Three Chapter 8

Einstein and the Photoelectric Effect

• Hertz in 1997 noticed that certain metallic surfaces lost their negative charge when exposed to ultraviolet light.
• The following apparatus can varify this observation

• As the light falls on the negatively charged zinc plate, the leaves of the electroscope will fall together.
• Because light and electricity was involved, the name photoelectric effect was given to this phenomenon.
• Photo Electrons - The electrons emitted by an object when light falls on the object
• The effect was studied by using the two set ups below.

• Case A
  • This case is for measuring photoelectric current.
  • There is a potential difference set up between anode and cathode so that no electrons flow between the electrodes when the apparatus is in the dark.
  • Light falls on the negatively charged cathode and causes the emission of photoelectrons.
  • The slightly positive anode causes all of the photoelectrons to be collected at the anode.
  • The ammeter measures the current and therefore counts the number of electrons.
• Case B
  • This case is for measuring the kinetic energy of the photoelectrons
  • Again, a potential difference is set up between the anode and cathode so that no electrons flow between the electrodes when the apparatus is in the dark.
  • Note that in this case the anode is negative and the cathode is positive.
  • Light falls on the positively charged cathode and causes the emission of photoelectrons.
  • Because the anode is negatevely charged, it repels the electrons.
  • By increasing the electric potential between the electrodes, the maximum kinetic energy of the photoelectrons can be determined
  • Current on the ammeter is zero when the potential difference is high enough to turn back all the electrons

Ek_max = q V_stop

• Experiments performed by using this apparatus gave some support to Planck's theories and provided the basis for Einstein's explanation of the photoelectric effect.

Einstein's Explanation

• The most significant results of the photoelectric effect are.
  • Electrons are emitted from the photoelectric surface when the incident light is above a certain frequency called the threshold frequency.
  • The intensity (brightness of the light) has no effect on the threshold frequency.
  • The threshold frequency, at which photoelectric emission first occurs, is different for different surfaces.
  • As the retarding potential that is applied to the anode is increased, the photo current (I) decreases, regardless of the intensity of the light.
  • If different frequencies of light, all above the threshold frequency, are directed at the same photoelectric surface, the cut-off potential is different for each. The higher the frequency of the light, the higher the cut-off potential.
  • When photo emission is occurring, the release of the electrons is immediate.
• None of these six observations is consistent with our wave view of light. Black body radiation is also not consistent with our wave view of light.
• If different metals are used as the cathode, and cut-off potentials are measured for different frequencies of light, the graph below is produced.

• Each line on the graph has the same slope. The slope = 6.63 X 10^-34 J.s. This value is called Planck's constant.
• To explain the effect, Einstein made the radical proposal that the energy of light is not transmitted in a continuous wave, but rather in concentrated bundles called photons.
• He also proposed that the energy in each bundle was given by Planck's equation:

E = hf

• Einstein was able to use this concept of the photon to explain the photoelectric effect. He also predicted new undetected effects from this photon model.
• The intensity of light was no longer related to wave amplitude, but to the rate of arrival of photons.
• If an electron gains energy from a photon (E=hf), and if the work required to remove the electron from the material is W, then the remaining energy (kinetic energy) will be given by:

qV_(stop) = Ek_(max) = hf - W

• W = the work function of the surface
• From the above equation, the larger the frequency, the larger the kinetic energy.
• If the photon has just enough energy to cause emission, then the photoelectrons will have zero kinetic energy after emission. Therefore we can write:

0 = hf - W (solving for W)

W = h(f_o) (f_o = the threshold frequency)

• Many things can happen at the surface of the metal.
  • Electrons get knocked back into the surface.
  • Electrons get knocked out of the surface at angles not equal to 90 degrees.
  • Electrons get knocked out of the surface at angles equal to 90 degrees.
• This means that not all electrons will be emitted with the same kinetic energy.
• When the electrons have to move against the force due to the electric field, only the most energetic electrons reach the anode.
• As the electric field is increased by increasing the potential difference, fewer and fewer electrons reach the anode until V = V_o (The stopping voltage) and then all electrons are turned back.
• It is for the above reason that the stopping voltage measures the maximum kinetic energy for the photoelectrons.
• Einstein's equation of the photoelectric effect explains the graph shown above, because his equation is the equation of a straight line with slope = h and y-intercept equal to -W.
• The x-intercepts for the different metals is the threshold frequency for that metal. Each metal has a different threshold frequency and work function.
• Millikan, In 1916 showed that Einstein's equation was quantitatively correct, and also he showed that Planck's constant had the value previously calculated by Planck.
• Note that there is another unit of energy called the electron volt (eV). It is the quantity of energy that an electron gains when it accelerates through a potential difference of 1 V.

eV = 1.6 X 10^-19J

Thermionic Effect

• There are limitations on electron flow through an evacuated tube. They are:
  • electrode size
  • electric potential difference.
• EDISON EFFECT - A plate positively charged inside of a turned on light bulb collects electrons but not if negatively charged.
• O.W. Richardson conducted research on the Edison effect. He suggested that heated surfaces in a vacuum evaporate electrons like molecules leaving a hot liquid. The positive plate then attracts electrons.
• THERMIONIC EMISSION - The process whereby electrons are emitted by a hot filament.
• DIODE - An electron tube which contains two electrodes.
  • A heated cathode is surrounded by a cylindrical anode or plate enclosed in an evacuated tube.
  • The current flows only from cathode to anode.
  • It was first used for detecting radio waves and converting alternating current to pulsating direct current.
  • By Introducing other charged plates:
    • current can be controlled.
    • current can be amplified.
    • current can be shut off.
• VACUUM TUBE - A device such as a diode.
  • Vacuum tubes are used in devices such as radios, televisions, sound amplifiers, rectifiers, radar equipment, and computers.
  • Transistors and integrated circuits now replace these vacuum tubes.

January 20, 2014