# Determination of the Boltzmann Constant through Measurement of Johnson Noise and Determination of the Elementary Electron Charge through Measurement of Shot Noise

Abstract

Two sources of noise, Johnson noise and shot noise, are investigated in this experiment. The Johnson noise, which is the voltage fluctuations across a resistor that arose from the random motion of electrons, is measured using the Noise Fundamentals box. The noise was measured across different resistances and at different bandwidths at room temperature, resulting in a calculation of the Boltzmann constant of $$1.4600 \pm0.0054 \cdot 10^{-23}\textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$$ and $$1.4600 \pm0.0052 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$$. The shot noise occurs due to the quantization of charge, and was measured by varying current in the system, with which we calculated the electron charge of $$1.649 \pm 0.007 \cdot 10^{-19} \textrm{ Coulombs}$$. They agree quite well with the accepted values of $$1.38064852 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ k}^{-1}$$, and $$1.64 \cdot 10^{-19} \textrm{C}$$ for the Boltzmann constant and electron charge respectively. Errors are discussed.