Trent Physics 203H Lab Helium Spectroscopy

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Helium Spectroscopy

Introduction

The electrons in an atom can only occupy discrete energy levels, called quantum states. An electron moving

between two atomic levels can correspond to light being absorbed or emitted, but only at the particular

wavelengths that match the energy differences between the levels. For light, the relationship between the

energy of the photons and the frequency and wavelength is given by the expression λν /hchE == , where E

is energy, λ is the wavelength, ν is the frequency, h is Planck’s constant and c the speed of light in the

medium in which it is travelling. The refractive index for air, n, is almost precisely unity (it is 1.0003) so c

can be treated to a good approximation as the speed of light in vacuum. In this experiment, an electric

discharge delivers energy to helium atoms via electron collisions. The atoms relax back to their ground state

(1s2 1

S) by emitting light; each wavelength is called a ‘spectral line’ because it shows up as a line in a grating

spectrometer. You will use a spectrometer to measure the visible wavelengths of the helium spectrum and

therefore learn about the energy structure of helium.

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 photodiode (which detects light).

Figure 1

The transitions you expect to see can be found from the Grotrian diagram in Appendix A, along with many

transitions which won’t be detectable (the grating and detector work only in the visible region of the

electromagnetic spectrum, from approx. 380 nm to 700 nm). In the Grotrian diagram the energy of each

quantum state is given in units of cm-1

corresponding to 1/λ, where λ is the wavelength of the light in cm

Trent Physics 203H Lab Helium Spectroscopy

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required for a transition to the atom’s ground state with respect to the ground state, 1s2 1

S. Therefore the

ground state lies at 0 cm-1

and is off the diagram. There are four sets of allowed transitions: 1

S ↔1

P, 1

P ↔1

D,

3

S ↔3

P and 3

P ↔3

D and note that the singlet states, e.g. 1

S, always lie above the corresponding triplet states,

e.g. 3

S. For example, one transition that lies between 300 nm and 700 nm is the 1s3p 1

P → 1s2s 1

S transition

at 501.7 nm (find it!), and corresponds to green light. Determine which other transitions should be visible

(you should predict about 15) and tabulate each observable transition, wavelength and expected colour.

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.

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. Ask your demonstrator to 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. Carefully place the helium

emission lamp close to the entrance slit of the spectrometer and turn it on. Look through the exit slit, and by

carefully moving the helium lamp (holding onto its base) you should be able to place it in the optimum

location. Next, attach the battery to the photodiode leads and place the cover on the photodiode housing.

Place it close to the exit slit and maximise the voltage output (on a mV scale) recorded on a voltmeter by

carefully moving the photodiode to the correct location (height and position).

Trent Physics 203H Lab Helium Spectroscopy

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Data collection

We use a MATLAB program (c:\Phys203H\lab_spectrometer.m) to control the spectrometer and record the

data. 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 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.

Now scan over a wavelength range from 380 nm to 700 nm in steps of 0.5 nm and ensure this data is saved.

You should have seen a peak at about 590 nm. To see the effect of decreased slit width ask your

demonstrator to set the slit widths to 100 µm and scan over this large peak in steps of 0.05 nm (pick a

sensible range). Again save this data (with a different filename than the first set). Provided you saw a visible

peak in this scan, repeat after asking the demonstrator to set the slits to 50 µm.

Trent Physics 203H Lab Helium Spectroscopy

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Analysis and Submitted Work

After copying your data files and the commented .m file from the lab PC to another PC available to you, use

Excel or MATLAB etc. to display one plot (called a spectrum) of the full wavelength range. Label all peaks

in increasing wavelength (a), (b), (c), etc. and include these labels on the plot. Complete the following table:

Peak Label Wavelength observed /nm Assigned transition Wavelength predicted /nm

On a second plot with smaller wavelength range show spectra of the line near 590 nm taken with slit widths

at 250 µm, 100 µm and 50 µm. Scale two traces vertically so that the heights of all three traces agree. Find

the full-width at half maximum (FWHM) of the peak in each case. What effect does the slit width make?

You should hand in within your lab report:

a) a copy of the .m file with your comments

b) your determination of the micrometer reading in Figure 2

c) your two plots with clear figure captions, axes and labels,

d) the table with a clear caption

e) a discussion that includes how well the measured wavelengths agree with those that you predicted. Is there

a systematic effect or are the differences randomly distributed?

Appendix A

Figure 3: Some Energy Levels of the Helium Atom