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  • PHY 350: Determination of fundamental unit of charge \(e\) and Boltzmann’s constant \(k_B\) from “noise”

    Significance of the experiment

    By measuring Johnson noise — the fluctuating voltage that arises due to the random walk motion of electrons in a resistor (even when current isn’t flowing through it) —- as a function of temperature and frequency “bandwidth”, we can determine Boltzmann’s constant \(k_B\), the fundamental constant connecting temperature \(T\) to energy \(k_B T\).

    By measuring Shot noise — the fluctuations in a measured current of electrons due to quantization of charge — we can determine the fundamental unit of charge \(e\) (the charge on an electron).

    Who would have thought you could discover fundamental physics from simple “noise?” That’s pretty neat!

    Conceptual Introduction

    Please carefully read the Noise Fundamentals Introduction and the Conceptual Introduction to Noise Fundamentals that are available on the TeachSpin website.

    Questions for first lab class

    1. how might you measure voltage fluctuations in a resistor without having current flowing through it?

    2. why would voltage fluctuations increase with resistance?

    3. why would voltage fluctuations decrease with temperature?

    Activities for first lab class

    To plan out your first full lab, please review the description of Johnson Noise in (Melissinos 2003) on pages 122 - 133 and the TeachSpin Noise Fundamentals Lab Manual, Section 7: A Practical Guide to Johnson-noise measurements.

    Your instructor will introduce you to apparatus you will use in these experiments, and give you some follow up readings to help you plan your course of experiments.

    Quantitative Description of Theory and Experiments

    When you are ready for a more detailed quantitative description of Johnson noise and the determination of \(k_B\) at room temperature, please consult the TeachSpin Noise Fundamentals Lab Manual, Chapter 1: Johnson Noise at Room Temperature. Additional recommended background reading includes

    • Chapter 2: Noise Density

    • Chapter 4: Johnson Noise as a function of temperature

    • Chapter 6, Section 6.4: Noise thermometry

    These discuss more precisely what is meant by ‘noise density’ and ’equivalent noise bandwidth,’ how to improve and enhance your measurement of \(k_B\) by studying its temperature dependence, and how to turn everything on its head and use noise as a thermometer.

    When you are ready for a more detailed quantitative description of Shot noise, and its applications, please consult the TeachSpin Noise Fundamentals Lab Manual, Chapter 3: Shot noise.

    Finally, you might like to review J. B. Johnson’s fascinating original experimental results (Johnson 1928) and H. Nyquist’s theoretical explanation (Nyquist 1928). The original paper reporting the phenomena of Shot noise (in German) is by W. Schottky (Schottky 1918).