The Photoelectric Effect

The photoelectric effect is the emission of electrons from the surface of a metal when electromagnetic radiation of a suitable frequency shines on it. Key observations that challenged the classical wave theory of light include: 1. **Instantaneous Emission**: Electrons are emitted almost instantaneously (within 10⁻⁹ s) once the light is switched on, provided the frequency is above the threshold. 2. **Threshold Frequency (f₀)**: For each metal, there is a minimum frequency of incident radiation, called the threshold frequency, below which no electrons are emitted, regardless of the intensity of the light. 3. **Intensity and Number of Electrons**: If the frequency is above the threshold, the number of electrons emitted per second is directly proportional to the intensity of the incident radiation. 4. **Frequency and Kinetic Energy**: The maximum kinetic energy of the emitted electrons (photoelectrons) is proportional to the frequency of the incident radiation, but is independent of its intensity.

In 1900, Max Planck proposed that energy is quantised, meaning it can only exist in discrete packets. Albert Einstein later applied this idea to light, suggesting that light consists of discrete packets of energy called photons. The energy of a single photon is directly proportional to its frequency.

The work function (φ) of a metal is the minimum energy required to remove an electron from the surface of that particular metal. It is a characteristic property of the metal. Electrons are held within the metal by attractive forces, so energy must be supplied to overcome these forces and allow an electron to escape. The work function is typically measured in Joules (J) or electronvolts (eV), where 1 eV = 1.602 × 10⁻¹⁹ J.

The threshold frequency (f₀) is the minimum frequency of incident radiation required to cause photoelectric emission from a particular metal. If the incident light has a frequency below the threshold frequency, no electrons will be emitted, no matter how intense the light or how long it shines on the metal. This is because the individual photons do not have enough energy to overcome the work function of the metal.

Einstein explained the photoelectric effect by applying the principle of conservation of energy to the interaction between a photon and an electron. When a photon of energy hf strikes the surface of a metal, some of its energy (φ) is used to overcome the work function and release an electron. Any remaining energy is converted into the kinetic energy of the emitted electron. The maximum kinetic energy (½mv²_max) occurs when the electron is emitted from the very surface of the metal without any energy loss due to collisions.

The stopping potential (V_s) is the minimum negative potential difference applied to the collector electrode that is just sufficient to stop the most energetic photoelectrons from reaching it. At the stopping potential, the work done by the electric field on the electron (eV_s) is equal to the maximum kinetic energy of the electron.