data table(s) together with the
date!
4. Submit a complete laboratory report of yours, i.e., laboratory worksheet together with Excel spreadsheet(s) within
ONE week after your laboratory session to level 1 Physics laboratory (S12‐04‐02) before 5.00 pm daily (check the
above submission deadline). In the event that the above submission deadline falls on a public/school holiday or
you have a medical certificate due to illness, the submission deadline will be the next school day during office
hours (9 am – 5 pm).
5. If you fail to submit your report before the deadline, no grade will be given for that report.
8/19/2019 Expt 04 Atomic Spectra
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THEORY PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 2 of 10
The spectrum from a hot gas of an element consists of discrete
wavelengths that are characteristics of the element. In 1885, in an
attempt to understand these spectra, Johann Balmer published an
empirical relationship that described the visible spectrum of
hydrogen. Although Balmer published the relationship in a
somewhat different form, the modern equivalent is
3, 4, 5, 6, … . (Balmer’s formula)
where RH = 1.097 x 107 m‐1 is a constant called the Rydberg
constant, stands for the wavelength and n is an integer that takes
on successive values greater than 2.
In 1913, Neils Bohr was able to derive the Balmer relationship by
making a series of revolutionary postulates. The Bohr theory was
historically of great importance in the developments that
eventually led to modern quantum theory. In his attempts to
explain the spectrum of hydrogen, Bohr was influenced by several
recently developed theories. He incorporated concepts from the
quantum theory of Max Planck, from the photon description of
light by Albert Einstein and from the nuclear theory of the atom
suggested by Ernest Rutherford’s ‐particle scattering from gold.
The central ideas of Bohr’s theory are contained in a series of four
postulates that are stated below:
1. The electron moves in a circular orbits of radius r n around the
nucleus under the influence of the Coulomb force between the
negative electron and positive nucleus.
2. The electron of mass m can only have velocity v n and orbits r n
that satisfy the relationship
mr nv n = nh/2
where h = 6.626 x 10‐34 Js and n = 1, 2, 3, 4, ..., ∞.
3. In an allowed orbit the electron does not radiate energy. The
atom is stable in these orbits and this is called a stationary state.
This postulate was a radical departure from classical physics.
Classical electromagnetic theory predicts that an electron
moving in a circle is accelerated and must radiate
electromagnetic energy continuously.
4. The atom radiates energy only when an electron makes a
transition from one allowed orbit to another allowed orbit. If E i
and E f stand for the energies of the initial and final stationary
states, the energy radiated by the atom is in the form of a
photon of energy hf = E i – E f where f is the photon frequency.
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THEORY PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 3 of 10
With these postulates, it is possible to derive an expression for
the energy of the stationary states. They are given by
4
8023
1
2
with = 1, 2 , 3, 4, …, ∞ (Bohr’s energy formula).
This expression for allowed energies can be used to obtain valuesfor 1/ predicted by the Bohr theory. The transitions that produce
photons that correspond to the first four visible Balmer
wavelengths are those from the states n = 3, 4, 5, 6 down to the
n = 2 state. They are
1
4
8023
1
22
1
2
with n = 3, 4, 5 and 6 (Bohr’s wavelength formula).
Bohr showed that the value of the constant me4 / 8 02ch3 was in
excellent agreement with the value of the Rydberg constant in
Balmer’s formula. This is striking confirmation of the validity of
the Bohr theory of hydrogen. The four wavelengths of the visible
hydrogen spectrum that are easily seen and measured are also in
excellent agreement with the first four wavelengths predicted by
the above formula.
In this experiment, we will make use of the dispersive power of
a diffraction grating. A grating is a piece of transparent material
on which has been ruled a large number of equally spaced
parallel lines. The distance between the lines is called grating
spacing d.
Light that strikes the transparent material is diffracted by the
parallel lines. The diffracted lines passes through the grating at
all angles relative to the original light path.
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THEORY PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 4 of 10
When the power is on,
DO NOT touch the surface of the power supply
DO NOT remove the spectra tube from its housing
DO NOT move the housing
as it is hot and will burn your hand.
You must take all the necessary precautions and
follow the instructions closely. If for any reason
the tube must be removed, call your
demonstrator.
Safety
Precautions
If diffracted light rays from adjacent lines on the grating interfere
and are in phase, an image of the light source can be formed.
Light rays from adjacent lines will be in phase if the rays differ in
path length by an integral number of wavelengths of the light.
The relationship between the wavelength of the light , the
grating spacing d and diffraction angle is as follows:
= d sin
In the Figure 1, the path length for Ray A s one wavelength longer
than the path length of Ray B. The grating disperses the beam of
light into a first order spectrum and higher order spectra. The
higher order spectra are broader and less bright than the first
order spectra and may overlap. Also, the grating used in this
experiment is blazed so one of the spectrum is much brighter
than the other.
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APPARATUS PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 5 of 10
Diffraction Grating
& Holder
Rotating Arm
Spectrophotometer Table
60cm Optics
Bench Black
Cloth
Focusing LensCollimating Lens Collimating Slits
Table lamp Rotary
Motion
Sensor
Spectrum Tube Lamps
Computer
Science Workshop
Interface
Figure 2: Atomic Spectra
Experimental Setup
Experimental Setup
Objective:
Investigate how well the visible light
wavelengths of Hydrogen predicted by the
Bohr theory agree with experimental values.
1
2 Determine an experimental value for theRydberg constant from a fit of the measured
values of hydrogen wavelengths to the form
of the Balmer equation.
