Question #c7b21

For starters, you know that the angular momentum quantum number, #l#, which gives you the energy subshell in which an electron is located in an atom, depends on the principal quantum number, #n#.

#l = {0, 1, ..., n- 1}#

In your case, you have

#n = 3#

which implies

# l = {0, 1, 2}#

This tells you that the third energy level contains a total of #3# energy subshells, each described by a value of the angular momentum quantum number.

Now, the magnetic quantum number, #m_l#, which tells you the specific orbital in which an electron is located, depends on the value of the angular momentum quantum number.

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

In your case, you have

• #l = 0 implies m_l = 0#

This tells you that #s# subshell, which is denoted by #l = 0#, contains #1# orbital.

• #l = 1 implies {(m_l = -1), (m_l = 0), (m_l = +1) :}#

This tells you that the #p# subshell, which is denoted by #l= 1#, contains #3# orbitals.

• #l = 2 implies {(m_l = -2), (m_l = -1), (m_l = 0), (m_l = +1), (m_l = +2) :}#

This tells you that the #d# subshell, which is denoted by #l = 2#, contains #5# orbitals.