Photoelectric Effect

Fig. 2.9 is a schematic of the apparatus used to demonstrate the photoelectric effect. The core idea is simple: light of a particular frequency strikes a clean metal surface inside an evacuated chamber, and electrons are ejected from that metal. Those ejected electrons — called photoelectrons — travel toward a detector, which measures their kinetic energy. An external circuit connects the detector, an ammeter, a battery, and the metal surface, with the battery’s polarity marked so that the metal is the negative electrode (cathode) and the detector is the positive electrode (anode). The ammeter measures the current due to the flow of photoelectrons.

The evacuated chamber is crucial: if air were present, ejected electrons would collide with gas molecules and lose energy before reaching the detector, making the measurement unreliable. The wavy arrow labelled “Light” represents the incoming electromagnetic radiation, and the straight arrow labelled “Electrons” shows the path of the photoelectrons from the metal to the detector. The battery provides the electric field that accelerates the electrons toward the detector; by varying the battery voltage, one can determine the maximum kinetic energy of the photoelectrons (the stopping potential).

What does this figure teach? It illustrates the experimental setup that led to three key observations that classical wave theory could not explain:

1. No time lag — electrons are ejected the instant light strikes the metal, regardless of how dim the light is.
2. Threshold frequency — for each metal, there is a minimum frequency $\nu_0$ below which no electrons are ejected, no matter how intense the light.
3. Kinetic energy depends on frequency, not intensity — the maximum kinetic energy of ejected electrons increases linearly with the frequency of the incident light, but is independent of its brightness.

These results forced physicists to abandon the classical wave picture of light for this phenomenon. Einstein explained them in 1905 by treating light as a stream of particles (photons), each carrying energy $E = h\nu$, where $h$ is Planck’s constant ($6.626 \times 10^{-34}\ \text{J·s}$) and $\nu$ is the frequency of the radiation.

Here:

• $K_{\text{max}}$ is the maximum kinetic energy of an ejected photoelectron ($\frac{1}{2}m_e v^2$).
• $h\nu$ is the energy of a single incident photon.
• $h\nu_0 = W_0$ is the work function — the minimum energy required to eject an electron from that particular metal.
• $\nu_0$ is the threshold frequency (characteristic of the metal).

The figure itself does not show a graph — it is a diagram of the equipment. But the formula above is the central result that the textbook develops using this experimental setup. The ammeter reading tells you how many electrons are flowing (proportional to light intensity), while the stopping potential (the battery voltage needed to just stop the current) gives you $K_{\text{max}}$. By varying the frequency of the incident light and measuring the stopping potential, one can verify that $K_{\text{max}}$ is a linear function of $\nu$, with slope $h$ and intercept $-W_0$. …