Regarding electrons and their quantum numbers

Question

1. What would be the maximum number of electrons in a given atom that can occupy each of the following?

(a) n = 3 shell

(c) 2p orbital

(b) 2p_z orbital

(d) 2d orbital

2. How many electrons in a given atom can have with the following quantum numbers?

(a) n = 2, l = 1

(b) n = 1

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

(d) n = 3, l = 2, m = 0

Answer 1

1. What would be the maximum number of electrons in a given atom that can occupy each of the following?

(a) n = 3 shell. If the 3rd shell is completely occupied, the maximum # of electrons in that atom would be 18 b/c it would the configuration of argon (3s + 3p + 3d = 2 + 6 + 10 = 18)

(c) 2p orbital. The maximum # of electrons in the 2p orbital is 6, (2p_x + 2p_y + 2p_z = 2 + 2+ 2 = 6) but the max. # of electrons in that atom would be all those in 1s2 + 2s2 + 2p6 which would be 10 electrons (2 + 2 + 6 = 10)

(b) 2p_z orbital. The maximum # of electrons in the 2p_z orbital is 2, but the max. # of electron in that atom would be all those in 1s2 + 2s2 + 2p_z2 which would be 6 electrons (2 + 2 + 2 = 6).

(d) 2d orbital. The maximum # of electron in the d orbital is 10, but there are no electrons in the 2d orbital since the d orbital doesn't become occupied until the 3rd shell

2. How many electrons in a given atom can have with the following quantum numbers?

(a) n = 2, l = 1. Since l = 1, this is a p orbital which can have 6 electrons

(b) n = 1. In the 1st shell (n=1), we have only 2 electrons in the s orbital

(c) n = 4, l = 3, m = +2, s = +1/2. Since all 4 quantum numbers are given, there can be only 1 electron.

(d) n = 3, l = 2, m = 0. In the 3rd shell (n=3), d orbital (l=2), one of the 5 d orbitals (m=0) = 2 electrons.