What is the ml quantum number for an electron in the 5d orbital?

Dec 25, 2015

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

Explanation:

As you know, the position and spin of an electron in an atom are determined by a set of four quantum numbers

In your case, you're interested about figuring out what value of the magnetic quantum number, ${m}_{l}$, would correspond to an electron located in a 5d-orbital.

The magnetic quantum number gives you the exact orbital in which the electron is located. The subshell that holds that orbital is determined by the angular momentum quantum number, $l$.

As you can see, the values of ${m}_{l}$ depend on the value of $l$, which can be

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

In your case, $l = 2$, since you're dealing with a d-subshell. This means that ${m}_{l}$ can take any of the following values

${m}_{l} = \left\{- 2 , - 1 , \textcolor{w h i t e}{-} 0 , \textcolor{w h i t e}{-} 1 , \textcolor{w h i t e}{-} 2\right\}$

Each d-subshell contains a total of five orbitals. In the case of a 5d-subshell, these orbitals correspond to the following ${m}_{l}$ values

• ${m}_{l} = - 2 \to$ the $5 {d}_{x y}$ orbital
• ${m}_{l} = - 1 \to$ the $5 {d}_{x z}$ orbital
• ${m}_{l} = \textcolor{w h i t e}{-} 0 \to$ the $5 {d}_{y z}$ orbital
• ${m}_{l} = \textcolor{w h i t e}{-} 1 \to$ the $5 {d}_{{x}^{2} - {y}^{2}}$ orbital
• ${m}_{l} = \textcolor{w h i t e}{-} 2 \to$ the $5 {d}_{{z}^{2}}$ orbital