In this problem you are to obtain the Bohr results for the energy levels in hydrogen without using the quantization condition of Equation 4-17. In order to relate Equation 4-14
to the Balmer-Ritz formula, assume that the radii of allowed orbits are given by r_n = n²r₀, where n is an integer and r₀ is a constant to be determined.

(a) Show that the frequency of radiation for a transition to n_f = n - 1 is given by f ≈ kZe²/hr₀n³ for large n.

(b) Show that the frequency of revolution is given by

(c) Use the correspondence principle to determine r₀ and compare with Equation 4-19.

Transcribed Image Text:

& rev kZe² 2 4m² mron