Question

Give the set of four quantum numbers that represent the last electron added (using the aufbau principle to the cl atom.

Answer 1

An element has four quantum numbers associated with it. We have

1. principal quantum number ($n$)
2. azimuthal quantum number ($l$)
3. magnetic quantum number ($m_{l}$)
4. spin quantum number ($m_{s}$)

To look for each quantum  number of Chlorine (Cl), we mus first recall its electronic configuration: $1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}$.

1. For $n$, we need to look for its highest energy level or by simply checking the period that the element belongs to. So for this case, it's $n = 3$.

2. For $l$, we need to look for the sublevel where the last electron was assigned. The sublevels, p, d, f are assigned to a value of 0, 1, 2, and 3, respectively. Since the last electron was assigned in p, then $l = 1$.

3. And for $m_{l}$, the number of orbitals present in Cl is $2l+1 = 3$. The possible magnetic quantum numbers for $p$ are -1, 0, +1. Since there 5 electrons we count starting at -1. So, we have $m_{l}=+1[tex].\\4. Lastly, for [tex]m_{s}$, we need to determine the spin. Since we have 5 electrons, all the arrows upward are filled in. That means the fifth electron has a spin of +1/2. 

Answers: $n =3, l = 1, m_{l} = 0, m_{s} =+1/2$