Question

A second important result is that electrons will fill the lowest energy states available. This would seem to indicate that every electron in an atom should be in the n=1 state. This is not the case, because of Pauli's exclusion principle. The exclusion principle says that no two electrons can occupy the same state. A state is completely characterized by the four numbers n, l, ml, and ms, where ms is the spin of the electron. An important question is, How many states are possible for a given set of quantum numbers? For instance, n=1 means that l=0 with ml=0 are the only possible values for those variables. Thus, there are two possible states: (1, 0, 0, 1/2) and (1, 0, 0, −1/2). How many states are possible for n=2? Express your answer as an integer.

Answer 1

Answer:

• 8

Explanation:

1) Principal quantum number, n = 2

• n is the principal quantum number and indicates the main energy level.

2) Second quantum number, ℓ

• The second quantum number, ℓ,  is named, Azimuthal quantum number.

The possible values of ℓ are from 0 to n - 1.

Hence, since n = 2, there are two possible values for ℓ: 0, and 1.

This gives you two shapes for the orbitals: 0 corresponds to "s" orbitals, and 1 corresponds to "p" orbitals.

3) Third quantum number, mℓ

•    The third quantum number, mℓ, is named magnetic quantum number.

The possible values for mℓ are from - ℓ to + ℓ.

Hence, the poosible values for mℓ when n = 2 are:

• for ℓ = 0: mℓ = 0

• for ℓ = 1, mℓ = -1, 0, or +1.

4) Fourth quantum number, ms.

• This is the spin number and it can be either +1/2  or -1/2.

Therfore the full set of possible states (different quantum number for a given atom) for n = 2 is:

• (2, 0, 0 +1/2)
• (2, 0, 0, -1/2)
• (2, 1, - 1, + 1/2)
• (2, 1, -1, -1/2)
• (2, 1, 0, +1/2)
• (2, 1, 0, -1/2)
• (2, 1, 1, +1/2)
• (2, 1, 1, -1/2)

That is a total of 8 different possible states, which is the answer for the question.