The aim of this experiment is to use two kind of spectrometer to identify the atomic spectra of different atoms. We learned to use the calibration curve obtained from a known spectrum or measure the angle of diffraction to find out the wavelengths of unknown spectral lines.
As we know, every atom has a set of discrete energy levels occupied by its electrons. A photon is emitted when an electron makes a transition from a higher energy level to a lower energy level. The wavelength λ of the photon is related to the change in energy ΔE of the electron by ∆E=hcλ
Because there are many possible transitions between the energy levels in a given atom, photons of different frequencies will be produced. An atom’s emission spectrum is the set of all these photon frequencies. Since different elements have different atomic structures and different atomic energy levels, the spectrum will be different for each element. In this way, an emission spectrum can be used to identify an element.
A spectrometer is an instrument for analyzing the spectra of radiations. In its simplest form, a spectrometer consists of three basic components: a collimator, a refracting or diffracting element to separate light into its various components, and a telescope. By using the spectrometer, each constituent color of the atomic spectrum can be viewed and the angle can be measured. These angles can be used to determine the wavelengths that are present in the light. For more precise work and recording the relative intensity of each color of light, we use a diffraction grating with a spectrophotometer system with data logging capabilities. By interfacing the light sensor and a rotary motion sensor with the computer, relative light intensities across a whole range of angles can be recorded. Caution that all the recording of the spectra has to be done in the dark.
A diffraction grating consists of many equally spaced, parallel lines. Light rays diffracted from adjacent lines can interfere constructively to form an image of the light source. In this experiment, we use the first-order diffraction grating to let rays from adjacent lines differ in path length by one wavelength of the light. By using a grating spectrometer system with data-logging capabilities, we can record the relative light intensities across a whole range of angles. As shown in Figure 1 on Page 2, the relationship between the wavelengths of light λ, the diffraction line spacing d, and diffraction angle θ, is: λ=d sinθ
Using the angles recorded and the equation, we can calculate the wavelengths of light rays of different intensities.
Part 1: Obtaining a Calibration Curve for the Glass Prism Spectrometer 1. Turned on the mercury and sodium lamp once reached the lab to let it warm up. 2. Set up the glass prism spectrometer as Figure 3. To level the spectrometer table, adjusted the three thumbscrews.
3. In order to focus the telescope and collimator, brought the cross-hairs into sharp focus by moving the eyepiece, and made sure that one of the cross-hairs is vertical. Afterwards, focused the telescope on a distant object and turned it directly opposite the collimator. Finally, adjusted the focus knob on the collimator and bring the slit into sharp focus. 4. Placed the glass prism onto the spectrometer table and the mercury light source several centimeters behind the slit. 5. Darken the surroundings using curtains and the opaque cloth, then looked through the telescope to find the mercury line spectrum. 6. Found the minimum angle of refraction by rotating the spectrometer table to a point where the spectral line changed its moving direction. Used the fine adjust knobs to make sure that the vertical cross-hair precisely aligned with the fixed edge of the violet part of the slit image. Then read the angle on the vernier scale to be D2. 7. Removed the prism and aligned the cross-hair with the fixed edge of the undiffracted beam. The angle on the scale was the reference angle D1. The absolute value of the subtraction of D1 and D2 was the minimum angle of deviation for the violet part. 8. Repeated step 6 & 7 to determine the minimum angle of deviation for each spectral line. 9. Obtained the calibration curve by using the given wavelengths of different colors in the atomic mercury emission spectrum,
Part 2: Measurement of Wavelength Using the Calibration Curve
1. Repeated step 3~8 in Part 1 using the sodium lamp.
2. Obtained the yellow and extremely bright one.
Part 3: Recording the Hydrogen Spectrum with the Grating Spectrometer
1. Set up the grating spectrometer as shown in Figure 4. Figure 5 shows exactly how to align the apparatus.
Figure 4 Figure 5
2. Fixed the hydrogen spectral tube into the cloth hood as the light source. 3. Used the spirit level as well as the ring stand clamps to make the optics bench at the same level as the light source. 4. After darkening the room, turned on the light source. Then adjusted the collimating slit to the largest one and checked that the back-reflection of the incident light went right back to the source. 5. Images of the central ray and the spectral lines on the aperture disk and aperture screen were clear as the light source warmed up. Then turned the aperture disk to the smallest slit, which was in line with the central ray. 6. Then connected the Light Sensor and the Rotary Motion Sensor to correct channels and checked the settings. 7. Created a calculation of the actual angular position of the degree plate in DataStudio. To do so, we keyed in Actual Angular Position = x/60 under Definition, and defined x = Angular Position, Ch 1&2 (deg) under Variables. 8. Set the GAIN select switch of the High Sensitivity Light Sensor to 100. 9. Rotated the degree plate by 180° to scan the spectrum all the way through the first order spectral lines on both sides of the central ray. Then the computer plotted the graph of Light Intensity against Angular Position automatically. 10. Repeated step 9 by selecting different GAIN levels or slit widths, and found that the scan was best if set the GAIN level to be 100 and the slit width at 5 (the widest one). 11. Recorded the coordinates of points at the seven crests on the curve representing different colors.
