Quantum numbers give information about the location of an electron. There are four quantum numbers - the Principle quantum number, Angular quantum number, Magnetic quantum number and the spin quantum number. Quantum numbers also come with a set of restrictions which gives useful information about where electrons cannot not be located. A full set of quantum numbers describes a unique electron for a particular atom.

Principle quantum number (n)
The Principle quantum number describes the energy level of an electron. Denoted by n, the value of n ranges from 1 to the shell containing the outermost electron of that atom. It is an indicator of the orbital size. Electrons in atoms reside in atomic orbitals that are referred to as s,p,d,f.. type orbitals. As we go further away from the nucleus, the orbitals get bigger in size. So a 2s orbital is larger than a 1s orbital. A 3p orbital is larger than a 2p orbital. As the energy of the electron increases, so does the principal quantum number. The Principle quantum number cannot be equal to 0.

Angular quantum number (l)
Also called as the Azimuthal quantum number, the angular quantum number indicates the shape of the orbital. It gives the magnitude of the orbital angular momentum. Each type of orbital (s,p,d,f..) has a characteristic shape associated with it. The orbitals described by l = 0,1,2,3... are s,p,d,f... orbitals, respectively. The value of l can be zero. Angular quantum number can also be a positive integer, but it cannot be larger than one less than the principal quantum number (n-1). That is the angular quantum number ranges from 0 to n-1.

Magnetic quantum number (ml)
The Magnetic quantum number indicates the orientation of a particular orbital in space. Its value depends on the angular quantum number. Take the case of p orbitals. This is a set of orbitals consisting of three p-orbitals that have a unique orientation in space. In Cartesian space, each orbital can be represented along an axis (x, y, or z) with the center around the origin at 0. Though each orbital is a p-orbital, we can further uniquely describe each orbital using its position in Cartesian space. Therefore, in this example there will be three magnetic quantum numbers, each uniquely describing one of the p orbitals. The magnetic quantum number is an integer and can have values of −l to l.

Spin quantum number (ms)
The spin quantum number indicates the 'spin' of the electron in an atomic orbital. It is also called the spin projection quantum number. As two electrons can reside inside one atomic orbital, we can use the electron’s spin to uniquely identify each electron. Two electrons in one atomic orbital cannot have the same 'spin'. Spin up is generally denoted as ms = ½ that is the electron has an upward spin and spin down is generally denotes as ms = -½ and the electron has a downward spin. The electron spin quantum number is used to determine if an atom has the ability to generate a magnetic field.

Did you know: No two electrons can have the exact same four quantum numbers.

Thus the quantum numbers not only tell us where electrons will be (in the ground state) and can be (in the excited state), but also tell where electrons cannot be in an atom (due to the restrictions for each quantum number).


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