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October 29


PHYSICS                            2012

ubmitted by: - Swarup Kumar Boro
 ass: - XII
Contents
1. Photoelectric Effect


2. Laws of Photoelectric Emission



3. The Classical Wave Explanation



4. Hertz’s Observations



5. Lenard’s Observations



6. Einstein’s Photoelectric Equation:

7. Application of Photoelectric Effect:


8. de Broglie wave:


9. Davisson and Germer Experiment
Photoelectric Effect
The photoelectric effect posed a significant challenge to
the study of optics in the latter portion of the 1800s. It
challenged the classical wave theory of light, which was
the prevailing theory of the time. It was the solution to
this physics dilemma that catapulted Einstein into
prominence in the physics community, ultimately earning
him the 1921 Nobel Prize.




    Though originally observed in 1839, the photoelectric
effect was documented by Heinrich Hertz in 1887 in a
paper to the Annalen der Physik. It was originally called
the Hertz effect, in fact, though this name fell out of use.
When a light source (or, more generally, electromagnetic
radiation) is incident upon a metallic surface, the surface
can emit electrons. Electrons emitted in this fashion are
called photoelectrons (although they are still just
electrons). This is depicted in the image to the right.



Setting Up the Photoelectric
Effect
       To observe the photoelectric effect, you create a
vacuum chamber with the photoconductive metal at one
end and a collector at the other. When a light shines on
the metal, the electrons are released and move through the
vacuum toward the collector. This creates a current in the
wires connecting the two ends, which can be measured
with an ammeter. (A basic example of the experiment can
be seen by clicking on the image to the right, and then
advancing to the second image available.)


