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Photoelectric Effect-Stopping Potential: Definitions, Formulas, Practice Problems

Photoelectric Effect-Stopping Potential: Definitions, Formulas, Practice Problems

Have you ever wondered how solar cells work? Or how street lights illuminate without any electricity? Their process of working involves the principle and modulation of Photo-electric effect. 

The effect was first discovered by Hertz. He observed that, when ultraviolet light shines on two metal electrodes with a voltage applied across them, the light changes the voltage at which sparking takes place. This relation between light and electricity (hence photoelectric). He demonstrated that electrically charged particles are liberated from a metal surface when it is illuminated and that these particles are identical to electrons, Further research showed that the photoelectric effect represents an interaction between light and matter that cannot be explained by classical physics, which describes light as an electromagnetic wave.

Experiments like interference and diffraction were able to explain the wave nature of light but were unable to explain the particle nature. The photoelectric effect, on the other hand, gave proof of particle nature. Energy comes in form of particle-like energy packets- basics of quantum physics. (energy of one packet (quantum) depends on the frequency of the incident light wave, a lightwave has a collection of energy of packets).

Table of contents

  • Photoelectric Effect
  • Some important terms
  • Mathematical form of Einstein’s Photoelectric Equation
  • Effect of the intensity of light
  • Stopping potential
  • Accelerating Potential Voltage
  • Practice Problems
  • Frequently Asked Questions-FAQs

Photoelectric Effect

The phenomenon in which a beam of light of sufficient frequency falls on a metal surface, and electrons are ejected from the metal is known as the photoelectric effect. 

In the above experiment, a beam of light of suitable frequency is incident on the metal surface, and electrons are ejected from the metal. The ejected electrons are attracted by the positive electrode. Electrons are ejected as soon as the beam of light of sufficient frequency strikes the metal surface. Photoelectric current is observed with the help of an ammeter. It shows a deflection when a beam of light falls on the metal surface.

Some important terms:

Photoelectrons: The electrons ejected from the metal surface are known as photoelectrons

Photocurrent: It is the flow of charge per unit time due to the movement of ejected photoelectrons. It is proportional to the number of photoelectrons ejected per unit of time.

Threshold frequency: It is the minimum frequency of the incident radiation required for the ejection of electrons from a metallic surface. All the frequencies above this will result

in the emission of electrons.

Threshold wavelength: It is the maximum wavelength of the incident radiation required for the

ejection of electrons from a metallic surface. All the wavelengths below this wavelength will result in the emission of electrons.

Threshold energy: It is the minimum energy of the incident radiation required for the ejection of

electrons from a metallic surface. All the energies above this energy will result in the emission of

electrons. This threshold energy is also called the work function of the metal and each metal has its own characteristic work function.

 

where is the threshold energy, is the speed of light, is the threshold frequency, is the threshold wavelength and is the Plank’s constant.

When < , ejection of electrons does not take place regardless of the intensity of the incident radiation.

Mathematical form of Einstein’s Photoelectric Equation

Work function (): It is the minimum energy required for the ejection of electrons from a metallic surface. It purely depends upon the metal i.e., it has different values for different metals.

Maximum K.E. of photoelectrons = Incident energy - Work function

The minimum energy required to eject an electron is, work function () =

Kinetic energy = =

Energy of the incident photon = + KE = +

Effect of intensity of light

  • A more intense beam of light consists of a larger number of photons, consequently, the number of electrons ejected is also larger as compared to that in an experiment in which a beam of the weaker intensity of light is employed.
  • It has been observed that though the number of electrons ejected depends upon the intensity of light but the kinetic energy of the ejected electrons does not.
  • The  

Stopping potential

The minimum potential applied to stop the photoelectric current is called stopping potential, which is .

⇒ If stopping potential = ,

then K.E.max =

Where ‘’ is the charge of electron having a value of  

Accelerating Potential Voltage ()

  • It is the voltage () applied to increase the kinetic energy of the emitted electrons (in ).
  • The kinetic energy of the photoelectron emitted lies in the range of to (where, denotes stopping potential).
  • The minimum kinetic energy of a photoelectron = (When K.E. of ejected electron =0)
  • Maximum kinetic energy of photoelectrons = ; (When K.E. of ejected electron = K.E.max = )

Practice problems:

Q1. The work function of the metal is 2.35 eV. The longest wavelength that can cause photoelectron emission from the metal is approximately

  1. 3456.76
  2. 5276.6
  3. 4326.6
  4. 2345.8

Answer: (B)

Solution: we know,

= longest wavelength

= (work function)

 = = 5276.6

Q2. When electromagnetic radiation of wavelength 413.5 fall on the surface of cesium, electrons are emitted with K.E. = 1.75 . Determine the work function () of cesium

  1. 1.25
  2. 1.75
  3. 2
  4. 3.65

Answer: (A)

Solution: we can directly use relation, 

  (when is in )

  (when is in )

 

Q3. Select incorrect graphs

  1. None of these

Answer: (D)

Solution: The frequency of the incident light actually shows the energy of the incident photon.

The number of photoelectrons emitted ∝ Intensity of the incident radiation

Q4. A photon of 6 eV energy falls on the top surface of the metal producing photoelectrons of the maximum kinetic energy of 4.5 eV. The required stopping voltage for these electrons is

  1. 6 eV
  2. 2.5 eV
  3. 10.5 eV
  4. 4.5 eV

Answer: (D)

Q5. A beam of 178 nm falls on the surface of a metal. The resulting stopping voltage is 2.32 V. Calculate the work function (in eV) of the metal. 

  1. 3.24 V
  2. 2.56 V 
  3. 7.98 V
  4. 4.65 V

Answer: (D)

Solution: Energy of incident photon = = 6.97 eV

stopping voltage = 2.32 V

K.E = 2.32 eV (for electron)

work function () = 6.97 - 2.32 eV = 4.65 eV

Frequently asked questions-FAQs

Question 1. What is the intensity of light?

Answer: The amount of energy that arrives per unit area, per unit time.

Question 2. Why do different metals have different work functions?

Answer: more the electropositive character of metal, the more easily electrons will be removed from metal and hence lower work function.

Question 3. If we compare Li, Pt & Cs which have the lowest work function?

Answer: Cs is the most electropositive metal so have the least value of work function. It is directly correlated with ionization energy.

Question 4. Why does the number of ejected electrons is increased with an increase in the intensity of light?

Answer: more the intensity of light means more number of photons arriving per unit area, per unit time with the same energy. So, the number of ejected electrons is increased.

Related topics:

Planck's Quantum Hypothesis Atomic Number and Mass Number
Dual nature of Matter-Wave nature of light Blackbody radiation
De-Broglie Hypothesis Heisenberg's uncertainity principle
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