Quantum Mechanics and Photoelectric Effect

Origin of Quantum Mechanics

• Many optical phenomena are explained by the wave nature of electromagnetic radiation.
• Other phenomena suggest electromagnetic radiation as a stream of particles.
• Experiments involving absorption or scattering of radiation in matter show transfer of radiation in discrete energy quanta.
• The concept of the photon is introduced as a particle of electromagnetic radiation.

Discovery of Photoelectric Effect

• Hertz discovered the photoelectric effect in 1887.
• He experimented with electric discharge between two electrodes.
• Ultraviolet light applied to one electrode causes a spark to jump greater distances.
• Hallwachs showed the emission of electrons from the electrode when exposed to ultraviolet light (photoelectrons).

Experimental Arrangement for Observing the Photoelectric Effect

• Modern setup: evacuated glass tube with two electrodes (photocathode C and anode A).
• Photocathode made of photosensitive material.
• Anode connected positively.
• Quartz window to allow monochromatic ultraviolet light onto the photocathode.
• Microammeter to measure photoelectric current.
• Variables in the experiment: intensity, frequency and voltage between cathode and anode.

Experiment 1: Intensity and Photoelectric Current

• Keeping frequency fixed, vary light intensity.
• Photoelectric current increases linearly with intensity.

Experiment 2: Voltage & Photoelectric Current

• Keeping intensity fixed, vary voltage.
• Current flows up to a certain negative voltage then drops to zero (stopping potential).
• Stopping potential (Vo) is independent of intensity.

Experiment 3: Stopping Potential and Frequency

• Vary frequency, keeping intensity constant.
• Stopping potential increases linearly with frequency.
• Minimum frequency (threshold frequency, v₀) exists below which no photoelectrons are emitted.

Laws of Photoelectric Emission

• Photoelectric current is directly proportional to the intensity of incident light.
• Maximum velocity of photoelectrons depends only on the frequency of incident light, not intensity.
• Photoelectric effect does not occur below a specific threshold frequency.

Einstein's Explanation of Photoelectric Effect

• Light consists of tiny bundles of energy called photons.
• Each photon carries energy (E = hv), where h is Planck's constant and v is frequency.
• When a photon strikes a metal, an electron absorbs all the photon's energy.
• Part of this energy overcomes the binding energy (work function, w₀).
• Remaining energy becomes the kinetic energy of emitted photoelectron (1/2mv²).
• E = w₀ + 1/2mv² (Einstein's photoelectric equation).
• Thus the maximum kinetic energy of emitted electrons depends on the frequency and not the intensity of the incident light.

Properties of Photons

• Photons have energy (E = hv).
• Photons travel at the speed of light (c).
• Photons have no charge.
• Photons have zero rest mass.
• Photons have momentum (p = hv/c).

Compton Effect

• Scattering of X-rays by a substance.
• Two components in scattered radiation: unmodified (same λ as incident) and modified (longer λ).
• Wavelength of modified radiation increases with scattering angle.
• The change in wavelength is related to the scattering angle and the mass of the electron and is known as the Compton Shift.

Kinetic Energy of Recoil Electron

• When a photon is scattered, the electron recoils.
• Expression for kinetic energy is explained using conservation of energy and momentum.

Dual Nature of Electromagnetic Radiation

• Electromagnetic radiation exhibits both wave-like and particle-like properties.
• Wave nature is observed in interference and diffraction.
• Particle nature is displayed in photoelectric and Compton effects.

Wave-Particle Duality of Matter

• Matter also exhibits wave-like properties.
• De Broglie wavelength (λ = h/mv) relates wavelength to momentum.
• This wavelength is significant for matter behaving as a wave such as electrons.
• The relationship is equally applicable in Compton effect with masses, not just photons.

Davisson-Germer Experiment

• Experiment to demonstrate the wave nature of electrons.
• Electrons were scattered from a crystal.
• Diffraction pattern consistent with wave nature observed.
• Results confirmed De Broglie's hypothesis.