Quantum numbers of electrons in a given atom

Question

How many electrons in a given atom can have the following quantum numbers:

(a) n = 2, l = 0

(b) n = 3

(c) n = 4, l = 3, m = +2, s = -1/2

(d) n = 3, l = 1, m = 0

Answer 1

(a) n = 2, l = 0 are the quantum numbers for a 2s orbital

So the answer is 2 electrons.

(b) n = 3 corresponds to the third row of the periodic table

so we have the 3s orbital (n = 3, l = 0) and three 3p orbitals (n = 3, l = 1, m_l = 1, 0, –1)

That's four orbitals, so 8 electrons

(Note that quantum numbers n = 3, l = 2 correspond to five 3d orbitals (10 electrons), but

there are high in energy and do not fill until after the 4s orbital.)

(c) n = 4, l = 3, m_l = +2, s = -1/2 corresponds to a single electron (since spin is specified)

So the answer is 1 electron.

(This is one of the 4f orbitals, BTW—useful to check just to make sure it's not a trick question

about a nonexistent orbital.)

(d) n = 3, l = 1, m_l = 0 corresponds to just one of the three 3p orbitals (since m_l is specified).

So the answer is 2 electrons. (Just one orbital means just 2 electrons.)