To determine the total number of atoms in 5 units of [tex]\( \text{Ca}_3(\text{PO}_4)_2 \)[/tex], we need to break down the composition and count the atoms systematically.
1. Identify the number of each type of atom in one unit of [tex]\( \text{Ca}_3(\text{PO}_4)_2 \)[/tex]:
- Calcium (Ca) atoms: There are 3 calcium atoms.
- Phosphorus (P) atoms: There are 2 phosphate ([tex]\(\text{PO}_4\)[/tex]) groups. Each phosphate group contains 1 phosphorus atom. So, there are [tex]\(2 \times 1 = 2\)[/tex] phosphorus atoms.
- Oxygen (O) atoms: Each phosphate group ([tex]\(\text{PO}_4\)[/tex]) contains 4 oxygen atoms. Since there are 2 phosphate ([tex]\(\text{PO}_4\)[/tex]) groups, the total number of oxygen atoms is [tex]\(2 \times 4 = 8\)[/tex].
2. Calculate the total number of atoms in one unit of [tex]\( \text{Ca}_3(\text{PO}_4)_2 \)[/tex]:
- Calcium atoms: 3
- Phosphorus atoms: 2
- Oxygen atoms: 8
- Total atoms in one unit = [tex]\(3 \text{ (Ca)} + 2 \text{ (P)} + 8 \text{ (O)} = 13\)[/tex] atoms
3. Calculate the total number of atoms in 5 units of [tex]\( \text{Ca}_3(\text{PO}_4)_2 \)[/tex]:
- Each unit contains 13 atoms.
- Therefore, 5 units contain [tex]\(5 \times 13 = 65\)[/tex] atoms.
Thus, the total number of atoms in 5 units of [tex]\( \text{Ca}_3(\text{PO}_4)_2 \)[/tex] is [tex]\( \boxed{65} \)[/tex].
So, the correct answer is:
b. 65
