Class 12 Physics · Chapter 11 NotesDual Nature of Radiation and Matter

The chapter begins with the discovery of the electron by J.J. Thomson in 1897, following earlier work on cathode rays by Crookes. Thomson determined the specific charge (e/m) of cathode ray particles, which was found to be independent of the gas and metal used, establishing the electron as a universal constituent of matter. Millikan's oil-drop experiment later measured the elementary charge, showing that charge is quantised. The chapter then discusses electron emission from metal surfaces. Free electrons in a metal are bound by attractive forces and require a minimum energy, called the work function (φ₀), to escape. This energy can be supplied by heating (thermionic emission), applying a strong electric field (field emission), or illuminating the surface with light of suitable frequency (photoelectric emission). The emitted electrons are called photoelectrons. The work function is measured in electron volts (eV), where 1 eV = 1.602 × 10⁻¹⁹ J.

• Work function (φ₀)minimum energy needed for an electron to escape from a metal surface.
• 1 eV = 1.602 × 10⁻¹⁹ J.
• Thermionic emissionheating supplies energy.
• Field emissionstrong electric field pulls out electrons.
• Photoelectric emissionlight of suitable frequency ejects electrons.

The photoelectric effect was discovered by Hertz in 1887 when he noticed that ultraviolet light enhanced sparking across a detector loop. Hallwachs and Lenard investigated further. Hallwachs found that a negatively charged zinc plate lost its charge when illuminated with ultraviolet light, and an uncharged plate became positively charged. Lenard observed that when ultraviolet light fell on an emitter plate in an evacuated tube, a current flowed, which stopped when the light was removed. These observations indicated that light causes electrons to be emitted from the metal surface. It was also found that below a certain minimum frequency, called the threshold frequency (ν₀), no emission occurs, regardless of intensity. The threshold frequency depends on the material. Alkali metals respond to visible light, while metals like zinc, cadmium, and magnesium require ultraviolet light.

• Photoelectric effectemission of electrons from a metal surface when illuminated by light of suitable frequency.
• Threshold frequency (ν₀)minimum frequency required for photoelectric emission.
• Photoelectronselectrons emitted in the photoelectric effect.

The experimental setup consists of an evacuated glass or quartz tube with a photosensitive plate C (emitter) and a metal plate A (collector). Monochromatic light passes through a quartz window and falls on C, emitting electrons that are collected by A, creating a photocurrent. The potential difference between C and A can be varied, and its polarity reversed. The photocurrent is measured with a microammeter. Key observations: (1) For a fixed frequency and potential, photocurrent increases linearly with intensity, implying the number of photoelectrons per second is proportional to intensity. (2) As the positive potential on A increases, photocurrent increases and eventually saturates (saturation current). When a negative potential is applied, photocurrent decreases and becomes zero at a critical value called the stopping potential (V₀). The stopping potential is related to the maximum kinetic energy of photoelectrons: K_max = eV₀. (3) For a given frequency, the stopping potential is independent of intensity. (4) The stopping potential varies linearly with frequency for a given material, and there exists a threshold frequency below which no emission occurs. (5) Emission is instantaneous, with no time lag.

• Saturation currentmaximum photocurrent when all emitted electrons reach the collector.
• Stopping potential (V₀)minimum negative potential to stop photocurrent.
• K_max = eV₀.
• Stopping potential is independent of intensity but depends on frequency.
• Threshold frequencyminimum frequency for emission.

The wave theory of light, which successfully explains interference, diffraction, and polarisation, fails to explain the photoelectric effect. According to wave theory, the energy of light is continuously distributed over the wavefront. A more intense light wave has a larger amplitude, so electrons should absorb more energy and be emitted with greater kinetic energy. However, experiments show that the maximum kinetic energy of photoelectrons is independent of intensity. Also, wave theory predicts that even low-frequency light, if intense enough, should eventually supply sufficient energy for emission, so there should be no threshold frequency. But experiments show a threshold frequency below which no emission occurs, regardless of intensity. Furthermore, wave theory suggests that energy absorption is gradual, so there should be a time lag between illumination and emission. In reality, emission is instantaneous (within about 10⁻⁹ s). Thus, wave theory contradicts the key observations.

