To determine which of the given ions is isoelectronic to the oxide anion [tex]\( O^{2-} \)[/tex], we need to compare the number of electrons in each of these ions. Two species are said to be isoelectronic if they have the same number of electrons.
First, let’s identify the number of electrons in the oxide anion [tex]\( O^{2-} \)[/tex]:
- The atomic number of oxygen (O) is 8, which means a neutral oxygen atom has 8 electrons.
- The [tex]\( O^{2-} \)[/tex] ion has gained 2 additional electrons, so it has [tex]\( 8 + 2 = 10 \)[/tex] electrons.
Now let's calculate the number of electrons for each given ion:
1. Sulfur ion [tex]\( S^{2-} \)[/tex]:
- Sulfur (S) has an atomic number of 16, so a neutral sulfur atom has 16 electrons.
- The [tex]\( S^{2-} \)[/tex] ion has gained 2 additional electrons, so it has [tex]\( 16 + 2 = 18 \)[/tex] electrons.
2. Lead ion [tex]\( Pb^{2+} \)[/tex]:
- Lead (Pb) has an atomic number of 82, so a neutral lead atom has 82 electrons.
- The [tex]\( Pb^{2+} \)[/tex] ion has lost 2 electrons, so it has [tex]\( 82 - 2 = 80 \)[/tex] electrons.
3. Potassium ion [tex]\( K^{+} \)[/tex]:
- Potassium (K) has an atomic number of 19, so a neutral potassium atom has 19 electrons.
- The [tex]\( K^{+} \)[/tex] ion has lost 1 electron, so it has [tex]\( 19 - 1 = 18 \)[/tex] electrons.
4. Chlorine ion [tex]\( Cl^{-} \)[/tex]:
- Chlorine (Cl) has an atomic number of 17, so a neutral chlorine atom has 17 electrons.
- The [tex]\( Cl^{-} \)[/tex] ion has gained 1 additional electron, so it has [tex]\( 17 + 1 = 18 \)[/tex] electrons.
5. Magnesium ion [tex]\( Mg^{2+} \)[/tex]:
- Magnesium (Mg) has an atomic number of 12, so a neutral magnesium atom has 12 electrons.
- The [tex]\( Mg^{2+} \)[/tex] ion has lost 2 electrons, so it has [tex]\( 12 - 2 = 10 \)[/tex] electrons.
Comparing the numbers of electrons:
- [tex]\( O^{2-} \)[/tex] has 10 electrons.
- [tex]\( S^{2-} \)[/tex] has 18 electrons.
- [tex]\( Pb^{2+} \)[/tex] has 80 electrons.
- [tex]\( K^{+} \)[/tex] has 18 electrons.
- [tex]\( Cl^{-} \)[/tex] has 18 electrons.
- [tex]\( Mg^{2+} \)[/tex] has 10 electrons.
The ion that is isoelectronic with the oxide anion [tex]\( O^{2-} \)[/tex] (i.e., has the same number of electrons) is [tex]\( Mg^{2+} \)[/tex], which also has 10 electrons.
Therefore, the ion that is isoelectronic to the oxide anion [tex]\( O^{2-} \)[/tex] is [tex]\( Mg^{2+} \)[/tex].
