Quantum Mechanical Model of Atoms
While the concepts put forth by Bohr offered a reasonable explanation for the structure of the
hydrogen atom and ions containing only one electron (such as He+ and Li2+), they did not explain the
structures of atoms containing more than one electron. This is because Bohr’s model does not take
into consideration the repulsion between multiple electrons surrounding one nucleus. Modern
quantum mechanics has led to a more rigorous and generalized study of the electronic structure of
atoms. The most important difference between the Bohr model and modern quantum mechanical
models is that Bohr’s assumption that electrons follow a circular orbit at a fixed distance from the
nucleus is no longer considered valid. Rather, electrons are described as being in a state of rapid
motion within regions of space around the nucleus, called orbitals. An orbital is a representation of
the probability of finding an electron within a given region. In the current quantum mechanical
description of electrons, pinpointing the exact location of an electron at any given point in time is
impossible. This idea is best described by the Heisenberg uncertainty principle, which states that it
is impossible to determine, with perfect accuracy, the momentum and the position of an electron
simultaneously. This means that if the momentum of the electron is being measured accurately, its
position cannot be pinpointed, and vice versa.
QUANTUM NUMBERS
Modern atomic theory states that any electron in an atom can be completely described by four
quantum numbers n, l, ml, and ms. Furthermore, according to the Pauli exclusion principle, no two
electrons in a given atom can possess the same set of four quantum numbers. The position and
energy of an electron described by its quantum numbers are known as its energy state. The value of
n limits the values of l, which in turn limits the values of ml. The values of the quantum numbers
qualitatively give information about the orbitals: n about the size and the distance from the
nucleus, l about the shape, and ml about the orientation of the orbital. All four quantum numbers
are discussed below.