Modern Physics Laboratory

Quantitative experiments to measure constants and test modern physics models.

Conceptual context

A modern physics laboratory turns a quantum idea into a direct measurement. When a photosensitive surface is illuminated with radiation of different $f$, the emitted electrons do not all carry the same energy. The $V_s$ selects the energetic edge of that distribution and links it to $K_max$. The purpose is not merely to observe photocurrent, but to determine which property of light controls electron energy and how the slope of a graph reveals $h$. The surface also introduces its own energy cost, $\Phi$, which fixes $f_0$.

🟢 Essential level

Each emitted electron receives energy from one photon. As $f$ increases, the energy available per photon increases and, once $f_0$ is exceeded, $K_max$ rises.

The $V_s$ measures this energetic limit electrically: a reverse voltage is applied until even the fastest electrons cannot reach the collector. Light intensity mainly changes how many electrons are emitted, not their maximum energy. The material matters because $\Phi$ sets the minimum energy needed to release an electron. When $V_s$ is plotted against $f$, the data should approach a straight line. Its slope contains the ratio between $h$ and $e$, while the horizontal intercept identifies $f_0$. This makes the graph a bridge between a measurable voltage, a controllable optical frequency, and a universal quantum constant experimentally. Increasing the intensity of the incident light increases the number of photoelectrons emitted, and therefore the measured photocurrent, but does not shift the $V_s$ needed to stop them, confirming that the energy depends on $f$, not on intensity, exactly as the quantum picture of light predicts.

🔵 Formal level

Basic formulas

The quantitative description starts with the energy balance for one photon absorbed by a surface electron:

Einstein photoelectric equation

Photon energy associated with $f$ is divided between $\Phi$ and $K_max$. The experiment does not directly measure electron speed; it converts the maximum energy into a potential difference through:

Photoelectric stopping potential

Real student questions

Why does intensity not increase $K_max$? It increases photon flux, not the energy of each photon when $f$ is fixed.

Is $V_s$ negative? The sign depends on the wiring convention; its positive magnitude is often reported as the required retarding voltage.

Why can the vertical intercept disagree with the ideal model? Contact potentials, nonuniform surfaces, stray light, and systematic errors can shift it.

Can $h$ be measured from one point? Not robustly. A slope requires several pairs of $f$ and $V_s$.

How do $f_0$ and $\Phi$ differ? They express the same barrier in frequency and energy units.

Final synthesis

The graph of $V_s$ against $f$ turns an electrical signal into quantum evidence. Its slope measures $h$, while its intercept reveals $\Phi$. Reliable results require both a sound model and careful control of surface condition, optical frequency, voltage, and noise.