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• Unit 11 discusses the dual nature of matter and radiation for Class 12 Physics.
• Umesh Rajoria is the author.
• Science Career Coaching is the publisher.

Introduction

• The discovery of interference, diffraction, and polarization established light's wave nature.
• Maxwell's equations and Hertz's experiments supported the concept of light as a wave.
• In the 20th century, the photoelectric effect and Compton effect were explained by the quantum theory of light.
• Light consists of packets of energy called photons (hv) that travel in straight lines at the speed of light, establishing the particle nature of light.

Free Electrons

• In metals, valence electrons are loosely bound and can move freely within the metal surface but cannot leave it.
• These loosely bound electrons are called free electrons.
• Free electrons are held inside metals by the attractive force of the surface, known as restraining forces.

Work Function (Φ₀)

• Work function is the minimum energy needed for an electron to escape from a metal surface to overcome restraining forces.
• Work function is represented by Φ₀ and measured in electron volts (eV).

Electron Emission

• Emission of electrons from a metal surface is called electron emission.
• Electron emission requires electrons to possess energy exceeding the metal's work function.
• This energy is supplied to free electrons through physical processes.

Thermionic Emission

• Thermionic emission is the emission of electrons from a metal surface when heated.
• The required energy is supplied by thermal energy.
• Emitted electrons are called thermal electrons or thermions.
• The number of thermions emitted depends on the temperature of the metal surface.

Secondary Emission

• Secondary emission involves the emission of a large number of electrons from a metal surface when struck by fast-moving electrons (primary electrons).
• Fast-moving electrons are high-energy electrons.
• As they fall on a metal surface, they transfer their energy to the free electrons of the metal.
• This energy is transferred in amounts greater than the work function of the metal, then released from the metal surface.
• The emitted electrons are called secondary electrons.

Photoelectric Emission

• Photoelectric emission is the phenomenon of electron emission from a metal surface when light radiation of suitable frequency falls on it.
• Light supplies energy to free electrons for emission.
• Emitted electrons are called photoelectrons.
• The number of photoelectrons emitted depends on the intensity of the incident light.

Field Emission/Cold Cathode Emission

• Field emission is the emission of electrons from a metal surface under the application of a strong electric field.
• A strong electric field (10⁸ V/m) causes the metal to emit electrons.

Photoelectric Effect

• It’s the emission of electrons from the surface of a metal when radiation of a suitable frequency falls on them.
• The electrons emitted are called photo-electrons.
• The current produced due to the effect is called a photoelectric current.

Experimental Study of Photoelectric Effect

• The apparatus consists of an evacuated glass or quartz tube enclosing a photosensitive plate C (emitter) and a metal plate A (collector).
• A transparent window W is sealed on the glass tube for specific radiation, covered by a filter to allow the light of a particular wavelength to pass through it.
• Plate A can be given a desired positive or negative potential with respect to plate C, which uses the arrangement shown in the figure.

Working of Photoelectric Effect Experiment

• When monochromatic radiation of suitable frequency from source S falls on the photosensitive plate C, photoelectrons will be emitted.
• Photoelectrons are then accelerated toward plate A (collector) if it is kept at a positive potential.
• Electrons flow resulting in a photoelectric current, due to it, the microammeter shows a deflection.
• A microammeter measures the photoelectric current.
• The experimental setup is used to study the variation of photoelectric current.

Effect of Intensity of the Incident Radiation

• By varying the intensity, while keeping the frequency constant, the photoelectric current varies linearly with the intensity of the incident radiation.
• The number of photoelectrons emitted per second is directly proportional to the intensity.

Effect of Potential of Plate A w.r.t. Plate C

• The photoelectric current increases gradually with the increase in positive potential of plate A.
• At a certain positive potential of Plate A, the photoelectric current reaches a maximum or saturation point .
• After this, increasing the potential of plate A will not result in any additional increase in the photoelectric current.
• This maximum current value is called saturation current.
• The saturation current corresponds to the state when all photoelectrons emitted from C reach plate A.

