Experiment 19

Experiment 19: Diffraction Grating Spectroscope

Purpose

(1)  To observe spectra.

(2)  To measure wavelengths in line spectra.

Apparatus

(a) a diffraction grating spectroscope; a mercury lamp; a desk lamp

(b) on the side: 4-5 helium gas tubes with bases

(c) tungsten filament (with a spare spectroscope), 2-3 sodium lamps with bases

Theory

(I) The Diffraction Grating Spectroscope.

Light passing through a narrow slit is collimated by a lens, resulting in coherent plane waves falling upon a diffraction grating (Fig. 1). If the light is monochromatic, of wavelength λ, the image of the slit can be observed only at particular angles θm given by formula (1) where d is the distance between adjacent grooves in the grating and m is an integer, called the order of the image.

/ (1) / BASIC FORMULA
d·sin θm= m· λ

(II) Spectra.

If the light source emits light of several specific wavelengths, then the angles θm will be different for different wavelengths, and the images of the slit will appear as a set of lines of different colors, called a line spectrum.

For each order m (except for m = 0) there will be two identical spectra, to the right and to the left from the central image, which corresponds to m = 0 and contains the mixture of all wavelengths present in the source.

Glowing gases (at low density) produce such line spectra, each gas with its own specific wavelengths. Glowing solids and liquids produce continuous spectra, containing all wavelengths.

Preliminary Procedure: Optical Adjustments

The Central Image:

1) Your spectroscope is shown in Fig. 2. Familiarize yourself with it.

2) Turn on the mercury lamp. Align the collimator and telescope tubes and look straight into the lamp. You should see a white, vertical, central image (zero order image) of the slit.
Note: If the slit image is not vertical, call your instructor. /

3) Move the whole spectroscope as closely as possible to the cardboard slit on the lamp. Move the whole spectroscope slightly to the left or to the right until the image is

as brilliant as possible. It should be so brilliant as to be uncomfortable to the eye!

AT THIS POINT, CALL YOUR INSTRUCTOR TO CHECK THAT YOU HAVE A GOOD SPECTRUM. HE OR SHE CAN HELP YOU ADJUST THE COLLIMATOR.

Note: If you wear reading glasses, take them off; if you wear driving glasses, keep them on.

The Focusing:

4) Relax your eye. Move the image focusing knob (Fig. 2) back and forth until the slit image is sharp.

5) Move the telescope tube (only!) slightly sideways to get the slit image out of the field of view. You should see the cross-hairs. Relax your eye completely. Then,

hand until you see the cross-hairs very sharply. Rotate the eyepiece until you see the cross-hairs at 45º to the horizontal (that is, like X, rather than like +).

6) Move the telescope back to make the cross-hairs coincide with the slit image. Quite possibly, the image will not be now sharp (out of focus). Repeat (4) to re-focus the slit image; then repeat (5) to re-focus the cross-hairs and so on, until both the slit image and the cross-hairs are sharp.

To check if you have it correctly: Move your eye sideways: if the slit image and the cross-hairs appear to move together, without any mutual displacement, your adjustment is correct. Otherwise, repeat (4), (5) and (6). Call your instructor if in doubt.

7) With the cross-hairs sharply centered on central image, the angle indicator should read 0º or within 0.5º from it (if not, call your instructor to adjust it). This is your zero reading. Record it, estimating down to one tenth of a degree, to the best of your ability; also record whether it is “to the right” or “to the left” (if it is exactly zero, record it as 0.0º ).

8) Swing the telescope by some 15º to 20º to the right. You should see a line spectrum, that is a set of colored images of your slit. Warning: during this motion the collimator tube must remain motionless. If not, alert your instructor immediately.

If the lines are too high or too low, (or if they are missing altogether) call your instructor; do not try any adjustments of your own.

AT THIS STAGE, CHECK AGAIN WITH YOUR INSTRUCTOR. DO NOT PROCEED WITHOUT HIS OR HER APPROVAL.

Procedure Part I: The Mercury Spectrum

9) Record the grating constant of your telescope:

K = 6,000cm-1 (K is the number of grooves per centimeter)

d = 1/K = 1.67 ´ 10-4 cm = 1.67 ´ 104 Angstroms[(]

10) Locate your first order spectrum as in (B), which should start at about 14º. You should be able to see at least nine lines, usually more, sketched in Fig. 3.

/ Line (Describe
and relate to
your sketch) / Order
m / Angle Readings
Right / Left

11) Set up your data sheet as shown in Figure 3. Sketch the lines that you see and can measure. Label them by color and brightness in the proper sequence.

Measure and record the angles of all lines that you can identify, estimating the readings to one tenth of a degree. Do this in first order both to the right and to the left of the central image. You may be able to observe the two violet lines in second order. If so, measure and record their angles (but do not go beyond the scale).

Procedure Part II: Other Spectra

12) Your instructor will provide you with a Helium gas tube (to be shared with other students). Sketch the helium spectrum, as in (10).

13) Measure and record the four brightest lines in first order both right and left. Identify them in your sketch and recording them as for the mercury spectrum.

14) Observe the spectrum of the tungsten filament which will be set aside on a spare spectroscope.

Lab Report

Part I

a) Set up the table below:

Line (Describe it with Reference to your own sketch) / Order m / Measured Angles / Sin θ / λ (Angstroms) / % Errors
To the Right / To the Left / Average / Measured / Known

Carry out calculations of λ accurate to four significant digits (NOT more). Display the calculation for the mercury green-yellow line (See Fig. 3).


The correct values of λ for the five strongest lines in mercury spectrum are:

Strong violet line 4,047 Angstroms

Strong blue line 4,358 Angstroms

(Strongest) green-yellow line 5,461 Angstroms

Orange/yellow doublet lower 5,770 Angstroms

higher 5,790 Angstroms

Enter these values in your table and calculate the % errors for these lines only. For other

lines, just calculate λ, leaving the last 2 columns blank. As a rule, your % errors should

not exceed 2%.

b) On the basis of your experience in the lab, and your calculations, pinpoint the two

most important sources of error. State them clearly.

c) Answer Question #1:

If your angle indicator could measure angles beyond 30º, calculate at what angle the

yellow-green 5461 A line of mercury would appear in third order? Also, comment on

this line in the fourth order.

Part II

d) Set up a table for helium as above. Calculate the measured values of the helium wavelengths in the same fashion as for mercury but leave the last two columns blank.

e) Answer the questions:

Question #2: In what fundamental aspect the observed spectra of mercury and helium different from the spectrum of tungsten filament? Why is this so?

Question #3: What is the major cause of discrepancies between the measured and the correct wavelengths (excluding your own possible negligence)?

100

[(]* The symbol for Angstroms is : 1  = 10-8 cm