Question

Question #6f111

Answer 1

`"9 electrons"`

Explanation:

The trick here is to realize that you're actually looking for the number of orbitals that are present on the third energy level in a given atom.

This is the case because, as you know, each orbital can hold a maximum of `2` electrons of opposite spins. In other words, for each orbital, you have one electron that has a spin quantum number, `m_s`, equal to `+1/2` and one electron that has a spin quantum number equal to `-1/2`.

Since you're only looking for the number of electrons that have spin-up, you need to take the total number of electrons present per orbital and divide it by `2`. This, of course, gives you the number of orbitals.

As you know, the total number of orbitals present on an energy level described by a principal quantum number `n` is given by

`color(blue)(ul(color(black)("no. of orbitals" = n^2)))`

In your case, you have

`n = 3`

which means that the third energy level can hold a maximum of

`"no. of orbitals" = 3^2`

`"no. of orbitals" = 9`

Since each orbital can hold a single electron that has `m_s = +1/2`, you can say that a total of `9` electrons can have

`n = 3, m_s = +1/2`

in a given atom.