**Expression for the Maximum Kinetic Energy of Electron Emitted from a Metal Surface**

When light of sufficient frequency is incident on a metal surface, electrons can be emitted from the surface. This phenomenon is known as the photoelectric effect. The maximum kinetic energy (K.E.) of the emitted electrons can be determined using the following expression:

**K.E. = hf - Φ**

where:
- K.E. represents the maximum kinetic energy of the emitted electrons
- h is the Planck's constant (6.62607015 × 10^-34 J·s)
- f is the frequency of the incident radiation
- Φ is the work function of the metal

Below, we'll explain the meaning of each term in the equation and provide a detailed explanation of the expression.

**Planck's Constant (h)**

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It has a value of approximately 6.62607015 × 10^-34 J·s. This constant was introduced by Max Planck to explain the observed behavior of light and matter at the atomic and subatomic levels.

**Frequency of the Incident Radiation (f)**

The frequency of the incident radiation represents the number of complete oscillations or cycles of the electromagnetic wave that pass a given point in one second. It is measured in hertz (Hz), where 1 Hz is equal to one cycle per second. The frequency of the incident radiation determines the energy of the photons striking the metal surface.

**Work Function (Φ)**

The work function of a metal is the minimum amount of energy required to remove an electron from the surface of the metal. It is a characteristic property of the metal and is usually measured in electron volts (eV). The work function represents the energy barrier that must be overcome for an electron to be emitted from the metal surface.

**Explanation of the Expression**

The expression for the maximum kinetic energy of the emitted electrons can be derived from the conservation of energy principle. When a photon of energy hf strikes the metal surface, it can transfer its entire energy to an electron, which can then be emitted from the surface. However, to overcome the work function Φ, a certain amount of energy is required.

Therefore, the maximum kinetic energy of the emitted electron is equal to the energy of the incident photon (hf) minus the work function of the metal (Φ). This means that if the energy of the incident photon is less than the work function, no electrons will be emitted from the surface.

In summary, the expression K.E. = hf - Φ relates the maximum kinetic energy of the emitted electrons to the frequency of the incident radiation and the work function of the metal. It describes the fundamental relationship between light and the emission of electrons from a metal surface, as observed in the photoelectric effect.