3 Identify an unknown element by examining
their visible optical spectra.High
‐
Sensitivity
Light
Sensor
Aperture
BracketAperture
Screen
Degree Plate
Base
ON Button
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(A) Set up the apparatus
PROCEDURE PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 6 of 10
Set up the Spectrophotometer next to a mercury discharge
tube as shown in Figure 3.
1
Use the base provided to raise the spectrophotometer to
the same level as the opening to the light source (see
Figure 2).
2
Switch on the AC outlet before switch on the light source(see Figure 2 for the light source ON button).3
Once it is warmed up, adjust (a) the Light Source, (b)
Collimating Slits, (c) Collimating Lens and (d) Focusing Lens
so that clear images of the central ray and the first order
spectral lines appear on (e) the Aperture Disk and (f)
Aperture Screen in front of the (g) High Sensitivity Light
Sensor.
4
Turn the Aperture Disk so the smallest slit on the disk is in linewith the central ray.5
Note: The focal length of the Collimating Lens is about 10cm so
the lens should be positioned about 10cm from the slits. Adjust
the distance between the Collimating Slits and Collimating Lens
so that the beam of light is neither converging nor diverging (i.e.
light rays are parallel).
2
3
1
4a4b
4c
4d
Focusing Lens Figure 3(b): Spectral line on the
Aperture Screen and Disk.
4e
4f 5
Figure 3(a): Top view of
collimation setup.
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PROCEDURE PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 7 of 10
(B) Set up the Software Interface
Depending on which computer you are using,
the userid and password are the same and are
either temp1 or tempuser1.
Figure 4:The Science
Workshop Interface
Connect the High Sensitivity Light Sensor cable to Analog
Channel A.
1
Connect the Rotary Motion Sensor cable to Digital Channel 1
and Channel 2.
2
Connect the Science Workshop interface to the computer and
turn on the interface box.
3
Select “Create Experiment”.6
Look for the Data Studio icon on the desktop and double
click on it to launch the program
5
Switch on the computer. Take note the following when login
into the computer:
4
Select the “Light Sensor” to be connected to Analog Channel
A.
7
8 Select the “Rotary Motion Sensor” to be connected to Digital Channel 1 and 2.
9 Set the Rotary Motion Sensor so that
the sample
rate
is
20Hz.
it measures Angular Position, Ch1 & 2 (rad).
it records 1440 divisions per rotation.
10 Set the Light Sensor so that it measures only the “Light Intensity, Ch A (% max)”. Uncheck “Voltage, ChA (V)”.
12 Use the experiment calculator in DataStudio to create a
calculation of the actual angular position of the degree plate.The angular position of the Rotary Motion Sensor must be
divided by the ratio of the radius of the degree plate and the
radius of the small post of the pinion. The ratio is
approximately 60 to 1. To do so,
under definition, input “Actual Angular Position = x/60”;
under variables, define x = Angular Position, Ch1&2 (rad).
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PROCEDURE PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 8 of 10
(B) Set up the Software Interface
In the program, select a graph display and set it to
show “Light Intensity (% max)” on its vertical axis
and “Actual Angular Position” on its horizontal axis
by using drag and drop method.
13
14 You are now ready to collect data.
(C) Measurements
Figure 5: Scan the spectrum
1 Cover the setup with the given cloth to block out theambient light.
2 To scan a spectrum, use the threaded post under the LightSensor to move the Light Sensor Arm so the Light Sensor
is beyond the far end of the first order spectral lines, but
not in front of any of the spectral lines in the second
order.
3 Set the GAIN select switch on top of the High SensitivityLight Sensor to 100. You may use a lower setting if you
find that the signal is too strong.
4 In the DataStudio program, click the start button toto begin recording data.
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PROCEDURE PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 9 of 10
Scan the spectrum continuously but slowly in one direction by
pushing on the threaded post to rotate the Degree Plate.
5
Scan all the way through the first order spectral lines on one
side of the central ray (zeroth order), through the central ray
and all the way through the first order spectral lines on the
other side of the central ray as shown in Figure 5.
6
You may repeat the scan by setting different light sensor gainlevels or slit widths to obtain the best scan. Your scan should
have at least FOUR spectral lines. Each spectral should also
have its counterpart at the other side of the spectrum.
8
Use the graph display to examine the plot of Light Intensity
versus Actual Position for your data.
9
Click the stop button to stop recoding data.7
Figure 6: Measure the angles for both first order spectral patterns
Use the built‐in analysis tools in the DataStudio graph
display to find the angle between the two matching
spectral lines. Record the angle as in Data Table 1.
10
Note: The angle of a particular spectral pattern is one‐half
of the difference of the angle between the chosen spectral
line in the first order on one side of the central ray and the
matching spectral line in the first order on the other side of
the central ray. If a dim spectral line only appears on one
side of the central ray, calculate where the central ray isusing a brighter spectral line than is visible on both sides of
the central ray. Then, determine the angle from the central
ray to the dim line to find the angle for that spectral line.
Mercury Spectrum
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PROCEDURE PC1144 Experiment 4 – Atomic Spectra
Level 1 Physics Laboratory (S12‐04‐02) Page 10 of 10
12 Repeat the process for hydrogen light source. Record yourresults in Data Table 2. Title the graph as “Spectrum for
Hydrogen”.
13 Repeat the procedure for the unknown discharge tube
labeled as A. Record your result in Data 3.
Cancel all zooms and fix up the graph window so that all data
collected can be seen. Title this graph as “Spectrum forMercury”. Label each spectral line on both sides of the central
peak using the functions available in DataStudio and then print
the graph.
11
Hydrogen Spectrum
Data Table 3: Unknown Spectrum A
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