LC-4: Photoelectric Effect Lab Worksheet Name_____________________________ In this lab you investigate the photoelectric effect, one of the experiments whose explanation by Einstein forced scientists into accepting the ideas of quantum mechanics. In the photoelectric effect, light knocks electrons out of a metal, which are then detected by an electrical circuit. Electrons are ejected because the light transfers energy to electrons in the metal. A particular electron absorbs energy from the light. It uses some of that energy to break free of the metal: the amount of energy required to break free is called the Work Function of the metal. The remaining energy shows up as kinetic energy of motion of the electron. The experimental observation is that electrons with a range of energies are ejected from the metal, and that the maximum electron kinetic energy observed depends on the frequency of the light, but does not depend on its intensity. Einstein’s solution is that light is ‘quantized’, meaning that its energy increases only in steps of hf, where h is a constant (Planck’s constant), and f is the frequency of light. An equivalent interpretation is that light is made up of particles called photons, each with energy hf. Another classic experiment, Compton scattering, showed that light interacts with electrons just as if they were both colliding balls, if the photon light ‘ball’ has energy ! E = hfand momentum! p = E /c. In your experiment you will use different frequencies of light to knock electrons out of a metal, measure the maximum kinetic energy in each case, and determine the relation between that maximum KE and the light frequency. The pieces of your experiment are: 1) A mercury vapor light source. 2) A diffraction grating to separate the different wavelengths from the mercury lamp, and a lens to make on image of these wavelengths on a photoelectric tube 3) The photodetector and track from the interference lab. You will use this to determine the mercury wavelengths. 4) A photoelectric tube containing two metal plates, one from which the light will eject electrons, and one that will collect the ejected electrons. The tube is inside a black box that says ‘h/e apparatus’. It needs to be switched on because the box also contains an amplifier. There are four parts to this lab: A) Measure the different wavelengths of light produced by the mercury lamp. B) Measure the photoelectric stopping potential for each wavelength and find wavelength dependence (this will let you determine Planck’s constant.) C) Measure the dependence of the stopping potential on light intensity. D) Measure the time ‘charging time’ of the photoelectric tube to learn something about the distribution of the ejected electrons.2 ! x L θ d dsinθ = path length difference θ Experiment A: Measure the wavelengths of the light coming from the mercury lamp. Turn on the mercury lamp now to let it warm up The mercury vapor lamp uses a diffraction grating to disperse the different wavelengths of light. Its effect is similar to a prism, but its operating principle is that of the two-slit interference phenomenon you looked at last week. Instead of just two slits separated by 0.4 mm, your diffraction grating has thousands of very narrow slits at a pitch of 600 ‘slits’/mm. And instead of using a single wavelength (red), you are using light from the mercury lamp, which contains many colors. Each individual color will give you a diffraction pattern like you saw last week. First, consider just two of the slits in the diffraction grating. A1) Think about the light arriving at the point on the screen shown. What is the condition for constructive interference of the two waves from the two adjacent slits shown at the location (answer in terms of d, θ, and λ)3 A2) Assuming that this constructive interference condition for two neighboring slits is met, what is the path length difference between waves originating from pairs of slits 2d apart? 3d apart? nd apart? A3) Suppose you measure that constructive interference occurs at a distance x from the central maximum on the screen. Write an equation for the x-distance on the screen from the central maximum at which constructive interference occurs. Answer in terms of λ, d, and L. Note: If you are considering using the ‘small-angle approximation’, look at the angle to the yellow line and see if you think it is small. If you are not using that approximation, don’t read this. A4) Determine the wavelength of the spectral lines from the mercury lamp (use the computer and the movable photodetector, and the DataStudio settings file from the interference lab LC-1_IntDiff.ds). i) Put the photodetector about 21 cm from the diffraction grating, and adjust the grating/lens position to give a reasonably focused image of the lamp slit on the photodetector wheel. ii) You may need to adjust the photodetector gain (slide switch on top) to get a good signal. You might also change the photodetector slit. iii) Make sure the motion of the photodetector is perpendicular to the undiffracted beam lamp. NOTE: one of the lines is in the ultraviolet, and only visible to your eye when the material it strikes fluoresces. The photodetector is not sensitive to the UV line. Line # Line color distance from central peak (cm) Wavelength (nm) 1 UV 365.48 nm 2 3 4 54 Experiment B: Measure the ‘stopping potential’ for each different wavelength to verify the quantum nature of light and to determine Planck’s constant. Your photoelectric tube is a shown below. B1) Suppose the photon transfers some energy to an electron in the cathode so that it has 1 electron-volt (eV) of energy after it is ejected. How fast is it traveling (me=9.11x10-31 kg, e=1.6x10-19 C)? B2) The ejected electron leaves the anode and ends up on the cathode What is the direction of the electric field after this charge transfer? What is the direction of the resulting force on the electrons? B3) What is the maximum kinetic energy of an ejected electron (cathode work function = W, incoming light has frequency f)? B4) The anode continues to charge up
View Full Document
Unlocking...