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PHOTOELECTRIC EFFECT:

1. Photoelectric effect is the phenomenon of emission of electron from surface of a metal surface when light of shorter wavelength is incident on it.
2. This was discovered in 1887 by Heinrich Hertz. Further developed by Hallwachs in 1888.
3. In 1899 Phillip Lenard(student of Hertz) showed that the carries of electricity emitted from a metal surface under the action of UV rays were electrons.

EXPERIMENTAL STUDY:

• It consists of an evacuated glass tube having two electrodes, one is emitter E (coated with Barium Oxide) & the other is collector C.
• Light from a source after passing through the quartz window W made to fall on the emitter E.
• Collecting electrode C can be provided with a variable potential with the help of commutator key. This can provide positive & negative potential.
• P.D between both the electrodes is noted with a voltmeter V while current is measured with the help  of ammeter A.
• When light is incident on E, electrons are ejected & goes to the plate C, producing photoelectric current if collector is provided with suitable potential.
Now let us study the effect of intensity, potential, frequency on photoelectric current.

A. Effect of Intensity:

• Keeping the collector potential fixed, the current is studied for different values of intensities.
• The graph between photoelectric current & intensity is found to be a straight line starting from origin, which shows that the photoelectric current is directly proportional to the intensity of incident radiation.
B. Effect of Collector potential on photoelectric current:

• Keeping the intensity & frequency of light constant, the value of current in the circuit was noted by changing the collector potential from positive to zero & to negative values.
• The graph above is plotted between collector potential with current for different intensities of light.
• Each curve shows that the current changes continuously with a change in potential of collector.
•  The potential attains a certain negative value for zero value of current, known as stopping potential.
• Presence of current for zero value of potential indicates that the electrons are ejected with some energy.
• A gradual change in the number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with varieties of velocities.
• For any potential of collector, the current in case of high intensity is greater than that for low intensity. This indicates that current depends on intensity of incident light.
• All the curves meet at the same position on X-axis indicating that the stopping potential is independent of intensity of incident radiation.
C. Effect of Frequency of light:
• Taking current in Y-axis & collector potential in X-axis, the experimented was repeated for different frequencies Î½1, Î½2 & Î½3 giving the same intensity of light.
• The curves shows that stopping potential depends upon the frequency of light. Greater is the frequency of light, greater is the stopping potential. Saturation current is independent of frequency.

• A graph between stopping potential & frequency is plotted above. This line indicates that for frequency Î½0, there will be no current when collector is at zero potential. This is the minimum frequency capable of producing photoelectric effect & is called threshold frequency. Greater the frequency of light, greater the negative value of potential required to stop the current, hence maximum energy of the emitted electrons depends upon the frequency of light.
LAWS OF PHOTOELECTRIC EFFECT:
1. Photoelectric effect is an instantaneous process.
2. Photoelectric current is directly proportional to the intensity of incident radiation & independent of frequency of radiation.
3. The stopping potential & hence the velocity of electron depends upon the frequency of incident light & independent of intensity of light.
4. The emission of electrons stops below a certain frequency known as threshold frequency.
Quantum Theory of Photoelectric Effect/ Einstein Theory of Photoelectric Effect:
• In 1905, Einstein applied the quantum theory of radiation & satisfactorily explained the observables facts of photoelectric effect.
• Einstein assumed that the light of frequency is Î½ composed of localized bundles of electromagnetic energy called photons (that is quanta of energy) having energy E=hÎ½. The photon always moves with the speed of light & having the property of zero rest mass.
• The numbers of photons in a light beam is proportional to the intensity of incident radiation.
• Electrons at the surface of the metal are loosely bound to the metal with a binding energy w0. Thus minimum amount energy needed to free an electron from the metal surface known as work function (It is of the order of few electron volt)
•  When light of frequency Î½ is incident on the metallic surface, each photon interacts with one electron & completely transfers its energy to the electron, thus electron gains hÎ½.
• If hÎ½ >w0, then electrons from the metal surface is knocked out & the excess energy (hÎ½ -w0) appears as the kinetic energy of the ejected electron.
• The maximum value of kinetic energy equation can be written as,

• If Î½0 is the threshold frequency having energy hÎ½0, then w0=hÎ½0,
This is called Einstein Photoelectric equation.
• From the above equation, it is clear that greater the frequency of incident light, greater the kinetic energy, hence greater the negative potential to stop it. An increase in intensity of incident light, increases the number of photons which results in increase in more number of photoelectrons, hence photoelectric current is proportional to the intensity of light.
• If the frequency of incident radiation is less than Î½0, then the electron can't overcome the potential barrier.
NOTES:
If Vo=stopping potential

Thus the intercept of Î½0~Î½ curve on Î½-axis gives the value of threshold frequency.

Work function= e x (Intercept on V0 axis)
Planck's constant= e x (slope of Î½0~Î½ curve)

FAILURE OF CLASSICAL THEORY:
• Classical theory fails to explain that photoelectric effect is an instantaneous process, because according to classical theory light is a form of electromagnetic wave.
• According to classical theory, the greater the intensity of incident light, greater the kinetic energy of the photoelectrons. So it fails.
• Classical theory fails to explain the existence of threshold frequency.
QUESTIONS:

Q1: For a given metallic surface, the stopping potential is V1, for a radiation of wavelength  Î»1 & V2 for a radiation of wavelength  Î»2, then show that the Planck's constant is given by
Ans: The stopping potential is given by the equation,
Q2: The work function of sodium is 2.3 eV. it is illuminated with light of wavelength 3000A, what is the maximum kinetic energy of the emitted electrons ?
Ans:
Q3: The longest wavelength of radiation that can produce photoelectrons from a metal surface 8968A. Calculate the work function of the metal.
Ans:

MCQ:
Q1: The photoelectric emission could be explained by the ____________
A. Dual nature
B. Wave nature
C. Particle nature
D. other
Ans: C. Particle nature

Q2: Which part emit photoelectrons ?
A. Anode
B. Cathode
C. Ammeter
D. Voltmeter
Ans: B. Cathode

Q3:  Which of the following gases are filled inside the Photoelectric cells?
A. Oxygen
B. Argon
C. Helium
D. Hydrogen
Ans: B. Argon

Q4: The energy associated with a wavelength Î» is
A. h/Î»c
B. hc/Î»
C. Î»/hc
D. Î»c/h
Ans: B. hc/Î»

Q5: The photoelectric effect takes only when
A. above threshold wavelength
B. below threshold wavelength
C. equal to threshold wavelength
D. None
Ans: B. below threshold wavelength

Q6: The photoelectric effect involves only ______________
A. free electrons
B. bound electrons
C. both
D. none
Ans: B. bound electrons

Q7: If an electron can be stopped by a potential of 7 volts, its kinetic energy is _______
A. 7 volts
B. 7 cals
C. 7 joules
D. 7eV
Ans: D. 7eV

Q7: How does the intensity affect the photoelectric current?
A. As the intensity decreases, the photoelectric current becomes twice
B. As intensity increases, the photoelectric current increases
C. As the intensity increases, the photoelectric current decreases
D. No effect
Ans: B. As intensity increases, the photoelectric current increases

Q8: In photoelectric effect, energy of photoelectrons depends upon ______
C. Stopping potential
D. None

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