The F⁻ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula.

Solution

Chemistry ma’am · 3 steps

Start from hydroxyapatite and swap its OH⁻ for F⁻. The phosphate part stays exactly the same.

1. Tooth enamel. Hydroxyapatite is 3Ca₃(PO₄)₂ · Ca(OH)₂, which is the same as Ca₁₀(PO₄)₆(OH)₂. Its calcium phosphate units are neutral: 3(+2) + 2(-3) = 0.
2. Fluoride swaps in. F⁻ has the same charge as OH⁻ and nearly the same size, so it takes the place of OH⁻ in the crystal. Only the Ca(OH)₂ part changes, and it becomes CaF₂.

   3Ca₃(PO₄)₂ · Ca(OH)₂ + 2F⁻ → 3Ca₃(PO₄)₂ · CaF₂ + 2OH⁻

   Option	Phosphate unit	Second part	Verdict
   (a)	Ca₃(PO₄)₂, neutral	CaF₂	fluoroapatite
   (b)	Ca₃(PO₄)₂, neutral	Ca(OH)₂	hydroxyapatite, the starting enamel
   (c)	Ca₃(PO₄)₃: +6 - 9 = -3	CaF₂	unit is not neutral
   (d)	Ca₂(PO₄)₂: +4 - 6 = -2	Ca(OH)₂	not neutral, and no fluoride

3. So. Fluoroapatite is 3Ca₃(PO₄)₂ · CaF₂, that is, Ca₁₀(PO₄)₆F₂. The answer is option (a).

The idea to keep. Fluoroapatite is hydroxyapatite with F⁻ in place of OH⁻. Before you pick a formula, check that Ca₃(PO₄)₂ balances its charges: three Ca²⁺ against two PO₄³⁻.

Answer from the NTA final answer key. Solution by PrepWiser.