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Because electrons are fermions, the Pauli exclusion principle forbids these particles from having all the same quantum numbers. Therefore, for two electrons to occupy the same orbital, and thereby have the same orbital quantum number, they must have different spin quantum numbers. This also limits the number of electrons in the same orbital to two.
The p z orbital is the same as the p 0 orbital, but the p x and p y are formed by taking linear combinations of the p +1 and p −1 orbitals (which is why they are listed under the m = ±1 label). Also, the p +1 and p −1 are not the same shape as the p 0, since they are pure spherical harmonics.
For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m ℓ are equal. In that case, the two values of m s (spin) pair must be different. Since the only two possible values for the spin projection m s are +1/2 and −1/2, it follows that one electron must have m s = +1/2 and one m s = −1/2.
This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell. The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, [ a ] in particular the Pauli exclusion principle , which states that no two ...
Due to the Pauli exclusion principle, two electrons cannot share the same set of quantum numbers within the same system; therefore, there is room for only two electrons in each spatial orbital. One of these electrons must have, (for some chosen direction z) m s = 1 ⁄ 2, and the other must have m s = − 1 ⁄ 2. Hund's first rule states that ...
Distributing 8 electrons over 6 molecular orbitals leaves the final two electrons as a degenerate pair in the 2pπ* antibonding orbitals resulting in a bond order of 2. As in diboron, these two unpaired electrons have the same spin in the ground state, which is a paramagnetic diradical triplet oxygen.
The p orbital consists of six lobed shapes coming from a central point at evenly spaced angles. The p orbital can hold a maximum of six electrons, hence there are six columns in the p-block. Elements in column 13, the first column of the p-block, have one p-orbital electron. Elements in column 14, the second column of the p-block, have two p ...
Hund's rule asserts that if multiple orbitals of the same energy are available, electrons will occupy different orbitals singly and with the same spin before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+ 1 ⁄ 2 and − 1 ...