A physicist attempts to analyze the hydrogen atom using purely classical considerations
PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter
Problem
A physicist attempts to analyze the hydrogen atom using purely classical considerations. They assume the electron of mass me moves in a circular orbit of radius r1=5.3×10−11m (the Bohr radius) with an initial speed determined by equating the electrostatic and centripetal forces. According to classical electrodynamics, an accelerating charge radiates energy at a rate given by the Larmor formula P=6πε0c3e2a2, where a is the magnitude of the electron’s acceleration.
(a) Determine the magnitude of the electron’s initial acceleration a for the stated orbit.
(b) Using the Larmor formula, calculate the initial power P radiated by the electron.
(c) Assuming the electron’s total mechanical energy at radius r is E=−2rke2, estimate the time τ it would take for the electron to radiate an amount of energy equal to ∣E∣ at the constant power found in part (b).
(d) Compare the time scale τ obtained in part (c) with typical atomic lifetimes (on the order of 10−8s) and discuss the implications of this comparison for the validity of the purely classical description.