• Wave theory cannot explain the independence of K_max from intensity.
• Wave theory cannot explain the existence of threshold frequency.
• Wave theory cannot explain the instantaneous nature of photoelectric emission.

In 1905, Einstein proposed that light consists of discrete quanta of energy, called photons, each of energy hν, where h is Planck's constant and ν is the frequency. In the photoelectric effect, an electron absorbs a single photon. If the photon energy exceeds the work function φ₀, the electron is emitted with a maximum kinetic energy given by Einstein's photoelectric equation: K_max = hν – φ₀. This equation explains all observations: (1) K_max depends linearly on ν and is independent of intensity, because the energy of each photon depends only on frequency. (2) A threshold frequency ν₀ = φ₀/h exists; below this, photon energy is insufficient to overcome the work function. (3) The number of photoelectrons emitted per second is proportional to the number of incident photons, which is proportional to intensity, so photocurrent is proportional to intensity. (4) The absorption of a photon is an instantaneous process, so emission is immediate. Millikan later verified this equation experimentally and determined h.

• Einstein's photoelectric equationK_max = hν – φ₀.
• Threshold frequencyν₀ = φ₀/h.
• Stopping potentialeV₀ = hν – φ₀.
• Photon energyE = hν.
• Planck's constanth = 6.626 × 10⁻³⁴ J s.

The photoelectric effect provides evidence that light behaves as a stream of particles called photons. Each photon has energy E = hν and momentum p = hν/c = h/λ, where c is the speed of light and λ is the wavelength. Photons are electrically neutral and are not deflected by electric or magnetic fields. The intensity of light of a given frequency is determined by the number of photons incident per second; increasing intensity increases the number of photons but not their energy. In collisions between photons and particles, total energy and momentum are conserved, but the number of photons may change (e.g., a photon can be absorbed or created). The particle nature of light was further confirmed by Compton's X-ray scattering experiment in 1924. Thus, light exhibits both wave and particle nature, a concept known as wave-particle duality.

• Photon energyE = hν = hc/λ.
• Photon momentump = hν/c = h/λ.
• Photons are electrically neutral.
• Intensity is proportional to the number of photons per second.
• Wave-particle dualitylight behaves as both wave and particle.

In 1924, Louis de Broglie proposed that matter, like radiation, has a dual nature. He suggested that particles of matter also exhibit wave-like properties. The de Broglie wavelength λ associated with a particle of mass m moving with speed v is given by λ = h/p = h/(mv), where p is the momentum. This relation combines wave (λ) and particle (p) concepts. For a photon, this relation gives λ = h/p, consistent with electromagnetic wave theory. The de Broglie wavelength is significant only for subatomic particles; for macroscopic objects, it is extremely small and unobservable. For example, an electron with speed 5.4 × 10⁶ m/s has a wavelength of about 0.135 nm, comparable to atomic spacings, while a ball of mass 150 g moving at 30 m/s has a wavelength of about 1.47 × 10⁻³⁴ m. The wave nature of electrons was experimentally confirmed by the Davisson-Germer experiment.

• de Broglie relationλ = h/p = h/(mv).
• Matter waveswaves associated with moving particles.
• de Broglie wavelength is inversely proportional to momentum.
• Significant for subatomic particles, negligible for macroscopic objects.

The dual nature of radiation and matter is a fundamental concept in quantum mechanics. Light exhibits wave nature in phenomena like interference, diffraction, and polarisation, and particle nature in photoelectric effect and Compton effect. Similarly, particles like electrons show wave nature in diffraction experiments. The nature of the experiment determines which description is appropriate. For example, the eye lens focuses light using wave properties, but the absorption of light by the retina involves photons. This is known as complementarity: the wave and particle aspects are complementary, and both are needed for a complete description. The de Broglie relation embodies this duality, linking the wave attribute λ with the particle attribute p. The chapter concludes that the classical distinction between waves and particles is not valid at the quantum scale.

• Wave-particle dualityradiation and matter exhibit both wave and particle properties.
• Complementaritythe wave and particle aspects are complementary.
• The choice of description depends on the experiment.
• de Broglie relationλ = h/p.