         By administering a negative voltage potential (the
black box in the picture) to the collector, it takes more
energy for the electrons to complete the journey and
initiate the current. The point at which no electrons make
it to the collector is called the stopping potential Vs, and
can be used to determine the maximum kinetic energy
Kmax of the electrons (which have electronic charge e) by
using the following equation:
Kmax = eVs
It is significant to note that not all of the electrons will
have this energy, but will be emitted with a range of
energies based upon the properties of the metal being
used. The above equation allows us to calculate the
maximum kinetic energy or, in other words, the energy of
the particles knocked free of the metal surface with the
greatest speed, which will be the trait that is most useful
in the rest of this analysis.
Laws of Photoelectric Emission
  i) For a given substance, there is a minimum value of
     frequency of incident light called threshold frequency
     below which no photoelectric emission is possible,
     howsoever, the intensity of incident light may be.
 ii) The number of photoelectrons emitted per second
     (i.e. photoelectric current) is directly proportional to
     the intensity of incident light provided the frequency
     is above the threshold frequency.
iii) The maximum kinetic energy of the photoelectrons is
     directly proportional to the frequency provided the
     frequency is above the threshold frequency.
iv) The maximum kinetic energy of the photoelectrons is
     independent of the intensity of the incident light.
 v) The process of photoelectric emission is
     instantaneous. I.e. as soon as the photon of suitable
     frequency falls on the substance, it emits
     photoelectrons.
vi) The photoelectric emission is one-to-one. i.e. for
     every photon of suitable frequency one electron is
     emitted.
The Classical Wave Explanation
In classical wave theory, the energy of electromagnetic
radiation is carried within the wave itself. As the
electromagnetic wave (of intensity I) collides with the
surface, the electron absorbs the energy from the wave
until it exceeds the binding energy, releasing the electron
from the metal. The minimum energy needed to remove
the electron is the work function phi of the material. (Phi
is in the range of a few electron-volts for most common
photoelectric materials.)
Three main predictions come from this classical
explanation:
  1. The intensity of the radiation should have a
     proportional relationship with the resulting maximum
     kinetic energy.
  2. The photoelectric effect should occur for any light,
     regardless of frequency or wavelength.
  3. There should be a delay on the order of seconds
     between the radiation’s contact with the metal and
     the initial release of photoelectrons.
The Experimental Result
By 1902, the properties of the photoelectric effect were
well documented. Experiment showed that:
  1. The intensity of the light source had no effect on the
     maximum kinetic energy of the photoelectrons.
  2. Below a certain frequency, the photoelectric effect
     does not occur at all.
  3. There is no significant delay (less than 10-9 s)
     between the light source activation and the emission
     of the first photoelectrons.
Hertz’s ObservatiOns
The phenomenon of photoelectric effect was discovered
by Heinrich Hertz in 1887. While performing an
experiment for production of electromagnetic waves by
means of spark discharge, Hertz observed that sparks
occurred more rapidly in the air gap of his transmitter
when ultraviolet radiations was directed at one of the
metal plates. Hertz could not explain his observations but
other scientists did it. They arrived at the conclusion that
the cause was the emission of electron from metal plate
due to incidence of high frequency light. This is
photoelectric effect.
Lenard’s ObservatiOns
Phillip Lenard observed that when ultraviolet radiations
were made incident on the emitter plate of an evacuated
glass tube enclosing two metal plates (called electrodes),
current flows in the circuit, but as soon as ultraviolet
radiation falling on the emitter plate was stopped, the
current flow stopped. These observations indicate that
when ultraviolet radiations fall on the emitter (cathode)
plate C, the electrons are ejected from it, which are
attracted towards anode plate A. The electrons flow
through the evacuated glass tube, complete the circuit and
current begins to flow in the circuit. Then Hallwach’s and
Lenard studied the phenomenon in detail.
Hallwach’s studied further by taking a zinc plate and an
electroscope. The zinc plate was connected to an
electroscope. He observed that :
(i) When an uncharged zinc plate was irradiated by
ultraviolet light, the zinc plate acquired positive charge.
(ii) When a positively charged zinc plate is illuminated by
ultraviolet light, the positive charge of the plate was
increased.
(iii) When a negatively charged zinc plate was irradiated
by ultraviolet light, the zinc plate lost its charge.
All these observations show that when ultraviolet light
falls on zinc plate, the negatively charged particles
(electrons) are emitted.
Further study shows that different metals emit electrons
by different electromagnetic radiations. For example the
alkali metals (e.g., sodium, cesium, potassium etc.) emit
electrons when visible light is incident on them. The
heavy metals (such as zinc, cadmium, magnesium etc.)
emit electrons when ultraviolet radiation is incident on
them.
Cesium is the most sensitive metal for photoelectric
emission. It can emit electrons with less-energetic infrared
radiation.
In photoelectric effect the light energy is converted into
electrical energy.
einstein’s PHOtOeLectric
Equation:
   When a photon of energy hν falls on a metal surface,
the energy of the photon is absorbed by the electron and is
used in two ways:
i) A part of energy is used to overcome the surface
   barrier and come out of the metal surface. This part
   of the energy is called ‘work function’       (Ф =
   hν0).
ii) The remaining part of the energy is used in giving a
    velocity ‘v’ to the emitted photoelectron. This is
    equal to the maximum kinetic energy of the
    photoelectrons ( ½ mv2max ) where ‘m’ is mass of the
    photoelectron.
    According to law of conservation of energy,
            hν = Ф + ½ mv2max
               = hν0 + ½ mv2max
            ½ mv2max = h (ν - ν0)
Application of Photoelectric
    Effect:
  1. Automatic fire alarm
  2. Automatic burglar alarm
  3. Scanners in Television transmission
  4. Reproduction of sound in cinema film
  5. In paper industry to measure the thickness of paper
  6. To locate flaws or holes in the finished goods
  7. In astronomy
  8. To determine opacity of solids and liquids
  9. Automatic switching of street lights
  10.   To control the temperature of furnace
  11.   Photometry
  12. Beauty meter – To measure the fair complexion of
  skin
   13. Light meters used in cinema industry to check the
light
  12.   Photoelectric sorting
de Broglie wave:
      According to de Broglie, a moving material particle
      can be associated with a wave. i.e. a wave can guide
      the motion of the particle.
      The waves associated with the moving material
      particles are known as                de Broglie
      waves or matter waves.




      Expression for de Broglie wave:


      According to quantum theory, the energy of the
      photon is


According to Einstein’s theory, the energy of the photon
is
E=mc2
So,
Or
           Where p = mc is momentum of a photon
If instead of a photon, we have a material particle of mass
m moving with velocity v, then the equation becomes
         . This is the expression for de Broglie
wavelength.

