What values of #l# are permitted for an electron with n = 3?

1 Answer
Dec 31, 2016

Answer:

#l=0,1,2#. See below.

Explanation:

There are four quantum numbers: the principle quantum number, #n#, the angular momentum quantum number, #l#, the magnetic quantum number, #m_l#, and the electron spin quantum number, #m_s#. For this question we are concerned only with the first two.

The principle quantum number, #n#, describes the energy and distance from the nucleus, and represents the shell.

For example, the #3d# subshell is in the #n=3# shell, the #2s# subshell is in the #n = 2# shell, etc.

The angular momentum quantum number, #l#, describes the shape of the subshell and its orbitals, where #l=0,1,2,3...# corresponds to #s, p, d, # and #f# subshells (containing #s, p, d, f# orbitals), respectively. Each shell has up to #n-1# types of subshells/orbitals.

Therefore, the #n=3# shell has subshells of #l=0,1,2#, which means the #n=3# shell contains #s#, #p#, and #d# subshells (each containing their respective orbitals).