Question

Write down Einstein's equation for the photoelectric effect.

Hint:

For the photoelectric effect, remember that the kinetic energy of the emitted electron is given by \(K_{\text{max}} = E_{\gamma} - \Phi\), where \(E_{\gamma}\) is the energy of the photon and \(\Phi\) is the work function. If \(E_{\gamma} < \Phi\), no electron is emitted.

Answer 1

Einstein's equation for the photoelectric effect describes the relationship between the energy of an incoming photon and the kinetic energy of the emitted photoelectron. The equation is: \[ E_k = h\nu - \Phi \] Where:
- \(E_k\) is the kinetic energy of the emitted photoelectron,
- \(h\) is Planck's constant, which has a value of \(6.626 \times 10^{-34}~\text{J} \cdot \text{s}\),
- \(\nu\) is the frequency of the incident light,
- \(\Phi\) is the work function of the material (the minimum energy required to release an electron from the surface of the material).
This equation shows that when light of a certain frequency strikes a material, the energy of the photons is used to overcome the work function \(\Phi\) of the material. The remaining energy is transferred to the emitted electron as kinetic energy. The photoelectric effect therefore confirms the particle nature of light, as only photons with energy greater than the work function can eject electrons from the material.
This equation also suggests that the energy of the emitted photoelectron does not depend on the intensity of the light, but only on its frequency. If the frequency of the incident light is below the threshold frequency (corresponding to the work function), no photoelectron is emitted regardless of the intensity of light.
Thus, the photoelectric effect demonstrates that light behaves as particles (photons) and that the energy of each photon is quantized.