Measurement of the electron charge $q_e$ using Schottky noise. Problem of the 6-th Experimental Physics Olympiad. Sofia 8 December 2018

Abstract

Several consecutive experiments are described with a printed circuit board PCB set-up, especially designed for these experiments. Doing the consecutive experimental tasks opens up possibility to determine the value of electron charge $q_e.$ The fluctuations of the voltage $U(t)$ should be measured for different illuminations of a photodiode. The voltage is amplified 1 million times $Y=10^6$. The amplified voltage $YU(t)$ is applied to the device, which gives the result of the value of the time averaged square of the voltage $U_\mathrm{S}=\left<(Y U(t))^2\right>/U_0$. This voltage $U_\mathrm{S}$ is measured with a multimeter. The series of measurements gives the possibility to determine the $q_e$ using the well known Schottky formula for the spectral density of the current noise $(I^2)_f=2q_e\left .$ For the junior high school students, the basic problem is to analyze the analog squaring. Students' work is separated and graded in four categories S, M, L, XL divided by age of students. For the last XL categories, the tasks contain problems oriented to physics university education program and include theoretical research of the PCB set-up as an engineering device. This is the problem of EPO6, December 2018 ``Day of the Charge'' considered. EPO6 is organized by Sofia branch of Union of physicists in Bulgaria in cooperation with Faculty of physics of Sofia University and Society of Physicists of Republic of Macedonia.