Quantum States of Atoms: The Bohr Model

Z. Ficek

This chapter considers Schrodinger's model of hydrogen atom and analyzes in details the quantum wave mechanics approach to the motion of the electron in the hydrogen atom. The stationary Schrodinger equation is not easy to solve as it stands, and the whole problem looks rather complicated when expressed in terms of Cartesian coordinates. An essential difference between Bohr's and Schrodinger's models is that there are three quantum numbers, n , l , m , rather than the one number n describing a state of the electron. Moreover, in Bohr's model the atom is, at each instant, in one and only one energy state, that is., at each instant, the state of the atom is definite, but according to Schrodinger's model, the atom can exist in a superposition of states. In other words, the atom can be simultaneously in more than one energy state at a given instant. This is clearly incompatible with Bohr's model.

FranÇois Rafie

In 1913, Niels Bohr developed an accurate model for the hydrogen atom. The mathematics involved and the simplicity of this model is easily understood. The intention of the paper is not to replace Bohr's model, but to find a similar model for all atoms. The model discussed, which was developed on the same basis as Bohr's model for the hydrogen atom, calculates the radii and the energies of the orbits. The wavelength of an emitted photon when an electron makes a ‘jump’ from a higher state to a lower state can also be calculated from the model. Finally, the paper demonstrates that the model obeys the de Broglie's hypothesis that the moving electron exhibits both wave and particle properties.

Hongpu Yang

Bohr’s atomic model, though superseded by quantum mechanics, retains pedagogical value for its intuitive picture of quantized orbits. This paper reinterprets Bohr’s model within Energy-Efficiency Theory (EET), revealing its deep connection to the energy ratio η = E˙ resp/E˙ main. We show that the principal quantum numbern corresponds to the inverse square of η: ηn ∝ 1/n2 . In the ground state (n = 1), η ≪ 1, and the electron is particle-like; in highly excited states (n ≫ 1), η approaches 1, and the electron becomes wave-like. This provides a continuous picture of the transition from quantum to classical behavior, and offers a pedagogical bridge from Bohr’s model to modern quantum theory.

David E. Laird