Orbitals and Quantum Numbers
In the 1920s, Werner Heisenberg put forth his uncertainty principle, which states that, at any one time, it is impossible to calculate both the momentum and the location of an electron in an atom; it is only possible to calculate the probability of finding an electron within a given space. This meant that electrons, instead of traveling in defined orbits or hard, spherical “shells,” as Bohr proposed, travel in diffuse clouds around the nucleus.
To describe the location of electrons, we use quantum numbers. Quantum numbers are basically used to describe certain aspects of the locations of electrons. For example, the quantum numbers n, l, and ml describe the position of the electron with respect to the nucleus, the shape of the orbital, and its special orientation, while the quantum number ms describes the direction of the electron’s spin within a given orbital.
Below are the four quantum numbers, showing how they are depicted and what aspects of electrons they describe.
Orbitals that have the same principal quantum number, n, are part of the same electron shell. For example, orbitals that have n = 2 are said to be in the second shell. When orbitals have the same n and l, they are in the same subshell; so orbitals that have n = 2 and l = 3 are said to be 2f orbitals, in the 2f subshell.
Finally, you should keep in mind that according to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. This means no atomic orbital can contain more than two electrons, and if the orbital does contain two electrons, they must be of opposite spin.
In the 1920s, Werner Heisenberg put forth his uncertainty principle, which states that, at any one time, it is impossible to calculate both the momentum and the location of an electron in an atom; it is only possible to calculate the probability of finding an electron within a given space. This meant that electrons, instead of traveling in defined orbits or hard, spherical “shells,” as Bohr proposed, travel in diffuse clouds around the nucleus.
To describe the location of electrons, we use quantum numbers. Quantum numbers are basically used to describe certain aspects of the locations of electrons. For example, the quantum numbers n, l, and ml describe the position of the electron with respect to the nucleus, the shape of the orbital, and its special orientation, while the quantum number ms describes the direction of the electron’s spin within a given orbital.
Below are the four quantum numbers, showing how they are depicted and what aspects of electrons they describe.
- Principal quantum number (n)-----Has positive values of 1, 2, 3, etc. As n increases, the orbital becomes larger—this means that the electron has a higher energy level and is less tightly bound to the nucleus.
- Second quantum number or azimuthal quantum number (l )-----Has values from 0 to n – 1. This defines the shape of the orbital, and the value of l is designated by the letters s, p, d, and f, which correspond to values for l of 0, 1, 2, and 3. In other words, if the value of l is 0, it is expressed as s; if l = 1 = p, l = 2 = d, and l = 3 = f.
- Magnetic quantum number (ml)-----Determines the orientation of the orbital in space relative to the other orbitals in the atom. This quantum number has values from -l through 0 to +l.
- Spin quantum number (ms)-----Specifies the value for the spin and is either +1/2 or -1/2. No more than two electrons can occupy any one orbital. In order for two electrons to occupy the same orbital, they must have opposite spins.
Orbitals that have the same principal quantum number, n, are part of the same electron shell. For example, orbitals that have n = 2 are said to be in the second shell. When orbitals have the same n and l, they are in the same subshell; so orbitals that have n = 2 and l = 3 are said to be 2f orbitals, in the 2f subshell.
Finally, you should keep in mind that according to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. This means no atomic orbital can contain more than two electrons, and if the orbital does contain two electrons, they must be of opposite spin.