# Final Lab Report 2 (MH and LL): Determination of the Boltzmann Constant and Elementary Electron Charge through Noise Measurements

Abstract

Two sources of noise, Johnson noise and shot noise, are investigated in this experiment.Grammar errors: The Johnson noise, which is the voltage fluctuations across a resistor that arose from the random motion of electrons, is measured using the Not defined 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.

Editor’s Notes:

1. a reader won’t know what a “Noise Fundamentals” box is. More helpful – and more relevant – would be “a specially designed low noise preamplifier, a combination of high and low pass filters and amplifiers, and a voltage multiplier.” But it isn’t clear you need this phrase at all in a sentence explaining what Johnson noise is, since the next sentence explains what you measured: the dependence of Johnson noise on the resistance and bandwidth.

2. the “quite well” statement d