Measurement of the ratio h/e with a photomultiplier tube and a set of LEDs

TL;DR

This paper describes a laboratory experiment for undergraduate students to measure the ratio h/e using a photomultiplier tube and LEDs, based on Millikan's method for studying the photoelectric effect.

Contribution

It introduces a practical, educational setup that enables measurement of h/e through a simplified, hands-on experiment using modern components and techniques.

Findings

Successful measurement of the h/e ratio consistent with known values.

Demonstration of the linear relationship between stopping potential and light frequency.

Educational value in illustrating the photoelectric effect principles.

Abstract

We propose a laboratory experience aimed at undergraduate physics students to understand the main features of the photoelectric effect and to perform a measurement of the ratio h/e, where h is the Planck's constant and e is the electron charge. The experience is based on the method developed by Millikan for his measurements on the photoelectric effect in the years from 1912 to 1915. The experimental setup consists of a photomultiplier tube (PMT) equipped with a voltage divider properly modified to set variable retarding potentials between the photocathode and the first dynode, and a set of LEDs emitting at different wavelengths. The photocathode is illuminated with the various LEDs and, for each wavelength of the incident light, the output anode current is measured as a function of the retarding potential applied between the cathode and the first dynode. From each measurement, a value of the stopping potential for the anode current is derived. Finally, the stopping potentials are plotted as a function of the frequency of the incident light, and a linear fit is performed. The slope and the intercept of the line allow respectively to evaluate the ratio h/e and the ratio W/e, where W is the work function of the photocathode.