Angular momentum quantization from Planck's energy quantization

TL;DR

This paper demonstrates that Bohr's angular momentum quantization can be derived from Planck's energy quantization, energy conservation, and the correspondence principle, providing a pedagogical alternative to traditional methods.

Contribution

It offers a novel derivation of Bohr's angular momentum quantization without relying on his original hypothesis, based solely on energy quantization and fundamental principles.

Findings

Bohr's hypothesis is a consequence of Planck's energy quantization.

The derivation uses energy conservation and the correspondence principle.

Provides a pedagogical approach to atomic orbital quantization.

Abstract

We present in this work a pedagogical way of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. In contrast to the usual treatment for the orbital quantization, we show that using energy conservation, correspondence principle and Plank's energy quantization Bohr's hypothesis can be deduced from and is a consequence of the Planck's energy quantization.