Part 4: Identification of Unknown Vapors using the Grating Spectrophotometer 1. Repeated the procedures in part 3 by using the unknown vapor. 2. By calculating the wavelength of the unknown vapor, identify the vapor.
Result & Discussions
Part 1: Obtaining a Calibration Curve for the Glass Prism Spectrometer After found the mercury line spectrum, primary data was collected as shown in the table below.
Table 1: The Atomic Mercury Emission Spectrum
Colour| Wavelength λ (nm)| Visual Intensity| D1 (deg)| D2 (deg)| Dmin =D2-D1 (deg)| Violet| 404.656| Strong| 211.65°| 152.92°| 58.73°| Violet| 407.781| Weak| 211.65°| 153°| 58.65°|
Turquoise| 491.604| Weak| 211.65°| 154.7°| 56.95°| Green| 546.074| Very Strong| 211.65°| 156.27°| 55.38°| Yellow| 576.959| Strong| 211.65°| 157.52°| 54.13°| Red| 690.700| Faint| 211.65°| 158.58°| 53.07°|
According to the table, the graph of Dmin (deg) was plotted, the minimum angle of deviation, against λ (nm) as shown on the next page. From this graph, we can clearly see that as the wavelength of light increases, the minimum angle of deviation decreases.
Graph 1: The Relationship between Dmin and λ for the Mercury Emission Spectrum
[Error Analysis 1]
The outcome of Part 1 and the graph may not be accurate enough due to the following reasons: 1. When reading from the vernier scale, there might be some errors. On one hand, the index mark was not aligned with a certain calibration perfectly. On the other hand, the inaccuracy of human eyesight is usually inevitable. 2. There were always light source that will influence our experiment.
Part 2: Measurement of Wavelength Using the Calibration Curve In order to make use of the calibration curve in part I, the initial angle for the undiffracted beam is the same. And the sodium spectrum data was shown in the table 2.
Table 2: The Atomic Sodium Emission Spectrum
Colour| Visual Intensity| D1 (deg)| D2 (deg)| Dmin (deg)| Red | Strong | 211.65°| 158.12°| 53.53°|
Orange | Strong | 211.65°| 157.7°| 53.95°|
yellow| Strong | 211.65°| 157.27°| 54.38°|
[Error Analysis 2]
The given value of the wavelength of the average of the doublet is 589.2 nm in our manual.
The error might come from:
1. Inaccurate reading of the vernier scale as in Part 1.
2. The wavelength of the yellow sodium line is estimated by human eyes, which can hardly be the exact value.
Part 3: Recording the Hydrogen Spectrum with the Grating Spectrometer The graph of Light Intensity against Angular Position plotted by the computer is shown in graph 2.
Graph 2: Light Intensity (% max) against Angular Position of Hydrogen Spectrum
Table 3: The Hydrogen Spectrum
colour| θ2-θ1| (θ2-θ1)/2| λ| accepted| difference| red| 46.483| 23.242| 657| 740| 11.2%|
blue| 33.963| 16.982| 487| 435| 12.0%|
violet| 31.691| 15.846| 455| 380| 19.7%|
[Error Analysis 3]
As shown in Table 3, the result of λ is not the same as the accepted λ. Several factors might have contributed to it: 1. Since the grating was not tightly fixed, it might have changed position, thus causing some deviation of light path. 2. Sometimes the rotary motion sensor could not function properly, which influenced the recording process of the angular position on the computer.
Part 4: Identification of Unknown Vapors using the Grating Spectrophotometer
Table 4: The unknown vapor Spectrum
colour| θ1| θ2| θ2-θ1| (θ2-θ1)/2| sinθ| λ=d*sinθ| yellow| 21.571| 101.129| 79.558| 39.779| 0.219199991| 365.187185| green| 37.321| 87.812| 50.491| 25.2455| 0.139793415| 232.895829| violent(mid-weak)| 41.575| 83.25| 41.675| 20.8375| 0.115505498| 192.43216| violent(weak)| 0| 62.242| 62.242| 31.121| 0.172034357| 286.609238|
Graph 3: Light Intensity (% max) against Angular Position of unknown vapor Spectrum
[Error Analysis 4]
Since there was something wrong with our primary data, we were failed to determine what the unknown vapor was. There were several reasons that will cause the error:
1. The coordinates of the crests may be not well fitted with the color it should be. 2. The other light sources may also influences on the precise of the experiment. 3. The sensor may be not sensitive enough to sense some of the color precisely.
Using the glass prism spectrometer and the grating spectrometer, we were able to measure the wavelengths of unknown spectral lines. Although there were some factors that make the results inaccurate during the experiment, the errors are still within acceptance. Therefore, our results almost agree with the expected outcomes. What’s more, we learned how to measure the wavelength by observing the spectrum and decide some kind of unknown vapor by measure its wavelength. In conclusion, our experiment was almost successed.