Revision: Dual Nature of Radiation and Matter >> Dual Nature of Radiation and Matter Physics Science (English Medium) Class 12 CBSE

The phenomenon of emission of electrons from the metal surface is called "Electron Emission".

The minimum energy needed for an electron to escape from the metal surface is called the work function of that metal. Its unit is electron volt (eV).

It is a phenomenon where light falling on a material (usually a metal) causes it to emit electrons, generally called photoelectrons.

The minimum value of energy required for the emission of photoelectrons from a metal surface is called the Work Function.

The retarding potential (–V₀) for which the photocurrent becomes zero is called the Stopping Potential.

The limit of photocurrent at which the increase in photocurrent stops even if the collector plate potential (V) is increased is called the Saturation Current.

The stopping potential is defined as the potential necessary to stop any electron from reaching the other side.

Threshold frequency is the lowest frequency of electromagnetic radiation that will result in the emission of electrons from a specified metal surface.

The minimum value of frequency of incident radiation required for the emission of photoelectrons from a metal surface is called the Threshold Frequency.

The photoelectric effect demonstrates that light behaves as if it consists of energy packets called quanta or photons.

The wavelength associated with a moving material particle is called the de Broglie wavelength.

The emission of electrons from a metal surface by heating it to high temperature is called thermionic emission.

The emission of electrons from a metal surface by applying a strong electric field is called field emission.

A microscope that uses accelerated electron beams instead of visible light to obtain high-resolution images is called an electron microscope.

A device that uses the photoelectric effect to convert light energy into electrical energy is called a photocell.

The quantum (bundle) of electromagnetic radiation having energy E = hν is called a photon.

The property of electromagnetic radiation to exhibit both wave nature and particle nature is called wave–particle duality of electromagnetic radiation.

The change in wavelength of X-rays after scattering from electrons is called the Compton shift.

The hypothesis that matter, like radiation, exhibits both wave and particle nature is called the de Broglie hypothesis.

The waves associated with moving material particles are called matter waves.

The minimum frequency of incident radiation required to eject electrons from a metal surface (ν₀ = ϕ₀/h) is called the threshold frequency.

The maximum kinetic energy of emitted photoelectrons given by KE_max⁡ = hν − ϕ₀​ is called Einstein’s photoelectric equation.

The minimum energy required to remove an electron from the surface of a metal is called the work function of the metal.
It is denoted by ϕ₀.

Electromagnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields, both perpendicular to the direction of propagation of the wave.

The phenomenon of emission of electrons from a metal surface when radiation of appropriate frequency is incident on it is called the photoelectric effect.

A surface that emits electrons when illuminated with suitable radiation is called a photosensitive surface.

Electrons emitted from a metal surface due to incident light are called photoelectrons.

When the anode is at positive potential with respect to the cathode, it accelerates the emitted electrons. This potential is called accelerating potential.

When the anode is at negative potential with respect to the cathode, it opposes the motion of electrons. This is called retarding potential.

The minimum negative potential applied to the collector to reduce the photocurrent to zero is called the stopping potential (cut-off potential).

The relation E = hν, which connects the energy of a photon with its frequency, is called Einstein’s relation.

\[V_0=\frac{hv}{e}-\frac{\phi_0}{e}=\frac{K.E_{max}}{e}\]

\[\phi_0=hv_0=h\frac{c}{\lambda_0}\]

λ = \[\frac {h}{p}\]

\[
\lambda = \frac{h}{mv}
\]

\[
e = 1.602 \times 10^{-19}\,\text{C}
\]

\[
1\,\text{eV} = 1.602 \times 10^{-19}\,\text{J}
\]

\[
\frac{e}{m} = 1.76 \times 10^{11}\,\text{C/kg}
\]

\[
K_{\text{max}} = eV_0
\]

             or

\[
K_{\text{max}} = h\nu - \phi_0
\]

Linear Form:

\[
V_0 = \frac{h}{e}\nu - \frac{\phi_0}{e}
\]

\[
p = \frac{h\nu}{c} = \frac{h}{\lambda}
\]

\[
\nu_0 = \frac{\phi_0}{h}
\]

\[\Delta\lambda=\lambda^{\prime}-\lambda=\frac{h}{m_ec}(1-\cos\theta)\]

• Light (and all radiation) behaves both as a wave and as a particle, depending on circumstances.
• Wave properties: Interference, diffraction, polarisation — explained by wave theory.
• Particle properties: Photoelectric effect, Compton effect — explained by quantum/photon theory.
• Key idea: No single model (wave or particle) explains all phenomena; both are needed.
• Radiation properties of light: spreads as waves, cannot be touched, but can be experienced.
• Material properties of light: moves in straight rays, has momentum, carries definite energy.

Three Types of Electron Emission:

• Hertz (1887) observed that UV light falling on a metal cathode caused sparks to jump more easily across the gap of his oscillator.
• He noticed high voltage sparks were enhanced when the emitter plate was illuminated with UV light from an arc lamp.
• The phenomenon was later identified as the Photoelectric Effect — emission of electrons when light strikes a metal.
• Hertz also found that maximum spark length was produced when the apparatus was kept in a dark box, confirming light-induced emission.
• Hertz Experiment Setup: Oscillator with brass knobs joined by an induction coil; spark balls separated by a micrometre air gap and a ring receiver.

Hallwachs' Observation:

Hallwachs confirmed that UV light incident on a negatively charged zinc plate caused it to lose charge (emit electrons).

Lenard's Observations:

• Lenard measured electron kinetic energy vs light frequency.
• Found: Maximum KE of emitted electrons is directly proportional to the frequency of incident light.
• Changing the intensity of light had no effect on kinetic energy — only on the number of electrons emitted.
• Below a certain threshold frequency (ν₀), no electrons are emitted regardless of intensity.
• The photocurrent was directly proportional to the intensity of the incident light.
• Setup: cathode illuminated with light → electrons travel through vacuum → reach anode → current measured via ammeter.

Setup:

• Monochromatic radiation of suitable frequency from source S falls on photosensitive plate C (cathode).
• Electrons emitted from C are collected at plate A (anode/collector), kept at positive potential.
• Photoelectrons flow in the outer circuit → microammeter shows deflection (measures photoelectric current).
• Quartz window allows UV light to enter the evacuated glass tube.

Effect of Intensity:

• Photoelectric current varies directly with intensity of incident light (more photons → more electrons).
• Graph: Linear relationship between photoelectric current and light intensity.

Effect of Potential:

• On increasing positive collector potential → photocurrent increases and reaches saturation current.
• Higher intensity → higher saturation current (more electrons).
• Even at zero potential, some current flows (electrons have kinetic energy).
• Applying negative potential reduces the current.

Stopping Potential (V₀)

• The minimum negative potential given to the collector to stop all photoelectrons is Stopping Potential.
• At stopping potential: \[K_{\max}=eV_{0}=\frac{1}{2}mv^{2}\]
• Stopping potential is independent of intensity (but depends on frequency).
• Higher frequency → larger stopping potential.

Effect of Frequency on Stopping Potential:

• Graph shows: V₀ varies linearly with frequency ν (for a given photosensitive material).
• There exists a threshold frequency ν₀ below which V₀ = 0 (no emission).
• Threshold frequency is a characteristic of the metal.

Laws of Photoelectric Emission:

1. If frequency of radiation < threshold frequency → no emission (regardless of intensity).
2. Maximum KE of photoelectrons depends on frequency of radiation, not intensity.
3. Saturation photocurrent increases with intensity, but is independent of frequency.
4. There is no time lag between incidence of radiation and emission of electrons.

• Einstein proposed that light consists of quanta (photons), each with energy E = hν.
• When a photon of energy hν falls on a metal, it is completely absorbed by one electron.
• The electron uses energy Φ (work function) to escape, and the rest appears as kinetic energy.

Einstein's Photoelectric Equation: K_max = hν − ϕ₀

or equivalently: \[\frac{1}{2}mv_{max}^2=h\nu-h\nu_0=h(\nu-\nu_0)\]

• If ν < ν₀: v₂ is negative → imaginary velocity → no photoelectric emission possible.
• If ν > ν₀: v₂ is positive → emission occurs.
• Increasing intensity → more photons → more electrons, but same KE per electron.
• Increasing frequency → more energy per photon → higher KE of emitted electrons.
• Photoelectric emission is a 'knock-out' process: one photon knocks out one electron with KE = ½mv².

