Which of the following is a possible set of quantum numbers for a 3d electron?

a) n=4, l=3, m _{l}=2, m_{s}=-1/2

b) n=3, l=2, m _{l}=0, m_{s}=-1/2

c) n=3, l=1, m _{l}=1, m_{s}=+1/2

d) n=3, l=3, m _{l}=2, m_{s}=+1/2

e) n=3, l=0, m _{l}=0, m_{s}=+1/2

###### Solution

We’re being asked to find **which set of quantum numbers** is **possible** for a **3d electron**.

Recall that the *quantum numbers* that define an electron are:

• *Principal Quantum Number* **(n)**: deals with the size and energy of the atomic orbital. The possible values for n are **1 to ∞**.

• *Angular Momentum Quantum Number ***(l)**: deals with the shape of the atomic orbital. The possible values for l are **0 to n – 1**.

• *Magnetic Quantum Number ***(m**_{l}): deals with the orientation of the atomic orbital in 3D space. The possible values for m_{l} are the range of **–l to +l**.

• *Spin Quantum Number ***(m**_{s}): deals with the spin of the electron. The possible values for m_{s} are either **–1/2 (spin down) or +1/2 (spin up)**.