For a gaseous carbon atom in its' ground state which of the following are possible sets of quantum numbers for two different electrons (electron 1 and electron 2) in the highest energy orbital(s)?
a. electron 1 electron 2 n l ml ms 2 0 1 –1/2, 2 1 1 +1/2.
b. electron 1 electron 2 n l ml ms 2 1 1 +1/2, 2 1 0 -1/2.
c. electron 1 electron 2 n l ml ms 2 0 0 –1/2, 2 0 0 +1/2.
d. electron 1 electron 2 n l ml ms 2 1 0 +1/2, 2 1 0 -1/2.
e. electron 1 electron 2 n l ml ms 2 1 0 +1/2, 2 1 -1 +1/2.

Option e=>

electron 1; n l ml ms = 2 1 0 +1/2.

electron 2;n l ml ms= 2 1 -1 +1/2.

Explanation:

The electronic configuration of carbon in its ground state is 1s2 2s2 2p2. The excited electronic configuration of carbon is given as; 1s2 2s1 2p3 because one of the electrons moves to the 2p sub- orbital because of the absorption of the atom.

Recall that there are four different types of quantum numbers and they are the principal quantum number,n; the Azimuthal quantum number, l; the magnetic quantum number, ml and the spin quantum number, Ms.

Our principal quantum number,n is TWO(2) which is the highest energy level from the electronic configuration written above.

The Azimuthal quantum number is 1 from l= n - 1.

The magnetic quantum number is -1 and 0 because we have two electrons filling the 3 orbitals of 2p sublevels. That is;

2px = -1 , 2py = 0 and 2pz = +1.

Only 2px and 2py will be considered because we have 2 electrons on the 2p in the ground state electronic configuration.

Therefore, the first electron will have ml= 0 and the second electron will have ml= -1.

Spin quantum number, ms; in both electrons the spins is an up spin so we have a +1/2 for both electron.

Hence; electron 1; n l ml ms = 2 1 0 +1/2.

Electron 2;n l ml ms= 2 1 -1 +1/2.