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The Bohr theory, to which I think you are referring with the reference to shells, is one such theory.
According to the Bohr theory of the atom, the chemical energy is characterized by the Rydberg constant.
(in Bohr theory) the path traced by an electron revolving around the nucleus of an atom.
The idea of the fixed orbit is considered a major component of the Bohr Atomic Model (or Bohr Theory).
The theoretical explanation for energy levels was discovered in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom.
He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.
It is worth noting that this expression was first obtained by A. Sommerfeld based on the old Bohr theory, i.e., before the modern quantum mechanics was formulated.
Lindsay and his wife Rachel translated Kramers' book, The Atom and the Bohr Theory of its Structure, in 1923, receiving approximately $125, on which they toured Europe.
Moseley's law advanced atomic physics by providing the first experimental evidence in favour of Niels Bohr's theory, aside from the hydrogen atom spectrum which the Bohr theory was designed to reproduce.
In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of self-consistency that Lindsay had introduced in his study of many electron systems in the context of Bohr theory.