Conclusion:
 i) de Broglie wavelength is inversely proportional to the
    velocity of the particle. If the particle moves faster,
    then the wavelength will be smaller and vice versa.
ii) If the particle is at rest, then the de Broglie
    wavelength is infinite. Such a wave cannot be
    visualized.
iii) de Broglie wavelength is inversely proportional to the
     mass of the particle. The wavelength associated with
     a heavier particle is smaller than that with a lighter
     particle.
iv) de Broglie wavelength is independent of the charge
    of the particle.



  Davisson and Germer Experiment
      A beam of electrons emitted by the electron gun is
made to fall on Nickel crystal cut along cubical axis at a
particular angle.
      The scattered beam of electrons is received by the
detector which can be rotated at any angle.
      The energy of the incident beam of electrons can be
varied by changing the applied voltage to the electron
gun.
      Intensity of scattered beam of electrons is found to
be maximum when angle of scattering is 50° and the
accelerating potential is 54 V



Electron diffraction is similar to X-ray diffraction.
Bragg’s equation 2dsinθ = nλ gives
λ = 1.65 Å
Physics

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Physics

  • 1. October 29 PHYSICS 2012 ubmitted by: - Swarup Kumar Boro ass: - XII
  • 2. Contents 1. Photoelectric Effect 2. Laws of Photoelectric Emission 3. The Classical Wave Explanation 4. Hertz’s Observations 5. Lenard’s Observations 6. Einstein’s Photoelectric Equation: 7. Application of Photoelectric Effect: 8. de Broglie wave: 9. Davisson and Germer Experiment
  • 3. Photoelectric Effect The photoelectric effect posed a significant challenge to the study of optics in the latter portion of the 1800s. It challenged the classical wave theory of light, which was the prevailing theory of the time. It was the solution to this physics dilemma that catapulted Einstein into prominence in the physics community, ultimately earning him the 1921 Nobel Prize. Though originally observed in 1839, the photoelectric effect was documented by Heinrich Hertz in 1887 in a paper to the Annalen der Physik. It was originally called the Hertz effect, in fact, though this name fell out of use.
  • 4. When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right. Setting Up the Photoelectric Effect To observe the photoelectric effect, you create a vacuum chamber with the photoconductive metal at one end and a collector at the other. When a light shines on the metal, the electrons are released and move through the vacuum toward the collector. This creates a current in the wires connecting the two ends, which can be measured with an ammeter. (A basic example of the experiment can be seen by clicking on the image to the right, and then advancing to the second image available.) By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and
  • 5. can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation: Kmax = eVs It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.
  • 6. Laws of Photoelectric Emission i) For a given substance, there is a minimum value of frequency of incident light called threshold frequency below which no photoelectric emission is possible, howsoever, the intensity of incident light may be. ii) The number of photoelectrons emitted per second (i.e. photoelectric current) is directly proportional to the intensity of incident light provided the frequency is above the threshold frequency. iii) The maximum kinetic energy of the photoelectrons is directly proportional to the frequency provided the frequency is above the threshold frequency. iv) The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light. v) The process of photoelectric emission is instantaneous. I.e. as soon as the photon of suitable frequency falls on the substance, it emits photoelectrons. vi) The photoelectric emission is one-to-one. i.e. for every photon of suitable frequency one electron is emitted.
  • 7. The Classical Wave Explanation In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is the work function phi of the material. (Phi is in the range of a few electron-volts for most common photoelectric materials.) Three main predictions come from this classical explanation: 1. The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy. 2. The photoelectric effect should occur for any light, regardless of frequency or wavelength. 3. There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
  • 8. The Experimental Result By 1902, the properties of the photoelectric effect were well documented. Experiment showed that: 1. The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons. 2. Below a certain frequency, the photoelectric effect does not occur at all. 3. There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
  • 9. Hertz’s ObservatiOns The phenomenon of photoelectric effect was discovered by Heinrich Hertz in 1887. While performing an experiment for production of electromagnetic waves by means of spark discharge, Hertz observed that sparks occurred more rapidly in the air gap of his transmitter when ultraviolet radiations was directed at one of the metal plates. Hertz could not explain his observations but other scientists did it. They arrived at the conclusion that the cause was the emission of electron from metal plate due to incidence of high frequency light. This is photoelectric effect.
