To determine the electron configuration for phosphorus (P), we need to know the atomic number of phosphorus. The atomic number tells us the number of electrons in a neutral atom. Phosphorus has an atomic number of 15, meaning it has 15 electrons.
Electrons fill orbitals in a specific sequence based on increasing energy levels, following the Aufbau principle, the Pauli exclusion principle, and Hund's rule. The order in which orbitals are filled is given by the sequence:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.
Let's go through the sequence step-by-step to distribute the 15 electrons in phosphorus:
1. 1s orbital: The 1s orbital can hold up to 2 electrons.
[tex]\[ 1s^2 \][/tex]
Phosphorus now has 13 electrons left.
2. 2s orbital: The 2s orbital can hold up to 2 electrons.
[tex]\[ 2s^2 \][/tex]
Phosphorus now has 11 electrons left.
3. 2p orbital: The 2p orbital can hold up to 6 electrons.
[tex]\[ 2p^6 \][/tex]
Phosphorus now has 5 electrons left.
4. 3s orbital: The 3s orbital can hold up to 2 electrons.
[tex]\[ 3s^2 \][/tex]
Phosphorus now has 3 electrons left.
5. 3p orbital: The 3p orbital can hold up to 6 electrons, but phosphorus only has 3 electrons left to fill.
[tex]\[ 3p^3 \][/tex]
By arranging the electrons in this way, the complete electron configuration for phosphorus is:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \][/tex]
Comparing this with the available options:
A. [tex]$1s^1 2s^2 3p^6 4d^6$[/tex] (Incorrect: The configuration does not follow the correct sequential filling order.)
B. [tex]$1s^2 2s^2 3s^2 3p^5$[/tex] (Incorrect: This configuration has too many electrons.)
C. [tex]$1s^2 2s^2 2p^6 3s^2 3p^3$[/tex] (Correct: Matches the electron configuration we determined.)
D. [tex]$3s^2 4p^3$[/tex] (Incorrect: This skips earlier orbitals.)
Thus, the correct electron configuration for phosphorus is:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \][/tex]
So, the correct answer is Option C:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \][/tex]
