Question

Question #673da

Answer 1

Two electrons.

Explanation:

As you know, we can use four quantum numbers to describe the position and spin of an electron inside an atom.

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Now, notice that the problem provides you with the energy level on which the electron is located, i.e. the principal quantum number, `n=3`, and the orbital in which it resides, i.e. the magnetic quantum number, `m_l = 2`.

This means that the answer to the question is `2` electrons.

That is the case because every energy level has its distinct orbitals. In this case, the `m_l=2` value designates one of the five d-orbitals located on the third energy level.

This particular orbital is unique because you can only have one set of d-orbitals on the third energy level, one set of d-orbitals on the fourth energy level, and so on.

Now, each orbital can hold a maximum of `2` electrons, one having spin-up, or `m_s = +1/2`, and the other having spin-down, or `m_s = -1/2`, as given by the Pauli Exclusion Principle.

This basically means that when you're given a specific orbital, i.e. the value of `n` and the value of `m_l`, the answer can only be `2` electrons.

In this particular case, you have

• `n=3, l=2, m_l = 2, m_s = +1/2`

This descrribes an electron located on the third energy level, in the d-subshell, in one of the five 3d-orbitals, that has spin-up

• `n=3, l=2, m_l = 2, m_s = -1/2`

This descrribes an electron located on the third energy level, in the d-subshell, in one of the five 3d-orbitals, that has spin-down