Published by Patrick Mutisya · 14 days ago
The photoelectric effect occurs when photons incident on a metal surface liberate electrons. The essential observations are:
Einstein’s photoelectric equation relates the maximum kinetic energy \$K_{\max}\$ of the emitted electrons to the photon energy:
\$K_{\max} = h\nu - \phi\$
where \$\phi\$ is the work function of the metal (the minimum energy required to remove an electron from the surface).
From this equation we see that \$K_{\max}\$ depends only on:
Intensity \$I\$ of the light is defined as the energy delivered per unit area per unit time:
\$I = \frac{P}{A} = \frac{N h\nu}{A\,t}\$
where \$N\$ is the number of photons arriving in time \$t\$ on area \$A\$. Changing the intensity changes \$N\$, i.e., the number of photons, but each photon still carries the same energy \$h\nu\$. Therefore, the kinetic energy of each emitted electron remains unchanged, giving a constant \$K_{\max}\$ independent of intensity.
The photoelectric current \$I_{\text{photo}}\$ is the flow of charge due to emitted electrons:
\$I{\text{photo}} = e\,\frac{dNe}{dt}\$
where \$e\$ is the elementary charge and \$dN_e/dt\$ is the rate at which electrons are emitted. Since each photon can liberate at most one electron, the emission rate is directly proportional to the photon arrival rate \$N/t\$, which is proportional to the light intensity:
\$I_{\text{photo}} \propto I\$
Thus, increasing the intensity (more photons per second) increases the number of electrons emitted per second, giving a larger current, while the energy per electron remains fixed.
| Quantity | Depends on | Effect of Changing Intensity |
|---|---|---|
| Maximum kinetic energy \$K_{\max}\$ | Photon frequency \$\nu\$ and work function \$\phi\$ | No change (independent) |
| Photoelectric current \$I_{\text{photo}}\$ | Number of incident photons per unit time (i.e., intensity) | Increases proportionally |