5.2 Photoelectric equation

3.1 Properties of matter waves
3.2 Application of de Broglie Hypothesis

5.1 Laws of Photoelectric emission
5.2 Photoelectric equation
5.3 Photoelectric Current
5.4 Stopping potential
5.5 Graph between $K{E_{max}}$ and frequency

8.1 Surface exposed to normal radiation
8.2 Surface exposed to radiation inclined at an angle

10.1 Radius of Orbit
10.2 Velocity of electron in the $n^th$ orbit
10.3 Orbital frequency of electron

11.1 Hypothetical Atomic Energy Level

13.1 Recoil speed of electron on emission of a photon

$$\begin{equation} \begin{aligned} \quad \quad E = W + K{E_{\max }} \\ \Rightarrow \quad h_f = h_{f_0} + \phi (K{E_{max}})...(1) \\\end{aligned} \end{equation} $$

where

$E = h_f$ is the energy of the incident photon.

$W$ is the work function of the metal

$K{E_{max}}$ is the maximum kinetic energy with which an electron may be ejected from the surface.

Now, when a photon incidents on a metallic surface (such that $E>W$) an electron absorbs some amount of its energy to overcome the force of attraction (=$W$) and rest of the energy is converted into the kinetic energy of the electron ($K{E_{max}}$). This electron now have to travel through obstructions to come out of the surface ($Fig\ 2$), during which it loses some of its kinetic energy.

This implies that electrons are emitted with a definite range of speeds. So, we write in the $(1)$ $K{E_{max}}$ and not that $KE$ with which electron is actually liberated from the surface to satisfy the law of conservation of energy. If the photon incident on metal surface has energy such that i.e., $h{f_0} = W$, the electron liberated will have zero kinetic energy.

Note: Equation $(1)$ is only applicable to a single photon-electron pair.