Which of the following transition metal ions has the lowest density?

Options

A. Copper
B. Nickel
C. Scandium
D. Zinc

Explanation

To determine which of the given transition metal ions (copper, nickel, scandium, and zinc) has the lowest density, we need to analyze the factors that influence density, which is defined as mass per unit volume.

### Step-by-Step Solution:

1. **Understand the Density Formula**:
Density (D) is given by the formula:
\[ D = \frac{\text{mass}}{\text{volume}} \]
Here, mass depends on the atomic number (more protons and neutrons means heavier mass), and volume is influenced by the interatomic forces in the crystal lattice.

**Hint**: Remember that density is a ratio of mass to volume.

2. **Identify Atomic Numbers**:
- Copper (Cu): Atomic number 29
- Nickel (Ni): Atomic number 28
- Scandium (Sc): Atomic number 21
- Zinc (Zn): Atomic number 30

**Hint**: Higher atomic numbers typically indicate heavier elements.

3. **Determine Electronic Configurations**:
- Copper (Cu): \( [Ar] 3d^{10} 4s^1 \)
- Nickel (Ni): \( [Ar] 3d^8 4s^2 \)
- Scandium (Sc): \( [Ar] 3d^1 4s^2 \)
- Zinc (Zn): \( [Ar] 3d^{10} 4s^2 \)

**Hint**: The electronic configuration helps determine the number of unpaired electrons.

4. **Count Unpaired Electrons**:
- Copper: 1 unpaired electron
- Nickel: 2 unpaired electrons
- Scandium: 1 unpaired electron
- Zinc: 0 unpaired electrons

**Hint**: Unpaired electrons influence the strength of metal-metal bonds.

5. **Analyze Interatomic Forces**:
Stronger metal-metal bonds lead to smaller volumes. The order of strength based on unpaired electrons is:
- Nickel (strongest, 2 unpaired)
- Scandium (1 unpaired)
- Copper (1 unpaired)
- Zinc (weakest, 0 unpaired)

**Hint**: More unpaired electrons generally mean stronger bonds and smaller volume.

6. **Determine Mass and Volume Relationships**:
- Zinc has the highest atomic number (30) and thus the highest mass.
- Scandium has the lowest atomic number (21) and thus the lowest mass.
- Zinc has the weakest interatomic forces due to having no unpaired electrons, leading to a larger volume.

**Hint**: Compare both mass and volume to assess density.

7. **Conclusion**:
Scandium has the lowest mass and weaker interatomic forces, leading to a larger volume. Therefore, it will have the lowest density among the given transition metal ions.

**Final Answer**: Scandium (Sc) has the lowest density.