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

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

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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 -># the s-subshell
• #l=1 -># the p-subshell
• #l=2 -># the d-subshell
• #l=3 -># 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 = color(white)(-)0 -># the #2p_z# orbital
• #m_l = -1 -># the #2p_y# orbital
• #m_l = +1 -># the #2p_x# orbital

In your case, #m_l = 0#, which means that your electron is located in the #2p_z# orbital.

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Finally, the spin quantum number, #m_s#, which tells you the spin of the electron, can only have two possible values, #-1/2# for spin-down and #+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 #-> n=2#
• located in the 2p-subshell #-> l=1#
• located in the #2p_z# orbital #-> m_l = 0#
• that has spin-up #-> m_s = +1/2#