The electron, its isolation and measurement and the determination of some of its properties

Chapter 38: APPENDIX G BOHR’S THEORETICAL DERIVATION OF THE VALUE OF THE RYDBERG CONSTANT

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About This Book

A systematic presentation of experimental and theoretical work that establishes the discrete, atomic character of electric charge and explains techniques used to isolate and measure the elementary charge. It traces historical ideas about electricity, extends electrolytic laws to gas conduction, analyzes ionization by penetrating radiation, examines Brownian motion in gases, and considers whether the electron is divisible. Later chapters discuss atomic structure and the behavior of radiant energy. Mathematical proofs, experimental data, and technical derivations are collected in appendices to keep the main text accessible to non-specialist readers.

APPENDIX G
BOHR’S THEORETICAL DERIVATION OF THE VALUE OF THE RYDBERG CONSTANT

The Newtonian equation of a circular orbit of an electron rotating about a central attracting charge , at a distance , with a rotational frequency , is The kinetic energy of the electron is . The work required to move the electron from its orbit to a position at rest at infinity is . If we denote this quantity of energy by , it is seen at once that If we combine this with (37), p. 213, there results at once Upon change in orbit the radiated energy must be and, if we place this equal to , there results the Balmer formula (34), p. 210, in which Since for hydrogen , we have and from (60)