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.