In the Bohr model, a hydrogen atom consists of an electron orbiting a one-proton nucleus.

(a) Derive an algebraic expression for the relationship between the electron's speed \(v\) and the radius \(R_{\text {orbit }}\) of its orbit.

(b) Review the derivation of Kepler's third law in Chapter 13 (page 409), and derive a corollary that relates the period \(T\) of the electron's orbital motion and the orbit radius \(R_{\text {orbit. }}\).

Data from Chapter 13

Transcribed Image Text:

Kepler's third law relates the planetary orbits to one another: The squares of the periods of the planets are proportional to the cubes of the semimajor axes of their orbits around the Sun.