Pre-lab Quiz/PHYS 224 THE DIFFRACTION GRATING AND THE OPTICAL SPECTRUM Your name Lab section 1. What are the goals of this experiment? 2. If the period of a diffraction grating is d = 1,000 nm, where the light with a wavelength of 500 nm is incident perpendicularly to the surface of the grating, at what angle do you expect to detect the first diffraction order?
Lab Manual / PHYS 224 THE DIFFRACTION GRATING AND THE OPTICAL SPECTRUM OF MERCURY AND HYDROGEN INTRODUCTION: A diffraction grating is an optical device made by ruling (or holographically writing) a large number of evenly spaced lines on a glass or metal surface. With this device it is possible to measure the wavelength of light because of a physical phenomenon known as constructive interference. The actual grating that will be used in this experiment is known as a replica because it is made by spreading a thin layer of a polymer on the surface of a ruled grating. This replica grating, when dry, is peeled off and mounted between two glass plates. It can then be used as a transmission grating. The number of lines per centimeter is marked on the grating, but this is generally only an approximate value so that the exact value will have to be determined experimentally. When the light falls onto the grating at right angles (in other words, the light beam is perpendicular to the grating surface), it is split into rays formed by constructive interference which are found at angles s given by: m λ = d sin θ (1) where d is the distance between two adjacent lines on the grating, is the wavelength of the light ray and m = 0, 1, 2 specifies the order of the spectrum. For m = 0 all of the wavelength will have the same angle = 0. This is known as the zero-th order beam and it is transmitted straight through the grating without any deviation regardless of the wavelength. It can be used as the reference direction for = 0. For m = 1, one obtains a 1 st order spectrum of lines, where each wavelength is observed at a particular angle. There is a 1 st order spectrum on each side of the zero-th order angle, which is named here left and right angles. Another set of spectral lines with m = 2, the 2 nd order spectrum, can be observed where each specific wavelength will be seen at a higher angle compared to the one observed for the 1 st order spectrum. However, in general, the two sets of spectral lines (for m =1 and m =2) may well overlap i.e., the violet of the 2 nd order may appear with increasing before the red of the 1 st
order. Higher orders of a spectrum are used to increase the resolving power. This is the ability to separate two spectral lines which are so close together that, unresolved, they appear as just one line. The hydrogen source will give three and possibly four strong lines of the Balmer series. The wavelengths in the Balmer series are given by the Rydberg equation: 1 λ = R ( 1 2 2 1 n 2 ) (2) Where n = 3, 4, 5 The red line will correspond to n=3, the next line to n = 4, etc. R is the Rydberg constant. PROCEDURE: A. First use a mercury light source. Place the Hg light source in front of the slit. The light that goes through the slit is then collimated by some optics inside the tube, which is called the collimator. B. Next, align the other part of the spectrometer (the telescope unit, which is connected to a rotation stage) so that the cross hair inside the telescope tube lies at the center of the slit. At this position, the collimator and the telescope are in a straight line. C. Place the diffraction grating at the center of the spectrometer table so that the surface of the diffraction grating is approximately perpendicular to the collimator telescope axis. The surface of the grating should also be approximately at the center of the rotation stage. D. Look through the telescope and, if needed, re-adjust the table slightly so that the cross hair is at the center of the slit. Read the angle that the cross hair is right at the center of the slit. All angles to be measured later should be referenced to this angle (you will subtract this angle from any angle read-out you will measure). E. In order to measure an angle for a spectrum line (a particular wavelength), swing the telescope slowly until the spectrum line lies on the cross hairs. Read the angle and by subtract the reference angle to determine the angle of diffraction for this particular spectral line and diffraction order. Record your data on the table below. Swing the telescope to the other side of the reference angle (by about the same amount you had for the previous diffraction angle) and search for the exact angle to observe the same spectral
line. Afer you subtract the reference angle, record the second angle of diffraction. The average of these two s should be used, to help correct for any error in aligning the grating. Record the positions and intensities of the main lines in the first order mercury spectrum. Repeat for the second order spectrum. In recording a spectral line specify the color, the angle with respect to the central maximum (m = 0) and the relative intensity. For relative intensity use a scale of 10 where the strongest line would have a weight of 10, and the weakest line, less than 1. F. Set up the hydrogen lamp as a light source and measure the angles for the three or four hydrogen lines of the Balmer Series. QUESTIONS & ANALYSIS 1. The green line of Mercury will be used to calculate an accurate value for d. The wavelength of this line is: = 546.1 nm = 5461 Å = 5461 10-10 m. Use this to calculate d from the equation: m λ = d sin θ, where is the experimental angle determined in step E. This value of d will be used for all future calculations. 2. Complete the tables for mercury and hydrogen. Calculate the value of R for each hydrogen line that you measured, average these separate values of R and compare with the value predicted by Bohr Theory. 3. For the hydrogen lines draw a graph of 1/ versus 1/n 2 and show that the data fit a straight line. 4. Using your value of R and Balmer s equation predict one or two other wavelengths to be expected in the hydrogen atom. Why don t you see more than 3 or 4 lines in this experiment? Could there be another line in the Balmer Series in the infrared region? Explain. 5. Physically, what does the 2 correspond to in the equation (2)? What does the n correspond to? 6. For the hydrogen spectrum compare your s and R with accepted values. 7. Why do higher orders of the grating spectrum overlap? Discuss numerically the s you have used. 8. What are the limitations on m and in any given spectrometer? (HINT: how large can sin be?)
MERCURY m (order) color R L average Intensity HYDROGEN color R L average n R