Identify the formula of hydroxyapatite

Tooth enamel is mainly hydroxyapatite, whose formula is commonly written as $\mathrm{Ca}_{10}(\mathrm{PO}_4)_6(\mathrm{OH})_2.$

This can also be written in the apatite form as $\left[3\left(\mathrm{Ca}_3(\mathrm{PO}_4)_2\right)\cdot \mathrm{Ca}(\mathrm{OH})_2\right].$

So option B corresponds to hydroxyapatite, not fluoroapatite.

Formation of fluoroapatite

When $\mathrm{F}^-$ ions replace $\mathrm{OH}^-$ ions in hydroxyapatite, fluoroapatite is formed.

Thus, $\mathrm{Ca}_{10}(\mathrm{PO}_4)_6\mathrm{F}_2$ is the formula of fluoroapatite.

Match this with the given options

Rewrite option A: $\left[3\left(\mathrm{Ca}_3(\mathrm{PO}_4)_2\right)\cdot \mathrm{CaF}_2\right].$

Expanding:

• $3\left(\mathrm{Ca}_3(\mathrm{PO}_4)_2\right)$ gives $\mathrm{Ca}_9(\mathrm{PO}_4)_6$
• Adding $\mathrm{CaF}_2$ gives $\mathrm{Ca}_{10}(\mathrm{PO}_4)_6\mathrm{F}_2$

This is exactly fluoroapatite.

Check other options briefly

• B: $\left[3(\mathrm{Ca}_3(\mathrm{PO}_4)_2)\cdot \mathrm{Ca}(\mathrm{OH})_2\right]$ = hydroxyapatite, not fluoroapatite.
• C: $\left[3(\mathrm{Ca}_3(\mathrm{PO}_4)_3)\cdot \mathrm{CaF}_2\right]$ has an incorrect phosphate composition.
• D: $\left[3(\mathrm{Ca}_2(\mathrm{PO}_4)_2)\cdot \mathrm{Ca}(\mathrm{OH})_2\right]$ is not the apatite formula.

Conclusion

The correct formula of fluoroapatite is $\left[3\left(\mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2\right)\cdot \mathrm{CaF}_2\right].$

Therefore, the correct option is A.