Balmer Spectrum of H. spectrum tube. monochromator photodiode detector. 10 kv. readout electronics. entrance slit. exit. Fig. 1. Experimental setup.

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1 Balmer Spectrum of H This lab has 3 purposes: 1. To measure and interpret the Balmer spectrum of the hydrogen atom. 2. To understand how a grating monochromator works; 3. To understand how a silicon photodetector works. Background: In the late 1800 s, Anders Angstrom made very precise measurements of the wavelengths of the four visible lines emitted by excited hydrogen atoms. The hydrogen was present in an evacuated glass tube with electrodes at either end, much like the apparatus you will use today. When a high voltage difference was applied to the two electrodes, the tube gave off light. Angstrom and others measured the spectrum of this light, and found that the spectrum was not a continuum. Instead, the spectrum consisted of a series of sharp lines. Angstrom used a grating spectometer to measure the spectrum, much as you will do today. spectrum tube monochromator photodiode detector 10 kv entrance slit exit slit readout electronics Fig. 1. Experimental setup. A. EMISSION TUBE The emission tube contains a small amount of water or hydrogen molecules. A power supply in the tube holder applies about 10,000 volts across the tube. The resultant strong field E inside the tube exceeds the breakdown voltage of the gas, creating a current of electrons and ions in the tube and breaking molecular bonds. Thus if the original gas is H 2 molecules, the operating tube contains H 2 molecules, H 2 + ions, H + ions, H atoms, and electrons. If the original gas in the tube is H 2 O, the operating tube will contain H +, H, OH -, electrons, and other fragments. The hydrogen ions do not emit visible light, but the hydrogen atoms do. Question A1. Assuming that the voltage across the spectrum tube is 10,000 V, what is the value of the electric field E? Question A2. Why don t the H + ions emit visible light?

2 B. MONOCHROMATOR To measure the emission spectrum, we will use a 1/8-meter grating monochromator with a 1200 lines/mm grating and variable-width entrance and exit slits. The diagram below shows the optical layout of the components inside this monochromator. Fig. 2. Optical configuration of the monochromator. Polychromatic light from the arc will pass through the entrance slit of width SW 1 at various angles. The mirror M 1 is a plane mirror, so the light leaves M 1 in the same range of angles. However, the slit is at the focal point of a curved mirror M 2, so all rays leave the curved mirror in a parallel beam. This parallel light falls on the plane grating with spacing d. The angle at which light leaves the grating and forms an intensity pattern that results from constructive interference is given by the grating equation, m = d (sin i sin m ), where i is the angle of incidence and m is the angle of diffraction for order m. The parallel light leaving the grating again falls onto the curved mirror M 2, which refocuses it m away. The mirror M 3 merely changes the direction of the beam. Light with the right wavelength will be focused on and emerge from the exit slit, because its value of corresponds to the position of the slit. Refocused light of other wavelengths falls to the right or left of the exit slit and thus does not escape from the monochromator because the

3 m i d Fig. 3. A cross sectional view of a simple ruled grating of spacing d. corresponding values of are too large or too small. Hence the name monochromator or single color maker. If, instead of an exit slit, one places a strip of film or a CCD chip at the exit focal plane of M 2, light of various wavelengths can be simultaneously detected. Such an instrument is called a spectrometer. Open the monochromator by removing the 4 screws circled in red on the case. You will be able to see the two flat mirrors, one curved mirror and the grating. DO NOT TOUCH or exhale ON THE MIRRORS or GRATING!! IF YOU DO, THE OPTICS and will get coated with grime and THE THROUGHPUT of the MONOCHROMATOR will decrease.. Now close up the monochromator again and reinstall the screws to keep out dust, fingers, etc. Question B1. What is the focal length of the curved mirror? Make an estimate. The f/number or f stop of a lens or mirror is a measure of the fraction of light emitted by a source which is collected by the lens. It is given by f/d, where f is focal length and d is the diameter of the lens. Larger values of f stop means less light is collected, because of the smaller included angle. If you are to use the monochromator properly, it is important to fill it, that is, to illuminate the entire grating. To do this you will need to place a suitable lens between the spectrum tube and the entrance slit. Question B2. What is the f-stop of M 2? Make a reasonable estimate. Question B3. Suppose 2 camera lenses, both with f=50 mm, are described as f/1.4 and f/3.2. Which is likely to be better for taking a picture in dim light?. C. Silicon photodetector. The Newport Corp doped silicon photodetector and associated electronics is a quantum detector, that is, it detects photons. The photoconductor can detect photons with wavelength between 200 and 1100 nm. In the Newport 818 UV device, the medium is doped silicon, with energy diagram as shown below. When a photon falls on the detector, it raises an electron from the valence band or a donor band into the conduction band, thereby increasing the conductivity.

4 EMF Signal Conduction Band Incident Light Load Resistor E g Contact Valence Band Contact Semiconductor (A) (B) Fig. 4. (A) A diagram showing the operation of a photoconductive detector. (B) A band level diagram showing the mechanism for photoconductivity. The photon energy must exceed the band gap E g for a current to be produced. Question C1. What is the energy, in ev, of 656 nm photons? Is an undoped Si crystal (bandgap = 1.1 Volts) able to detect this? Note that if the signal is too weak or noisy with this detector, you can always observe the output of the spectrometer with your eye. D. Measurement of the H-atom emission spectrum and tests of Balmer's formula. Using a hand-held grating and your eye as detector, look at the light given off by the tube. Is the spectrum a continuum? Does it consist of lines? What are the colors of the lines? How many can you see? Using the monochromator and Si detector, measure the wavelengths of as many lines as you can, starting at 656 nm. Use 1 mm slitwidths on the monochromator. Align the apparatus to maximize the detected signal near 656 nm, which is the brightest line. Use a lens to fill the entrance slit and focusing mirror M 2. Question D1. What are the values of n initial and n final for the 656 line? Find at least 3 more lines in the Balmer series. Question D2. What are the values of n initial and n final for each line?

5 Imagine you are Balmer and are trying to find an equation describing the wavelengths in the Hydrogen spectrum. Here are some possible things you might try in Excel, a program in which Balmer was a wizard: Question D3. Plot wavelength (y axis) against an integer n or n 2 or 1/n or 1/n 2, with n=3 for the 656 line. Are any of these 4 plots linear? Now try Balmer s formula, plotting wavelength against n 2 /(n 2-4). Use Excel to do these plots. What are the physical significance of the slope and intercept in the plot which works? Question D4. A simpler way to see the physics behind the hydrogen spectrum is to plot the data in terms of photon energy, rather than wavelength. Plot 1/ (y axis) against 1/n 2, again with n=3 for the 656 line. Is the plot linear? What do you conclude from your results? What is the significance of the slope and intercept? Question D5. Make an energy level diagram for the hydrogen atom. Label the lines by their value of n and show the transitions that correspond to the observed lines of the hydrogen spectrum.