An electron of mass and charge moves in a circular orbit of radius around a single proton
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics
Problem
An electron of mass me and charge −e moves in a circular orbit of radius r around a single proton. Two independent physical conditions must be satisfied simultaneously for the orbit to be allowed.
(a) Write an expression equating the magnitude of the electric force exerted by the proton to the required centripetal force for uniform circular motion.
(b) State the condition that the electron’s orbital circumference must satisfy in terms of an integer n and the electron’s wavelength.
(c) Using only the relationships from parts (a) and (b) and fundamental constants (h, e, me, and k), derive an explicit expression for the allowed radii rn of the electron in terms of the integer n.
(d) Evaluate the numerical value of the smallest allowed radius (n=1). Express your answer in meters to three significant figures.