Question

sch4u
structure and
properties of matter
assignment

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 the spin quantum number for electron 3

According to the Pauli exclusion principle, electrons in the same orbital have opposite spins. For electron 3, since it is in a \(p\) orbital (\(l = 1\)), and considering the Aufbau principle and Hund's rule, the spin quantum number \(m_s=+\frac{1}{2}\)

Step2: Determine the spin quantum number for electron 4

For electron 4, also in a \(p\) orbital (\(l = 1\)). Since electrons in different \(p\) - orbital (with different \(m_l\)) follow Hund's rule (parallel spins first), and assuming the previous spin for electron 3 is \(+\frac{1}{2}\), the spin quantum number \(m_s =+\frac{1}{2}\)

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	\(+\frac{1}{2}\)