Which of the following species will have the largest and the smallest size? `K, K^(+), Ca, Ca^(2+)`. Explain.

Answer

To determine which of the species \( K, K^+, Ca, Ca^{2+} \) has the largest and smallest size, we can follow these steps:

### Step 1: Understand Atomic Sizes
- Potassium (K) and Calcium (Ca) are both elements in the 4th period of the periodic table. Potassium is in Group 1 (alkali metal) and Calcium is in Group 2 (alkaline earth metal).
- Generally, as we move across a period from left to right, the atomic size decreases due to an increase in the effective nuclear charge, which pulls the electrons closer to the nucleus.

### Step 2: Compare Atomic Sizes
- Between K and Ca, K has a larger atomic size than Ca because K is to the left of Ca in the periodic table.

### Step 3: Consider the Ions
- \( K^+ \) is formed when potassium loses one electron. This reduces the electron-electron repulsion and results in a smaller size compared to neutral K.
- \( Ca^{2+} \) is formed when calcium loses two electrons. This also reduces electron-electron repulsion, and since it has a higher positive charge (more protons than electrons), it will be smaller than neutral Ca.

### Step 4: Compare Ionic Sizes
- Both \( K^+ \) and \( Ca^{2+} \) are isoelectronic species, meaning they have the same number of electrons (18 electrons). However, \( K^+ \) has 19 protons while \( Ca^{2+} \) has 20 protons.
- The ionic radius is inversely proportional to the number of protons. Therefore, \( Ca^{2+} \) will be smaller than \( K^+ \) because it has more protons.

### Step 5: Final Comparison
- Now we can summarize the sizes:
- \( K \) (largest)
- \( Ca \) (smaller than K)
- \( K^+ \) (smaller than K)
- \( Ca^{2+} \) (smallest)

### Conclusion
- The largest size among the species is \( K \).
- The smallest size among the species is \( Ca^{2+} \).

### Summary
- Largest size: \( K \)
- Smallest size: \( Ca^{2+} \)