To determine the correct order of size among the given ions and atoms (Ca²⁺, Ar, K⁺, Cl⁻, and H₂O), we will follow these steps:
### Step 1: Identify the number of electrons in each species
- **Ca²⁺**: Calcium loses 2 electrons, so it has 18 electrons (20 - 2).
- **Ar**: Argon has 18 electrons.
- **K⁺**: Potassium loses 1 electron, so it has 18 electrons (19 - 1).
- **Cl⁻**: Chlorine gains 1 electron, so it has 18 electrons (17 + 1).
- **H₂O**: Water is a molecule, but if we consider the oxygen atom in H₂O, it has 8 electrons. However, for comparison, we will consider the total number of electrons in H₂O as 10 (2 from H and 8 from O).
### Step 2: Determine the number of protons in each species
- **Ca²⁺**: Calcium has 20 protons.
- **Ar**: Argon has 18 protons.
- **K⁺**: Potassium has 19 protons.
- **Cl⁻**: Chlorine has 17 protons.
- **H₂O**: Oxygen has 8 protons, and Hydrogen has 1 proton each (2 total), so H₂O has 10 protons.
### Step 3: Identify which species are isoelectronic
All species except H₂O are isoelectronic (having the same number of electrons, which is 18):
- Ca²⁺, Ar, K⁺, and Cl⁻ are isoelectronic.
### Step 4: Compare sizes based on effective nuclear charge (Z_eff)
The size of the ions/atoms can be compared based on the effective nuclear charge (Z_eff), which is the net positive charge experienced by electrons in an atom. The more protons there are in the nucleus (while keeping the number of electrons constant), the smaller the size due to a stronger attraction between the nucleus and the electrons.
- **Ca²⁺**: 20 protons → smallest size
- **K⁺**: 19 protons → larger than Ca²⁺
- **Ar**: 18 protons → larger than K⁺
- **Cl⁻**: 17 protons → larger than Ar
- **H₂O**: 10 protons → largest size
### Step 5: Write the correct order of size
Based on the above analysis, the order from smallest to largest size is:
**Ca²⁺ < K⁺ < Ar < Cl⁻ < H₂O**
### Final Answer
The correct order of size is:
**Ca²⁺ < K⁺ < Ar < Cl⁻ < H₂O**
