Sure, let's break down the process to determine the number of protons, neutrons, and electrons in the ion [tex]\( { }_{13}^{27} Al ^{+3} \)[/tex].
1. Identify the atomic number and atomic mass number for Aluminum (Al):
- Atomic number (13): This number, written as a subscript, indicates the number of protons in an aluminum atom.
- Atomic mass number (27): This number, written as a superscript, indicates the total number of protons and neutrons in the nucleus of the aluminum atom.
2. Calculate the number of protons:
The atomic number is 13, so the number of protons [tex]\( p^+ \)[/tex] in this aluminum ion is:
[tex]\[ \text{Number of protons} = 13 \][/tex]
3. Calculate the number of neutrons:
The atomic mass number is 27, and the atomic number (number of protons) is 13. The number of neutrons [tex]\( n^0 \)[/tex] is found by subtracting the number of protons from the atomic mass number:
[tex]\[ \text{Number of neutrons} = \text{Atomic mass number} - \text{Atomic number} = 27 - 13 = 14 \][/tex]
4. Calculate the number of electrons:
This is a [tex]\( \text{Al}^{+3} \)[/tex] ion, indicating it has lost 3 electrons. The number of electrons [tex]\( e^- \)[/tex] in a neutral aluminum atom (with atomic number 13) would be equal to the number of protons, but because it's a [tex]\( +3 \)[/tex] ion, it has 3 fewer electrons than protons:
[tex]\[ \text{Number of electrons} = \text{Number of protons} - \text{Ion charge} = 13 - 3 = 10 \][/tex]
Based on this analysis:
- Number of protons: 13
- Number of neutrons: 14
- Number of electrons: 10
Therefore, the correct option is:
[tex]\[ 13 \, p^+, 14 \, n^0, 10 \, e^- \][/tex]
This corresponds to the third option:
[tex]\[ 13 \, p^*, 14 \, n^0, 10 \, e^- \][/tex]
