dual nature

• The Maxwell's equations of electromagnetism and Hertz experiments on the generation and detection of electromagnetic waves in 1887 strongly established the wave nature of light
• Experimental investigations on conduction of electricity (electric discharge) through gases at low pressure in a discharge tube led to many historic discoveries
• The discovery of X-rays by Roentgen in 1895, and of electron by J. J. Thomson in 1897, were important milestones in the understanding of atomic structure
• Cathode rays


  Streams of fast moving negatively charged particles discovered by William Crookes in 1870
• Cathode ray particles


  • Their speed ranged from about 0.1 to 0.2 times the speed of light
  • Their specific charge (e/m) was found to be independent of the nature of the material/metal used as the cathode (emitter), or the gas introduced in the discharge tube
• Electrons


  Fundamental, universal constituents of matter, named by J.J. Thomson in 1897
• In 1913, R.A. Millikan performed the pioneering oil-drop experiment for the precise measurement of the charge on an electron, establishing that electric charge is quantised
• Work function


  The minimum energy required for an electron to escape from the metal surface
• Processes that can supply the minimum energy required for electron emission

  • Thermionic emission
  • Field emission
  • Photoelectric emission
• The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz during his electromagnetic wave experiments
• Photoelectrons


  Electrons emitted from a metal surface when it is illuminated by light
• Hallwachs and Lenard observed that when ultraviolet light fell on the emitter plate, no electrons were emitted at all when the frequency of the incident light was smaller than a certain minimum value, called the threshold frequency
• Certain metals like zinc, cadmium, magnesium, etc. responded only to ultraviolet light, having short wavelength, to cause electron emission from the surface, while some alkali metals such as lithium, sodium, potassium, caesium and rubidium were sensitive even to visible light
• Experimental arrangement for studying photoelectric effect

  • Evacuated glass/quartz tube with a thin photosensitive plate (emitter) and a metal plate (collector)
  • Monochromatic light source to irradiate the emitter plate
  • Battery to maintain potential difference between emitter and collector plates
  • Voltmeter and microammeter to measure potential difference and photocurrent respectively
• Intensity of incident light is increased


  Photocurrent increases linearly
• The photocurrent is directly proportional to the number of photoelectrons emitted per second
• Experimental arrangement for study of photoelectric effect

  • Filter or coloured glass in the path of light falling on the emitter C
  • Intensity of light varied by changing distance of light source from emitter
• Effect of intensity of light on photocurrent

  1. Collector A maintained at positive potential to attract electrons from emitter C

  2. Intensity of light varied, photocurrent measured

  3. Photocurrent increases linearly with intensity of incident light

  4. Photocurrent directly proportional to number of photoelectrons emitted per second

  5. Number of photoelectrons emitted per second directly proportional to intensity of incident radiation
• Effect of potential on photoelectric current

  1. Plate A at positive potential with respect to plate C, illuminated with light of fixed frequency and intensity

  2. Positive potential of plate A varied, photocurrent measured

  3. Photocurrent increases with increase in positive (accelerating) potential

  4. At certain positive potential, all emitted electrons collected, photocurrent saturates (saturation current)

  5. Negative (retarding) potential applied to plate A, photocurrent decreases until it drops to zero at critical value of negative potential (cut-off or stopping potential)

  6. Stopping potential independent of intensity, depends only on frequency of incident radiation
• Effect of frequency of incident radiation on stopping potential

  1. Intensity of light adjusted, photocurrent vs collector plate potential studied for different frequencies

  2. Stopping potential more negative for higher frequencies

  3. Stopping potential varies linearly with frequency of incident radiation

  4. Minimum cut-off frequency (threshold frequency) exists below which no photoelectric emission occurs
• Photoelectric emission is an instantaneous process without any apparent time lag (~10^-9 s or less), even with exceedingly dim incident radiation
• Wave theory of light cannot explain the observations on photoelectric effect
• Einstein's photoelectric equation

  Kmax = hν - φ0, where Kmax is maximum kinetic energy of photoelectrons, h is Planck's constant, ν is frequency of incident radiation, and φ0 is work function of the metal
• Einstein's photoelectric equation accounts for all the observations on photoelectric effect
• Work function (f0)


  The minimum energy required to remove an electron from the metal surface
• More tightly bound electrons will emerge with kinetic energies less than the maximum value
• The intensity of light of a given frequency is determined by the number of photons incident per second
• Increasing the intensity will increase the number of emitted electrons per second
• The maximum kinetic energy of the emitted photoelectrons is determined by the energy of each photon
• Einstein's photoelectric equation


  Kmax = hν - f0
• Equation (11.2) accounts for all the observations on the photoelectric effect
• According to Eq. (11.2), Kmax depends linearly on ν

  Kmax is independent of intensity of radiation
• In Einstein's picture, photoelectric effect arises from the absorption of a single quantum of radiation by a single electron
• The intensity of radiation is irrelevant to the basic process of photoelectric effect
• There exists a threshold frequency ν0 below which no photoelectric emission is possible, no matter how intense the incident radiation may be
• In Einstein's picture, the basic elementary process involved in photoelectric effect is the instantaneous absorption of a light quantum by an electron
• Low intensity does not mean delay in emission, since the basic elementary process is the same
• The V0 versus ν curve is a straight line with slope = (h/e), independent of the nature of the material
• Millikan verified the photoelectric equation with great precision, for a number of alkali metals over a wide range of radiation frequencies
• Photon


  The particle-like behaviour of light