If an electron has a spin quantum no. of #"+1/2"# and a magnetic quantum no. of #-1#, it cannot be present in?

(a) d-orbital
(b) f-orbital
(c) p-orbital
(d) s-orbital

1 Answer
Apr 7, 2018

Answer:

(d) #s# orbital

Explanation:

The trick here is to realize that an #s# orbital cannot be described by a magnetic quantum number equal to #-1#.

The #s# subshell contains a single #s# orbital, which implies that the magnetic quantum number, which tells you the orientation of the orbital that holds a given electron, can only take #1# possible value.

More specifically, for an #s# subshell, you have

#l = 0#

The angular momentum quantum number, #l#, describes the energy subshell in which the electron resides.

For a given subshell, the relationship between the angular momentum quantum number and the magnetic quantum number is given by

#m_l = {-l, -(l-1), ..., - 1, 0, 1, ..., (l-1), l}#

This means that for the #s# subshell, you have

#m_l = 0#

as the only value that the magnetic quantum number can take.

Consequently, you can say that

#m_l = -1#

cannot describe an electron located in an #s# orbital because an #s# orbital can only be described by #m_l = 0#.