Four quantum numbers describe the behavior of electrons in an atom: principal, azimuthal, magnetic, and spin. These numbers give the quantum state of an electron, and no two electrons can share the same four quantum numbers. The principal quantum number refers to the distance of an electron’s orbit from the nucleus, while the azimuthal quantum number indicates the shape of the orbit. The magnetic quantum number describes the orientation of an electron’s orbital in space, and the spin quantum number specifies one of two spin states of an electron.
In the prevailing theoretical model of the atom, there are four quantum numbers that describe the behavior of electrons. These include the principal, azimuthal, magnetic, and spin quantum numbers. Together, these four numbers give the quantum state of an electron. A quantum state is the set of mathematical information needed to fully describe a certain system of matter and energy, such as an atom. No two electrons can share the same four quantum numbers, according to the Pauli exclusion principle of quantum mechanics.
The first of the quantum numbers is called the principal quantum number. This number, which can be any positive integer starting with 1, refers to the distance of an electron’s orbit from the atomic nucleus. Unlike planetary orbits, however, electrons are not free to orbit any distance. Rather, they are confined in orbit to discrete energy levels, or quanta, a central tenet of quantum mechanics. Similar to planetary orbits, on the other hand, electrons that orbit farther from the nucleus possess higher kinetic energy.
The azimuthal quantum number indicates the angular momentum of the atomic orbital of an electron. This number says something about the shape of an electron’s orbit around the nucleus. The electrons can orbit in more or less spherical showers around the nucleus, or they can exhibit a more complicated behavior. The idea of an electron as a solid particle orbiting the nucleus, however, is incorrect. The uncertainty principle of quantum mechanics states that the location of an electron is basically a matter of probability.
Based on the other quantum numbers, the magnetic quantum number says something about the orientation of an electron’s orbital in space. This property was first discovered when scientists exposed gases to magnetic fields and then observed how they interacted with light. The magnetic quantum number is also related to the energy levels of an atomic orbital.
Finally, the spin quantum number specifies one of two spin states of an electron. While the principal and azimuthal quantum numbers distinguish between different orbital positions of an electron, the spin quantum number can distinguish between two electrons in an otherwise identical quantum state. If two electrons in the same atom have the same previous three quantum numbers, their spin quantum numbers must be different. Electron spin isn’t quite the same sense of “spin” as we commonly think of, but it is a degree of freedom for an electron. It can take one of two possible values: -1/2 or +1/2.
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