The Photoelectric Effect

The photoelectric effect was explained by Albert Einstein in 1905. When light impinges on a metal surface, it is observed that for sufficiently high frequency light, electrons will be ejected from the surface as shown in the figure below:

Classical theory predicts that energy carried by light is proportional to its amplitude independent of its frequency, and this fails to correctly explain the experiment.

Einstein, borrowing Planck’s hypothesis about the quantized energy of an oscillator, suggested that light comes in packets or “quanta” with energy $E$ given by Planck’s formula with $n=1$

\begin{displaymath} E = h\nu \end{displaymath}

Since, according to both Planck and Einstein, the energy of light is proportional to its frequency rather than its amplitude, there will be a minimumfrequency $\nu_0$ needed to eject an electron with no residual energy. The corresponding energy is

\begin{displaymath} h\nu_0 = \Phi \end{displaymath}

where $\Phi$ is called the work function of the metal, and it is an intrinsic property of the metal. In general, if $\nu > \nu_0$, an electron will be ejected with some residual kinetic energy. If the electron has momentum $p$ leaving the surface, then this kinetic energy is $p^2/2m_e$, and because energy is conserved, we have the relation

\begin{displaymath} h\nu = \Phi + {p^2 \over 2m_e} \end{displaymath}

The left side is the energy of the impinging light, and the right side is the sum of the minimum energy needed to extract an electron and the residual kinetic energy it has when leaving the surface.

The strange implication of this experiment is that light can behave as a kind of massless “particle” now known as a photon whose energy $E=h\nu$can be transferred to an actual particle (an electron), imparting kinetic energy to it, just as in an elastic collision between to massive particles such as billiard balls.


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