Lecture_04: Outline Photoelectric Effect  Experimental facts  Einstein’s explanation  Problems

Experimental facts The photoelectric effect occurs when light incident on certain metallic surfaces causes electrons to be emitted from those surfaces –The emitted electrons are called photoelectrons When the tube is kept in the dark, the ammeter reads zero When plate E is illuminated by light having an appropriate wavelength, a current is detected by the ammeter The current arises from photoelectrons emitted from the negative plate and collected at the positive plate Additional voltage applied to the plates controls electron transport

Experimental facts Experimental results: At large values of V, the current reaches a maximum value –All the electrons emitted at E are collected at C The maximum current increases as the intensity of the incident light increases When V is negative, the current drops When V is equal to or more negative than V 0, the current is zero -V 0

Experimental facts Experimental facts: Dependence of photoelectron kinetic energy on light intensity –Classical Prediction As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy –Experimental Result The maximum kinetic energy is independent of light intensity

Experimental facts Experimental facts: Time interval between incidence of light and ejection of photoelectrons –Classical Prediction At low light intensities, a measurable time interval should pass between the instant the light is turned on and the time an electron is ejected from the metal This time interval is required for the electron to absorb the incident radiation before it acquires enough energy to escape from the metal –Experimental Result Electrons are emitted almost instantaneously, even at very low light intensities

Experimental facts Experimental facts: Dependence of ejection of electrons on light frequency –Classical Prediction Electrons should be ejected at any frequency as long as the light intensity is high enough –Experimental Result No electrons are emitted if the incident light falls below some cutoff frequency, ν 0 The cutoff frequency is characteristic of the material being illuminated

Experimental facts Experimental facts: Dependence of photoelectron kinetic energy on light frequency –Classical Prediction There should be no relationship between the frequency of the light and the electric kinetic energy –Experimental Result The maximum kinetic energy of the photoelectrons increases with increasing light frequency

Einstein’s explanation Photons: Radiant energy is quantized into localized bundles moving with velocity c and having energy proportional to the frequency These particlelike bundles are called photons In the photoelectric process one photon is completely absorbed by one electron

Einstein’s explanation w 0 is work function

Einstein’s explanation Dependence of photoelectron kinetic energy on light intensity Increasing the intensity means increasing the number of photons. Consequently, the number of electron (i.e. current) also increases. But the maximum kinetic energy determined by the stopping voltage depends on the frequency and remains the same.

Einstein’s explanation Time interval between incidence of light and ejection of photoelectrons Energy is supplied in concentrated bundles. For any low density, it would be at least one photon absorbed by some atom, so at least one electron escapes from the plate. Energy supplied by the electromagnetic wave is proportional not to the electric field magnitude squared but to the wave frequency.

Einstein’s explanation Dependence of photoelectron kinetic energy on light frequency Increasing of the frequency with the same work function means increasing of the maximal kinetic energy which manifest itself in larger stopping voltage.

Einstein’s explanation Dependence of ejection of electrons on light frequency If the light frequency is smaller than the work function, no electrons can be ejected The slope of this dependence (h/e) does not depend on the work function, is the same for all materials, and is determined by fundamental constants h = · J·s

Problems Molybdenum has a work function of 4.2 eV. (a) Find the cutoff wavelength and cutoff frequency for the photoelectric effect. (b) What is the stopping potential if the incident light has a wavelength of 180 nm? 1 eV = 1.6ּ J

Problems When green light with λ = nm (mercury lamp) is used for the photoelectric experiment, a stopping potential of V reduces the photocurrent to zero. (a) What is the work function for this metal? (b) What stopping potential would be observed if the yellow light with λ = nm (helium discharge tube) is used?

Problems Electrons are ejected from a metallic surface with speeds ranging up to 4.6ּ10 5 m/s when light with a wavelength of 625 nm is used. (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface?