Revision: Dual Nature of Matter and Radiation JEE Main Dual Nature of Matter and Radiation

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).

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

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

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

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

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

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

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

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

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

• 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:

• When light of frequency ≥ threshold frequency (ν₀) falls on a metal surface, electrons are emitted.
• If ν < ν₀ → no emission, regardless of intensity.
• The threshold frequency (ν₀) varies with metal.
• Energy equation: \[h\nu=h\nu_0+\frac{1}{2}mv^2\]
• Maximum kinetic energy depends only on frequency, not on intensity.
• Number of emitted electrons depends on intensity (for ν ≥ ν₀).
• Emission of electrons is instantaneous (no time lag).
• Increasing frequency increases the kinetic energy of electrons.
• Increasing intensity increases the number of electrons, not their energy.
• The photoelectric effect proves the particle (quantum) nature of light.

• 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.

1.  The experiment verified the de-Broglie hypothesis.
2. In this experiment, the wave nature of electron particles was studied with the help of a nickel crystal.
3. Electrons undergo interference and diffraction phenomena and produce alternate bright and dark rings.
4. When accelerating potential V = 54 V:
   λ = 0.165 nm (Experimental value)
   λ = 0.167 nm (Theoretical value from de-Broglie hypothesis)

• Proposed by Louis de Broglie in 1924: just as light shows both particle and wave nature, matter in motion also exhibits wave-like behaviour.
• The wave associated with a moving particle is called the matter wave or de Broglie wave.
• de Broglie wavelength equation: \[\lambda=\frac{h}{mv}=\frac{h}{p}\]
  

  where m = mass of particle, v = velocity, p = momentum.

• For an electron: λ = h/mv or λ = h/p