To determine the number of protons, neutrons, and electrons in the [tex]\[^{1+0_{58}} Ce ^{3+}\][/tex] ion, follow these steps:
1. Determine the Number of Protons:
The atomic number of cerium (Ce) is 58. This number represents the number of protons in the nucleus of the cerium atom.
Therefore, there are 58 protons in the [tex]\[^{1+0_{58}} Ce ^{3+}\][/tex] ion.
2. Determine the Number of Neutrons:
The notation [tex]\[^{1+0_{58}}\][/tex] indicates the mass number of the isotope, which is 140. The mass number is the sum of protons and neutrons in the nucleus.
We know the number of protons is 58. To find the number of neutrons, we can subtract the number of protons from the mass number:
[tex]\[
\text{Number of neutrons} = \text{Mass number} - \text{Number of protons}
\][/tex]
[tex]\[
\text{Number of neutrons} = 140 - 58 = 82
\][/tex]
Therefore, there are 82 neutrons in the [tex]\[^{1+0_{58}} Ce ^{3+}\][/tex] ion.
3. Determine the Number of Electrons:
The ion has a [tex]\(3+\)[/tex] charge. This means it has lost 3 electrons compared to its neutral state. In a neutral cerium atom, the number of electrons is equal to the number of protons (58).
Since the ion has lost 3 electrons:
[tex]\[
\text{Number of electrons in \(Ce^{3+}\)} = \text{Number of protons} - 3
\][/tex]
[tex]\[
\text{Number of electrons} = 58 - 3 = 55
\][/tex]
Therefore, there are 55 electrons in the [tex]\[^{1+0_{58}} Ce ^{3+}\][/tex] ion.
In summary, the [tex]\[^{1+0_{58}} Ce ^{3+}\][/tex] ion contains:
- 58 protons
- 82 neutrons
- 55 electrons
