Question

sch4u
assignment
structure and
properties of matter

1. complete the table below by providing a set of quantum numbers for the last four

electrons in an phosphorus atom. 4

Explanation:

Step1: Determine electron configuration

Phosphorus has atomic number 15. Its electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}\). The last four electrons are in the \(3s\) and \(3p\) orbitals. The first two electrons (labeled 1 and 2) are in the \(3s\) orbital (\(l = 0\)). The next two (labeled 3 and 4) are in the \(3p\) orbital (\(l=1\)).

Step2: Apply spin quantum number rules

For electrons in the same orbital, they have opposite spins. For the \(3s\) orbital (electrons 1 and 2), spins are \(+\frac{1}{2}\) and \(-\frac{1}{2}\) respectively. For the \(3p\) orbital (electrons 3 and 4), according to Hund's rule, electrons fill degenerate orbitals with parallel spins first. So both have \(+\frac{1}{2}\) spin.

Answer:

e-	Principle quantum number	Orbital Shape quantum numbers	Magnetic quantum number	Spin quantum number
2	3	0	0	\(-\frac{1}{2}\)
3	3	1	- 1	\(+\frac{1}{2}\)
4	3	1	0	\(+\frac{1}{2}\)