# What electron could have quantum numbers n=2, l=1, m_l = 0, m_s = +1/2?

Jun 26, 2016

Here's what I got.

#### Explanation:

As you know, four quantum numbers are used to describe the position and spin of an electron in an atom.

The problem provides you with a complete set of quantum numbers and asks you to find an electron that can be described using those quantum numbers.

In your case, the principal quantum number, $n = 2$, is used to describe an electron located on the second energy level.

The angular momentum quantum number, $l$, essentially tells you the subshell in which the electron resides. The values of the $l$ quantum number correspond to

• $l = 0 \to$ the s-subshell
• $l = 1 \to$ the p-subshell
• $l = 2 \to$ the d-subshell
• $l = 3 \to$ the f-subshell

In your case, the value $l = 1$ means that your electron is located in the p-subshell, more specifically, in the 2p-subshell.

The magnetic quantum number, ${m}_{l}$, tells you the exact orbital in which the electron is located.

The p-subshell contains a total of three orbitals, by convention assigned as

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

In your case, ${m}_{l} = 0$, which means that your electron is located in the $2 {p}_{z}$ orbital.

Finally, the spin quantum number, ${m}_{s}$, which tells you the spin of the electron, can only have two possible values, $- \frac{1}{2}$ for spin-down and $+ \frac{1}{2}$ for spin-up.

You can thus say that the quantum number set given to you describes an electron

• located on the second energy level $\to n = 2$
• located in the 2p-subshell $\to l = 1$
• located in the $2 {p}_{z}$ orbital $\to {m}_{l} = 0$
• that has spin-up $\to {m}_{s} = + \frac{1}{2}$