Photoelectric Effect
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency strikes it, demonstrating that light behaves as discrete packets of energy called photons rather than as a continuous wave. Albert Einstein explained this phenomenon in 1905 using Max Planck's quantum theory, for which Einstein was awarded the Nobel Prize in Physics in 1921. The effect is the foundation of photovoltaic cells, photodiodes, photomultiplier tubes, and modern solar energy technology.
Key Formula
KE_max = h × f − φ
LaTeX: KE_{max} = hf - \phi
| Symbol | Meaning | Unit |
|---|---|---|
| KE_max | Maximum kinetic energy of emitted electron | J or eV |
| h | Planck's constant (6.626 × 10⁻³⁴) | J·s |
| f | Frequency of incident light | Hz |
| φ | Work function of the metal (minimum energy to eject electron) | J or eV |
Worked Example
Problem
Ultraviolet light of frequency 1.5 × 10¹⁵ Hz strikes a sodium surface with work function φ = 2.28 eV. Calculate the maximum kinetic energy of the emitted electrons in eV. (h = 4.136 × 10⁻¹⁵ eV·s)
Solution
Step 1: Calculate photon energy. E = h × f = 4.136 × 10⁻¹⁵ × 1.5 × 10¹⁵ = 6.204 eV Step 2: Apply the photoelectric equation. KE_max = E − φ = 6.204 − 2.28 = 3.924 eV Step 3: Verify the effect occurs (E > φ): 6.204 eV > 2.28 eV ✓
Answer
KE_max ≈ 3.92 eV
Work Functions of Common Metals
| Metal | Work Function (eV) | Threshold Frequency (Hz) | Threshold Wavelength (nm) |
|---|---|---|---|
| Caesium (Cs) | 2.10 | 5.08 × 10¹⁴ | 590 |
| Sodium (Na) | 2.28 | 5.51 × 10¹⁴ | 544 |
| Aluminium (Al) | 4.08 | 9.87 × 10¹⁴ | 304 |
| Copper (Cu) | 4.70 | 1.14 × 10¹⁵ | 264 |
| Gold (Au) | 5.10 | 1.23 × 10¹⁵ | 243 |
Interactive Tools
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Related Terms
Speed of Light
The speed of light in vacuum, denoted by c, is a universal physical constant equal to exactly 299,792,458 metres per second, representing the maximum speed at which any information, energy, or matter can travel in the universe. As established by Albert Einstein's special theory of relativity (1905), c is invariant regardless of the motion of the source or observer. In transparent media such as glass or water, light travels at a reduced speed given by v = c/n, where n is the refractive index of the medium.
Electric Charge
Electric charge is a fundamental intrinsic property of matter that causes particles to experience a force when placed in an electromagnetic field, existing as either positive (carried by protons) or negative (carried by electrons) with an elementary charge unit of e = 1.602 × 10⁻¹⁹ coulombs. Charge is conserved in all physical processes (the total charge of an isolated system remains constant), and it is quantised, meaning any observable charge is an integer multiple of the elementary charge. Electric charge is the source of the electric force, which is described by Coulomb's Law and governs all electromagnetic interactions in nature and technology.
Electric Field
An electric field is a vector field that exists in the region around an electric charge or a changing magnetic field, representing the electrostatic force that would be exerted per unit positive charge placed at any point in space. The field lines emanate outward from positive charges and point inward toward negative charges, with the density of field lines indicating field strength. Electric fields are central to understanding capacitors, electromagnetic waves, semiconductor devices, and the operation of all electrical equipment from simple circuits to complex communication systems.
From Greek "phos/photos" (light) + "elektron" (amber, source of "electric"). The term was coined in the late 19th century; Heinrich Hertz first observed the effect in 1887, and Einstein provided the quantum explanation in 1905.