  • 10. Lenard’s ObservatiOns Phillip Lenard observed that when ultraviolet radiations were made incident on the emitter plate of an evacuated glass tube enclosing two metal plates (called electrodes), current flows in the circuit, but as soon as ultraviolet radiation falling on the emitter plate was stopped, the current flow stopped. These observations indicate that when ultraviolet radiations fall on the emitter (cathode) plate C, the electrons are ejected from it, which are attracted towards anode plate A. The electrons flow through the evacuated glass tube, complete the circuit and current begins to flow in the circuit. Then Hallwach’s and Lenard studied the phenomenon in detail. Hallwach’s studied further by taking a zinc plate and an electroscope. The zinc plate was connected to an electroscope. He observed that : (i) When an uncharged zinc plate was irradiated by ultraviolet light, the zinc plate acquired positive charge. (ii) When a positively charged zinc plate is illuminated by ultraviolet light, the positive charge of the plate was increased. (iii) When a negatively charged zinc plate was irradiated by ultraviolet light, the zinc plate lost its charge.
  • 11. All these observations show that when ultraviolet light falls on zinc plate, the negatively charged particles (electrons) are emitted. Further study shows that different metals emit electrons by different electromagnetic radiations. For example the alkali metals (e.g., sodium, cesium, potassium etc.) emit electrons when visible light is incident on them. The heavy metals (such as zinc, cadmium, magnesium etc.) emit electrons when ultraviolet radiation is incident on them. Cesium is the most sensitive metal for photoelectric emission. It can emit electrons with less-energetic infrared radiation. In photoelectric effect the light energy is converted into electrical energy.
  • 12. einstein’s PHOtOeLectric Equation: When a photon of energy hν falls on a metal surface, the energy of the photon is absorbed by the electron and is used in two ways: i) A part of energy is used to overcome the surface barrier and come out of the metal surface. This part of the energy is called ‘work function’ (Ф = hν0). ii) The remaining part of the energy is used in giving a velocity ‘v’ to the emitted photoelectron. This is equal to the maximum kinetic energy of the photoelectrons ( ½ mv2max ) where ‘m’ is mass of the photoelectron. According to law of conservation of energy, hν = Ф + ½ mv2max = hν0 + ½ mv2max ½ mv2max = h (ν - ν0)
  • 13. Application of Photoelectric Effect: 1. Automatic fire alarm 2. Automatic burglar alarm 3. Scanners in Television transmission 4. Reproduction of sound in cinema film 5. In paper industry to measure the thickness of paper 6. To locate flaws or holes in the finished goods 7. In astronomy 8. To determine opacity of solids and liquids 9. Automatic switching of street lights 10. To control the temperature of furnace 11. Photometry 12. Beauty meter – To measure the fair complexion of skin 13. Light meters used in cinema industry to check the light 12. Photoelectric sorting
  • 14. de Broglie wave: According to de Broglie, a moving material particle can be associated with a wave. i.e. a wave can guide the motion of the particle. The waves associated with the moving material particles are known as de Broglie waves or matter waves. Expression for de Broglie wave: According to quantum theory, the energy of the photon is According to Einstein’s theory, the energy of the photon is E=mc2 So,
  • 15. Or Where p = mc is momentum of a photon If instead of a photon, we have a material particle of mass m moving with velocity v, then the equation becomes . This is the expression for de Broglie wavelength. Conclusion: i) de Broglie wavelength is inversely proportional to the velocity of the particle. If the particle moves faster, then the wavelength will be smaller and vice versa. ii) If the particle is at rest, then the de Broglie wavelength is infinite. Such a wave cannot be visualized. iii) de Broglie wavelength is inversely proportional to the mass of the particle. The wavelength associated with a heavier particle is smaller than that with a lighter particle.
  • 16. iv) de Broglie wavelength is independent of the charge of the particle. Davisson and Germer Experiment A beam of electrons emitted by the electron gun is made to fall on Nickel crystal cut along cubical axis at a particular angle. The scattered beam of electrons is received by the detector which can be rotated at any angle. The energy of the incident beam of electrons can be varied by changing the applied voltage to the electron gun. Intensity of scattered beam of electrons is found to be maximum when angle of scattering is 50° and the accelerating potential is 54 V Electron diffraction is similar to X-ray diffraction. Bragg’s equation 2dsinθ = nλ gives λ = 1.65 Å