Important Note on Photocurrent vs Frequency:

• Increasing frequency does NOT increase the number of photoelectrons → photocurrent does not increase with frequency.
• Photocurrent depends only on the number of photons (i.e., intensity).

1. Interaction with Matter: Radiation behaves as particles when interacting with matter.
2. Energy and Momentum: Each photon has energy \[E={\frac{hc}{\lambda}}=h\nu\] and momentum \[p=\frac{hv}{c}=\frac{h}{\lambda}\].
3. Intensity and Energy: All photons of a given frequency/wavelength carry the same energy, regardless of radiation intensity.
4. Effect of Intensity: More intensity → more photons, but each photon has the same energy.
5. Speed of Photons: All photons travel at the speed of light c.
6. Frequency–Energy Relationship: A photon's frequency determines its energy; its frequency remains constant across different media.
7. Photon Velocity in Different Media: Velocity varies with wavelength change in different media.
8. Rest Mass of Photon: m₀ = 0 (zero rest mass), because it travels at the speed of light.
9. Electric and Magnetic Field Interaction: Photons are not deflected by electric/magnetic fields (they are electrically neutral).

Photon-Particle Collision:

• During collisions (like the photoelectric effect), energy and momentum are conserved.
• No new photons are created or destroyed — they are either absorbed or new photons are emitted.

• de Broglie (1924) Hypothesis: If radiation (waves) shows particle behaviour, then particles of matter should also show wave behaviour. This concept is called Matter Waves or de Broglie Waves.
• Nature's symmetry: electrons, protons, and neutrons can behave as waves under suitable conditions.

de Broglie Wave Equation:

For a particle of mass m moving with velocity v: \[\lambda=\frac{h}{p}=\frac{h}{mv}\]

Also written as: \[\lambda=\frac{h}{\sqrt{2mK.E}}\]

• Larger mass or velocity → smaller wavelength → harder to detect wave nature.
• For large (macroscopic) bodies, wavelengths are so tiny they cannot be measured — hence, no observable wave nature.

Experimental Proof of Matter Waves:

• Davisson and Germer experiment: Electrons showed diffraction patterns — direct proof of wave nature.
• G.P. Thomson's experiment also confirmed electron diffraction.
• Electrons have mass and move with definite velocity → can display wave-like behaviour.

Acceptance of Duality:

• Bohr's Law of Complementarity: Matter can be observed as either a particle or a wave, but not both simultaneously.
• Particle and wave aspects are complementary.

• Wave theory could not explain the instant emission of electrons; it predicted a time delay.
• It said higher intensity should give higher kinetic energy, but actually, kinetic energy depends on frequency, not intensity.
• Wave theory predicts emission at any frequency when intensity is high, but emission occurs only when the frequency is above the threshold frequency (ν₀).
• Even very low intensity light causes immediate emission, which contradicts wave theory.
• Hence, the photoelectric effect supported the particle (quantum) nature of light rather than the wave theory.

• Electrons are emitted only if the light frequency is greater than a minimum value, the threshold frequency (ν₀), which differs for different metals.
• Emission of electrons is instantaneous; there is no time delay between light falling and electrons coming out.
• At a fixed frequency, photocurrent increases with increasing light intensity.
• Photocurrent increases with accelerating potential and then becomes constant; this maximum value is called the saturation current.
• Saturation current depends on light intensity, not on its frequency (if ν > ν₀).
• The maximum kinetic energy of emitted electrons depends only on the frequency of light, not on its intensity.
• Stopping potential is the minimum negative potential needed to stop the photocurrent; it depends on frequency, not on intensity.

• Einstein extended Planck’s idea and proposed that light behaves as particles called photons, each carrying energy hνh\nuhν.
• A photon gives all its energy to a single electron; emission occurs only if this energy is equal to or greater than the work function of the metal.
• Photoelectric emission is instantaneous because energy transfer from photon to electron occurs in a single interaction.
• The intensity of light controls the number of emitted electrons (photocurrent), while the frequency controls the maximum kinetic energy of the electrons.
• Einstein’s photon theory successfully explained threshold frequency, stopping potential, saturation current, and all experimental observations of the photoelectric effect.