How do I write the four quantum numbers of an electron in Telangana 10th Physical Science, Structure of Atom?

Question

TS SSC Physical Science, chapter Structure of Atom. Our textbook has n, l, ml and ms, which is not there in my friend's CBSE book. I can't work out the four quantum numbers of the last electron, for example for sodium. Also how do I know 4s fills before 3d?

GradeHunt_Team · Answer

Four quantum numbers describe the address of an electron in an atom.

1. Principal quantum number (n): the main shell. n = 1, 2, 3, ... The higher n is, the farther the shell from the nucleus and the higher its energy.
2. Azimuthal (angular momentum) quantum number (l): the sub-shell. l takes values 0 to (n - 1).
l = 0 is s, l = 1 is p, l = 2 is d, l = 3 is f.
3. Magnetic quantum number (ml): the orbital, that is, the orientation in space. ml takes values from -l to +l, including 0. So there are (2l + 1) orbitals in a sub-shell: s has 1, p has 3, d has 5, f has 7.
4. Spin quantum number (ms): the spin of the electron, +1/2 or -1/2. One orbital holds at most 2 electrons, with opposite spins.

Worked example: valence electron of sodium (Z = 11)
Electronic configuration: 1s2 2s2 2p6 3s1
The last electron is in 3s:
n = 3 (third shell)
l = 0 (s sub-shell)
ml = 0 (only one value possible when l = 0)
ms = +1/2 (a single electron in the orbital is usually given +1/2)

Quick check with n = 2:
l can be 0 or 1, so the sub-shells are 2s and 2p.
Orbitals = 1 + 3 = 4, and electrons = 4 x 2 = 8 = 2n^2.

Why 4s before 3d? Use the (n + l) rule from the Aufbau principle. The sub-shell with the lower (n + l) value fills first.
4s: n + l = 4 + 0 = 4
3d: n + l = 3 + 2 = 5
So 4s fills first. If two sub-shells have the same (n + l), the one with the lower n fills first. For example, 3d (3 + 2 = 5) fills before 4p (4 + 1 = 5).

Common slips:
1. Writing l = n. The largest l is n - 1, so a 2d sub-shell cannot exist.
2. Giving ml a value outside -l to +l.
3. Writing ms as +1 or -1. It is always +1/2 or -1/2.

How do I write the four quantum numbers of an electron in Telangana 10th Physical Science, Structure of Atom?

1 answer