Bright Line Spectra
Saddleback College Physics Department
Purpose
Determine the grating spacing for a diffraction grating by using the known wavelength of the sodium doublet.
Determine the wavelengths of the spectral lines of Hydrogen and Mercury and compare them with the
corresponding handbook values. Determine the identity of an unknown gas by finding the wavelengths of its
emission spectra.
Sketch
Equipment
spectroscope, diffraction grating, sodium vapor lamp, gas discharge tubes (H, Hg), power supply
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1
Equipment Setup (adapted from PASCO Scientific):
2. The mounting pillars of the telescope and collimator can
be rotated by using an Allen wrench to loosen the screws
that attach the pillars to their respective bases. To loosen
the screw for the collimator, the spectrometer must be
removed from the wood base.
3. To be sure both optical units are square to the axis of
rotation, follow the focusing procedure described above,
adjusting the mounting pillars as necessary so the slit
image is well centered in the viewing field of the
telescope.
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Measuring Angles of Diffraction
When analyzing a light source, angles of diffraction are measured using the vernier scales. However, the
scales only measure the relative rotational positions of the telescope and the spectrometer table base.
Therefore, before making a measurement, it's important to establish a vernier reading for the undeflected
beam. All angles of diffraction are then made with respect to that initial reading (see Fig 5).
To obtain a vernier reading for the undeflected beam, first align the vertical cross-hair with the fixed
edge of the slit image for the undeflected beam. Then read the vernier scale. This is the zero point
reading ( ! o ).
Figure 5. Measuring an Angle of Diffraction
Now rotate the telescope to align the vertical cross-hair with the fixed edge of a deflected image. Read
the vernier scale again. If this second reading is ! , then the actual angle of diffraction is #! = ! " ! o .
If the table base is rotated for some reason, the zero point changes, and must be remeasured.
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9. Repeat steps 6-8 until the angles for the corresponding slit images are the same to within one minute of
arc.
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Making the Reading
Once the grating is aligned, do not rotate the rotating table or its base again. Diffraction angles are measured as
described in the previous section, Measuring Angles of Diffraction. (Since the vernier scales were moved when
the spectrometer table was adjusted, the point of zero diffraction must be remeasured).
Theory
The following formula is used to determine the location of the maxima lines for a given gas viewed
through a diffraction grating.
m = order number = 0, 1, 2, " " "
equation (1)
m" = d sin (#! )
where
$ = wavelength
d = grating spacing
!# = angle from central axis of grating
Procedure
BE CAREFUL WHEN USING THE GAS DISCHARGE TUBE POWER SUPPLY. IT WILL
SHOCK YOU if you touch the tube’s metal caps or the springs (5000 Volts)!
NOTE: The spectroscope scale is in degrees and minutes. The vernier scale is in minutes and the larger
scale is in degrees. 60 minutes = 1 degree
1. Be sure to level, align and focus the spectrometer according to the instructions given in Equipment
Setup above.
2. Align the spectroscope, Sodium vapor lamp and diffraction grating in a straight path such that the
light from the tube is shining directly through the grating and into the spectroscope such that the
angle reads ~ 0 o .
3. Focus on the slit and crosshairs.
4. Rotate the spectroscope to the left or the right until a sodium doublet is seen. (See Measuring
Angles of Diffraction & Reading Vernier Scales above.) Sometimes the doublet just looks like a
single line of lesser intensity than that seen in step 1. Place the cross hairs of the spectroscope over
the first line in the doublet, measure the angle (call it !1 ). Now rotate the spectroscope to the other
side, aligning the cross hairs with the sodium doublet. Measure the angle (call it ! 2 ) and average !1
& ! 2 to determine "! . Use equation 1 to determine the grating spacing, d.
o
Handbook value for the wavelength of Sodium: ! Na = 5890 A = 589.0 nm
5. Determine ! for various first order components of Hydrogen ( H 2 ) and Mercury (Hg) light by
measuring !1 & ! 2 as described in step 1 and using equation 1.
6. Identify the unknown gas by calculating the wavelengths of various light components similar to step
1 & 2.
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Wavelengths of Principal Lines of Emission Spectra (Handbook Values)
Helium
Hydrogen
Mercury
o
Red
7065 A
Red
6678 A
Yellow
5876 A
Green
5016 A
o
o
o
o
Blue-Green 4922 A
6700 A
Red
s6700 A
Blue
4900 A
Violet
4400 A
Violet
4200 A
o
o
o
o
o
Blue
4713 A
Blue
4471 A
Blue
4387 A
Violet
4121 A
Violet
4026 A
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o
Red
o
o
o
o
7
o
Yellow
5791 A
Yellow
5770 A
Green
5461 A
Blue-Green
4916 A
Blue
4358 A
Violet
4078 A
Violet
4046 A
o
o
o
o
o
o