# What are the quantum numbers for electrons in the 4d orbitals?

Sep 27, 2017

Here's what I got.

#### Explanation:

As you know, the principal quantum number, $n$, tells you the energy shell in which the electron is located.

In your case, the electron is said to occupy the $\text{4th}$ energy level, which is equivalent to saying that it is located in the $\text{4th}$ energy shell, so

$n = 4$

The angular momentum quantum number, $l$, tells you the energy subshell in which the electron is located. For this quantum number, you have

• $l = 0 \to$ the $s$ subshell
• $l = 1 \to$ the $p$ subshell
• $l = 2 \to$ the $d$ subshell
$\vdots$

and so on. In your case, you have

$l = 2$

Now, the $d$ subshell can hold a maximum of five $d$ orbitals, which are denoted by the values of the magnetic quantum number, ${m}_{l}$.

For the $d$ subshell, you have

${m}_{l} = \left\{- 2 , - 1 , 0 , 1 , 2\right\}$

Finally, the spin quantum number, ${m}_{s}$, which denotes the spin of the electron, can take two possible values

${m}_{s} = \left\{+ \frac{1}{2} , - \frac{1}{2}\right\}$

You now have all the information that you need to write the sets of quantum numbers that can describe an electron located on the $\text{4th}$ energy level, in the $4 d$ subshell.

I'll show you four sets to start you off

• $n = 4 , l = 2 , {m}_{l} = - 2 , {m}_{s} = + \frac{1}{2}$
• $n = 4 , l = 2 , {m}_{l} = 0 , {m}_{s} = - \frac{1}{2}$
• $n = 4 , l = 2 , {m}_{l} = 1 , {m}_{s} = - \frac{1}{2}$
• $n = 4 , l = 2 , {m}_{l} = 1 , {m}_{s} = + \frac{1}{2}$