How many electrons in an atom can share the quantum numbers n = 4 and l = 3?

Here we want to find the number of electrons that an atom can have for some given quantum numbers.

We will see that this atom can hold 14 electrons.

Now let's see how to get that

We know that for an atom with quantum numbers n and l, the orbitals can take the values from -l to l, so we will have 2*l + 1 orbitals.

And in each one of these orbitals, we can hold a maximum of two electrons (one for each spin, remember that these are fermions, thus we can't have two of them in the same state, so we can't have two electrons in the same orbital with the same spin, this is why each orbital can hold a maximum of two electrons).

Then the number of electrons that an atom with quantum numbers n and n can hold is:

2*(2*l + 1).

Now we have.

n = 4

l = 3

Then the number of electrons that this atom can hold is:

e = 2*(2*3 + 1) = 2*7 = 14

This atom can hold 14 electrons.

If you want to learn more, you can read:

link

Explanation:

If l = 3, the electrons are in an f subshell.

The number of orbitals with a quantum number l is 2l + 1, so there

are 2×3 + 1 = 7 f orbitals.

Each orbital can hold two electrons, so the f subshell can hold 14 electrons.

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