Question

scih4u
structure and
properties of matter
assignment
name: saadia mohamed
total: /40 appl.

1. complete the table below by providing a set of quantum numbers for the last four electrons in a phosphorus atom. 4
2. explain what is incorrect with respect to the following set of quantum numbers:

n = 3, l = 3, m₁ = -1 2

1. provide the complete set of quantum numbers for all the electrons that could populate the 3d subshell of an atom. 2

Explanation:

Question 1

Step1: Determine P's electron configuration

Phosphorus (atomic number 15) has electron configuration: $1s^22s^22p^63s^23p^3$. Last 4 electrons are in $3s^2$ and $3p^3$.

Step2: Assign quantum numbers for $3s^2$

For $3s$: $n=3$, $l=0$ (s orbital), $m_l=0$ (only 1 orientation). Spins: $+\frac{1}{2}, -\frac{1}{2}$.

Step3: Assign quantum numbers for $3p^3$

For $3p$: $n=3$, $l=1$ (p orbital). $m_l=-1,0,+1$ (Hund's rule: parallel spins first, so all $+\frac{1}{2}$). Last 4 electrons include 2 from $3s$ and 2 from $3p$ (wait: last 4 electrons are the 12th to 15th: 12=3s² (2nd), 13=3p¹,14=3p²,15=3p³).

The orbital shape quantum number $l$ must satisfy $0 \leq l \leq n-1$. For $n=3$, $l$ can only be 0,1,2. $l=3$ is invalid.

Step1: Identify $n$ and $l$ for 3d

3d subshell: $n=3$ (principal), $l=2$ (d orbital, $l=2$).

Step2: List $m_l$ values

For $l=2$, $m_l=-2,-1,0,+1,+2$ (5 orbitals).

Step3: List spin values

Each orbital holds 2 electrons with $m_s=+\frac{1}{2}$ and $-\frac{1}{2}$.

Answer:

e⁻	Principle (n)	Orbital Shape (l)	Magnetic (mₗ)	Spin (mₛ)
2	3	1	-1	+1/2
3	3	1	0	+1/2
4	3	1	+1	+1/2

Question 2