Key Points

Electron emission is the liberation of electrons from a metal surface. The minimum energy required for an electron to escape the surface is called the work function, denoted by $\phi_0$ and measured in electron volts (eV).

Electrons can be emitted from a metal surface through three primary processes: Thermionic emission (by heating), Field emission (by applying a strong electric field), and Photoelectric emission (by illumination with light of suitable frequency).

The photoelectric effect is the phenomenon of emission of electrons (called photoelectrons) from a metal surface when light of a sufficiently high frequency is incident on it.

For a given frequency above the threshold, the photoelectric current is directly proportional to the intensity of the incident light. Higher intensity means more photons per second, leading to more photoelectrons emitted per second.

Stopping potential ($V_0$) is the minimum negative potential applied to the collector plate that stops the photocurrent completely. It is related to the maximum kinetic energy of photoelectrons by the equation $K_{\text{max}} = eV_0$.

The stopping potential, and thus the maximum kinetic energy of photoelectrons, increases linearly with the frequency of the incident radiation. It is independent of the intensity of the light.

Threshold frequency ($\nu_0$) is the minimum frequency of incident radiation below which no photoelectric emission occurs, regardless of the intensity of the light. It is a characteristic property of the metal.

The classical wave theory failed to explain the photoelectric effect because it could not account for the existence of a threshold frequency, the instantaneous nature of emission, and the independence of kinetic energy from light intensity.

Einstein proposed that light consists of discrete energy packets called photons. The energy of each photon is given by $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency of light.

The maximum kinetic energy of an emitted photoelectron is given by $K_{\text{max}} = h\nu - \phi_0$. This equation states that the photon's energy is used to overcome the work function ($\phi_0$) and provide kinetic energy to the electron.

The work function of a metal is directly related to its threshold frequency by the formula $\phi_0 = h\nu_0$. This defines the minimum energy required for photoemission.

The relationship between stopping potential and frequency is linear: $V_0 = (\frac{h}{e})\nu - \frac{\phi_0}{e}$. A plot of $V_0$ versus $\nu$ is a straight line with slope $h/e$.

A photon has energy $E = h\nu$, momentum $p = \frac{h}{\lambda}$, and travels at the speed of light $c$. It is electrically neutral and is not deflected by electric or magnetic fields.

Radiation exhibits a dual nature. It behaves as a wave in phenomena like interference and diffraction, and as a particle (photon) in phenomena like the photoelectric effect and Compton scattering.

Louis de Broglie proposed that all moving particles of matter, like electrons, exhibit wave-like properties. These associated waves are called matter waves or de Broglie waves.

The wavelength ($\lambda$) associated with a particle of momentum $p$ (mass $m$, velocity $v$) is given by the de Broglie relation: $\lambda = \frac{h}{p} = \frac{h}{mv}$.