Applying Negative Potential on Plate A

• When a negative potential is applied to plate A there is a decrease in current.
• This is bcause the photoelectrons emitted from C are repelled by high energy.
• By increasing the negative potential of plate A, the photoelectric current decreases rapidly and becomes zero at a certain value of negative potential V₀.
• V₀ is also known as the stopping potential.
• This maximum negative potential V₀, is given to the plate A.
• The potential w.r.t. plate C at which the photoelectric current becomes zero is called stopping potential or cut off potential.
• The equation Kmax = eV₀ = (1/2)mVmax² allows to solve for velocity, and express maximum kinetic energy

Effect of Frequency on Stopping Potential

• The value of stopping potential is independent of intensity, but is more negative for higher incident frequency.
• Saturation current depends on incident radiation intensity, but is independent of radiation frequency.
• Stopping potential varies linearly with frequency.
• Every photosensitive material has a certain minimum cut-off frequency V₀ (threshold frequency).
• At the threshold frequency, the stopping potential becomes zero.
• The intercept on the potential axis = -Φ₀/e
• Work function Φ₀ from the magnitude of the intercept

Note on Threshold Frequency

• If the incident radiation frequency is higher than the threshold frequency, photoelectric emission begins almost instantly.
• This happens even if the incident light is very dim.
• The time lag between radiation incidence and photo-electron emission is less than 10⁻⁹ seconds.

Photoelectric Emission Laws

• For a given metal and frequency, the number of electrons ejected per second is directly proportional to the intensity of light.
• There is a minimum incident radiation frequency needed for photoelectric emission.
• The frequency is called threshold frequency.
• After exceeding the threshold frequency the maximum kinetic energy is independent of the intensity.
• The photoelectron emission is an instantaneous process with very small (less than 10⁻⁹ second) between radiation and emission.

Einstein's Photoelectric Equation

• Light radiations consist of tiny packets of energy called quanta.
• One quantum of light radiation is a photon.
• A photon travels with the speed of light.
• Energy of a Photon, E=hv.
• Planck's constant is depicted as "h"
• Variable v is depicting the frequency of light of a photon.
• Einstein assumed that one photoelectron is ejected from a suitable-light-radiated metal surface.
• The energy of a photon (hv) is spent in two ways: freeing an electron from a metal surface equal to work function ($₀).
• The photon’s remaining energy used in the maximum kinetic energy/Kmax= $o - 1/2mv_mx^2
• Also; the Einstein's photoelectric equation, Kmax = 1/2mv_max^2 = hv

Wavelength and Relation to Cut Off Potential, Frequency, and Threshold Frequency

• Energy equations when considering relation to cutoff potential and minimum frequency are
• Kmax = hv - Φ₀

•  Ev₀ = kv -kv₀
  

• The threshold frequency helps to obtain the max energy a the incident beam.

Photoelectric Effect and Particle Nature of Light

• In interactions with matter, radiation behaves like it is made of particles i.e. photons.
• Each photon has energy E = (hv=hv/λ) and momentum: P = e/c= h/λ
• Irrespective of radiation intensity all of a particular frequency of photons or wavelength all have energy E
• By increasing radiation the increase is only in the number of photons.
• All photons are emitted by a source with the same space velocity: "C" or the speed of light
• A photon can have its energy shown in a way that does not change when the photon travels.
• The photon velocity may be different but can have a due change in wave length.
• Photons are not electric and are neutral
• Zero rest mass
• According to the theory of relativity the mass of a particle moving with velocity when compared to the speed of light is given by

• M = m₀/1 -v²yc² or Mo=m√1-v²yc²

Failure of Wave Theory

• Huygen's wave theory of light could not explain the photoelectric emission due to the given points below:
• Increasing amplitude will instead increase the intensity in the wave which does not reflect the experimental facts of photoelectrons.
• Another experimental fact of failing to take place of emissions, the wave theory of light intensity is less than the threshold of no amount of high intensity.

Dual Nature of Radiation

• Radiation can behave as both a wave and particle.
• In particular experimental radiation happens with a different nature.
• Three categories of dividing phenomenon: "interference, refraction. polarization."
• All three categories can can be defined only on the basis of particle like nature of radiation.
• Rectilinear propagation, refraction and reflection can be the last phenomena/nature to use for radiation, like reflection.

De Broglie Dualistic

• Moving material moving or particle, waves that sometimes wave is associated.
• • (Lambda) H - MV

Davisson

• Electrons need to display nature that can both be established through division
• Electrons that surround filaments are at a negative potential the electrons might form converging beams

Note

• V=c/ wavelength
• Photo electric requires minimum wave theory
• Intensity can not be less than theoretical
• Photo electrons = intensity