To determine the correct order of the sizes of the ions \( \text{Ca}^{2+}, \text{K}^{+}, \text{Cl}^{-}, \text{S}^{2-} \), we will follow these steps:
### Step 1: Identify the Atomic Numbers and Protons
First, we need to identify the atomic numbers of the elements involved to determine the number of protons in each ion.
- Sulfur (S) has an atomic number of 16, so it has 16 protons.
- Chlorine (Cl) has an atomic number of 17, so it has 17 protons.
- Potassium (K) has an atomic number of 19, so it has 19 protons.
- Calcium (Ca) has an atomic number of 20, so it has 20 protons.
### Step 2: Determine the Number of Electrons in Each Ion
Next, we need to determine how many electrons are present in each ion after gaining or losing electrons.
- \( \text{S}^{2-} \): Sulfur gains 2 electrons, so it has \( 16 + 2 = 18 \) electrons.
- \( \text{Cl}^{-} \): Chlorine gains 1 electron, so it has \( 17 + 1 = 18 \) electrons.
- \( \text{K}^{+} \): Potassium loses 1 electron, so it has \( 19 - 1 = 18 \) electrons.
- \( \text{Ca}^{2+} \): Calcium loses 2 electrons, so it has \( 20 - 2 = 18 \) electrons.
### Step 3: Identify Isoelectronic Species
All four ions \( \text{Ca}^{2+}, \text{K}^{+}, \text{Cl}^{-}, \text{S}^{2-} \) are isoelectronic, meaning they all have the same number of electrons (18 electrons).
### Step 4: Compare the Number of Protons
Since they are isoelectronic, we compare the number of protons to determine the ionic radii. The effective nuclear charge increases with the number of protons, which pulls the electrons closer to the nucleus, resulting in a smaller ionic size.
- \( \text{Ca}^{2+} \): 20 protons (smallest size)
- \( \text{K}^{+} \): 19 protons
- \( \text{Cl}^{-} \): 17 protons
- \( \text{S}^{2-} \): 16 protons (largest size)
### Step 5: Determine the Order of Size
The order of ionic size from smallest to largest based on the number of protons is:
\[ \text{Ca}^{2+} < \text{K}^{+} < \text{Cl}^{-} < \text{S}^{2-} \]
### Final Answer
Thus, the correct order of the size of the ions is:
**\( \text{Ca}^{2+} < \text{K}^{+} < \text{Cl}^{-} < \text{S}^{2-} \)**
