To determine the number of protons, neutrons, and electrons in the ion [tex]\({ }_{79}^{197} Au ^{3+}\)[/tex]:
1. Protons:
- The atomic number of gold (Au) is 79. This means there are 79 protons in the nucleus of the gold atom.
- Therefore, the number of protons ([tex]\(p^{+}\)[/tex]) in this ion is 79.
2. Neutrons:
- The mass number of this gold ion is 197. The mass number represents the total number of protons and neutrons in the nucleus.
- To find the number of neutrons, subtract the number of protons from the mass number:
[tex]\[
\text{Number of neutrons} = \text{Mass number} - \text{Atomic number} = 197 - 79 = 118
\][/tex]
- Therefore, the number of neutrons ([tex]\(n^{0}\)[/tex]) in this ion is 118.
3. Electrons:
- In a neutral atom, the number of electrons is equal to the number of protons. Therefore, a neutral gold atom would have 79 electrons.
- However, this ion is [tex]\( Au^{3+} \)[/tex], which means it has lost 3 electrons.
- So, the number of electrons in this ion is:
[tex]\[
\text{Number of electrons} = \text{Number of electrons in neutral gold atom} - 3 = 79 - 3 = 76
\][/tex]
- Therefore, the number of electrons ([tex]\(e^{-}\)[/tex]) in this ion is 76.
Thus, the [tex]\({ }_{79}^{197} Au ^{3+}\)[/tex] ion has 79 protons, 118 neutrons, and 76 electrons. The correct option is:
79 p, 118 n, 76 e
