State the exclusion principle. What does it imply about the number and spin of electrons in an atomic orbital?

Question

Hayden Callahan

Chemistry

3 May, 09:21

State the exclusion principle. What does it imply about the number and spin of electrons in an atomic orbital?

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Sanaa Reeves · Answer 1

The Pauli exclusion principle was developed by Austrian physicist Ernst Pauli in 1925. This principle of quantum says that two electrons in an atom cannot have all four equal quantum numbers.

Explanation:

This fact would explain that electrons are dispersed in layers or levels around the nucleus of the atom and therefore, atoms that have more electrons occupy more space, because the number of layers of which the atom consists increases. The maximum number of electrons that a layer or level can have is 2n ^ 2.

In order to fully describe the electron within the hydrogen atom, we need to enter a fourth quantum number to those already known. Said fourth quantum number is represented by the letters ms, and is known as the quantum number of spin, which is closely related to the magnetic properties of electrons. The quantum number ms can only have two different values, + 1/2 or - 1/2. To electrons whose values of ms are equal, it is said that they have what is known as parallel spins, however, if the values that present more are different it is said that they have opposite spins or also called antiparallels.

In order to describe an orbital, three quantum numbers (the numbers n, l and ml) are needed, at the same time that an electron that is in an atom is given by a combination of four quantum numbers, the main three plus the number ms. Pauli's exclusion principle tells us that in an atom it is impossible for two electrons to coexist with the four identical quantum numbers. According to this principle, in an atomic type orbital, which is determined by the quantum numbers n, l, and ml, there can only be two electrons: one of them with a positive spin + 1/2 and another with its opposite spin negative - 1/2.

Then we say that each of the types of orbitals can only contain 2 electrons at most, which must necessarily have opposite spins. These electrons will have all their equal quantum numbers, and will only differ in the quantum number ms (spin).