Kinetic Energy (K.E.): The kinetic energy of the emitted electron is given by subtracting the work function (W) of the material from the energy of the incident radiation (E).

Expressions for Energy:
The energy of the incoming radiation is calculated using the formula:

The work function , which is the minimum energy needed to release an electron, when the radiation wavelength is at its longest , is:

De-Broglie Wavelength of the Electron:
The de-Broglie wavelength of the emitted electron is given by:

Substituting the Values:
The kinetic energy of the emitted electron can be expressed in terms of energies as:

Final Expression for :

Solving for , the de-Broglie wavelength of the electron, we have:

This expression determines the de-Broglie wavelength of the emitted electron based on the wavelengths of the incident and threshold radiation.