Download Iodine Spectroscopy

Trent Physics 461H Lab
Iodine Spectroscopy
Iodine Spectroscopy
Introduction
From the Schrödinger equation we know that every bound system of particles can have only discrete energy
levels. Such a system making a transition between two such levels can correspond to light being absorbed or
emitted, but only at the particular wavelengths that match the energy differences between the levels. In this
experiment, white light from a 12 V lamp is used to excite a gas of iodine molecules, and in doing so specific
wavelengths are absorbed. Each absorbed wavelength will be observed using a grating spectrometer, and
from it characteristics of the iodine molecule will be determined.
Before you start
The spectrometer uses a blazed reflection grating to split the incoming light into its constituent wavelengths
(see left hand image in Figure 1). Here I is the incoming light, GN the grating normal, FN the normal to each
face and R0 the zero-th order, undispersed, light. The shortest wavelength dispersed light is emitted near R0,
and the longer wavelengths emitted furthest away from R0. The blazed, or angled, character of the grating
causes more light to be diffracted into the first order than if we simply used a flat reflection grating. By
rotating the turret that holds the grating in the spectrometer (right hand image in Figure 1) using a MATLAB
program different dispersed wavelengths are sent to the exit slit and to the detector.
Figure 1
a) The grating and detector work only in the visible region of the electromagnetic spectrum, from approx.
380 nm to 700 nm. Some electronic states of iodine are shown in Figure 2, and each electronic state hosts
vibrational and rotational states. Examine the X 0g+ and B 0u+ states. If the molecule makes a transition from
the X state to the B state, what approximate wavelength of light would you expect to be absorbed?
b) To first order the vibrational states within each electronic level have energies given by solving the
Schrödinger equation for the simple harmonic oscillator:
k
E v = (v + 12 )h
µ
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Trent Physics 461H Lab
Iodine Spectroscopy
where k is the effective spring constant of each electronic state (assuming it to be harmonic), and µ is the
reduced mass of the system. We use v ′′ and v ′ to represent the lower and upper vibrational quantum
numbers, respectively. Calculate approximate energies for the 10 lowest vibrational levels of I2 in the X 0g+
and B 0u+ states. What is the expected relative population of each vibrational state in the X 0g+ state for an
iodine cell at room temperature?
c) To first order the energies of the rotational states
within each vibrational state are given by solving
the Schrödinger equation for a free rotator:
J ( J + 1)h 2
EJ =
2 I COM
where ICOM is the moment of inertia of the molecule
about an axis through its centre of mass. Note this
latter quantity depends upon the bond length of the
molecule, which you can infer from the potential
energy curve of each electronic state. Calculate
approximate energies for the 10 lowest rotational
energy levels of I2 in the X state, with v ′′ =0; and in
the B state, with v ′ =0. The maximum resolution of
the spectrometer is about 0.2 nm, and the rotational
selection rule for the absorption of light by I2 for
the B-X transition are ∆J = ±1 . By considering a
few transitions with different J ′′ and J ′ , determine
whether you will be able to distinguish individual
rotational transitions from each other.
Figure 2: Iodine molecular potential energy curves (adapted from [1])
d) Meanwhile, the relative strength of absorption from v ′′ → v ′ is given in terms of the vibrational
wavefunction for each state:
∞
∫ψ (R )ψ (R ) dR
v′
v ′′
0
Given the fraction of molecules in v ′′ =0, and v ′′ =2, that you calculated in part (b), estimate by carefully
looking at Figure 2 whether you would expect the 0 → 0 transition to be stronger than, say, the 2 → 10
transition.
Setting up the experiment
The entrance and exit slit widths of the spectrometer are adjustable with a micrometer knob that is graduated
in 10 µm increments and a vertical scale that is labelled in mm (look at the figure on the left below).
Determine the slit width setting for the picture on the right.
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Trent Physics 461H Lab
Iodine Spectroscopy
Figure 2
The slits are very sensitive (and expensive) and will be damaged if the micrometer knob is rotated below a
reading of 0.00 mm or above 3.00 mm. Set both entrance and exit slits to 250 µm.
Turn on the spectrometer at the black power supply – this will ensure the grating starts in “zero-th order”,
where light of all wavelengths are transmitted from entrance slit to exit slit. Look through the exit slit with
the 12 V lamp turned on – you should be able to see the light from this lamp, and its absence when it is
blocked by your lab partner.
The detector we use is a photomultiplier tube, which requires a high negative voltage to be applied to it. This
voltage accelerates electrons from dynode to dynode within the photomultiplier, thereby amplifying the
original signal which is produced due to the photoelectric effect from the first dynode.
Note:
i) high voltages are dangerous and you must be fully aware of all attachments before you switch the high
voltage power supply on.
ii) the photomultiplier will be damaged if the high voltage is on and the photomultiplier is exposed to too
much light (e.g. ambient light from the laboratory). Only switch on the high voltage when the photomultiplier
is in place.
The signal from the photomultiplier alone is insufficient for us to record directly using the computer
hardware. Therefore we further amplify the signal using an operational amplifier (remember Phys325H?).
Make a sketch of the circuit and record the values of the resistors and the pins of the chip used in the circuit.
We (finally) record the voltage from this operational amplifier circuit using a PCL-711 card in the computer,
and a MATLAB program (c:\Phy461H\lab_spectrometer.m), which also controls the spectrometer.
Set up the MATLAB windows so that they look as shown below, with the the .m file in the left window and the
command window one the right. Briefly study the MATLAB code to determine how the program works. You
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Trent Physics 461H Lab
Iodine Spectroscopy
can find out what any command in MATLAB (e.g. ceil) will do by typing help ceil in the command window.
The program saves and runs by pressing the F5 key.
Save your own copy of this program using a unique filename and add comments (using the “%” sign) to lines
1-4, 12-18 and 26-32 that tell the user what these lines do. Note in particular how to set the wavelength range
of the scan, the wavelength step between each data point, the number of samples per data point, and the name
of the data file you will write to. It is recommended that you include in your data filenames some letters that
are unique to you so that you can easily find your data files at the end of the day.
Data Collection
Carefully place the iodine cell on the mount in front of the entrance slit. Attach the photomultiplier to the exit
slit housing and, when light-tight, switch on the high voltage supply to –1400 V. Using the spherical lens
optimise the light from the iodine cell through to the exit slit of the spectrometer by observing the voltage
from the photomultiplier tube. Now scan over a suitable wavelength range in steps of 0.5 nm and ensure this
data is saved. Do this several times, for a variety of slit widths down to 80 µm. You should see periodic
absorptions associated with many vibrational transitions. We will work through the analysis of this data
together.
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