Question

Write Einstein’s photoelectric equation. How did Millikan prove the validity of this equation?

Hint:

Einstein’s photoelectric equation provides a direct relationship between the energy of the incident light, the work function of the material, and the kinetic energy of the emitted electrons. Millikan confirmed the validity by his precise measurements of stopping potential and electron energy.

Answer 1

Step 1: Einstein’s photoelectric equation is given by:
\[ E_{\text{kin}} = h\nu - \phi \] where:
- \( E_{\text{kin}} \) is the kinetic energy of the emitted photoelectron,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( \nu \) is the frequency of the incident radiation,
- \( \phi \) is the work function of the material (the minimum energy required to release an electron from the surface).
This equation expresses the energy conservation in the photoelectric effect: the energy of the incoming photons is used to overcome the work function, and the excess energy is imparted as kinetic energy to the emitted electron. Step 2: Millikan's experiment validated this equation by measuring the stopping potential required to stop the emitted photoelectrons. He measured the maximum kinetic energy of the photoelectrons for various frequencies of incident light, which allowed him to confirm the linear relationship between the kinetic energy and frequency of the incident radiation, as predicted by Einstein’s equation.