There are 16 neutrons in one atom of phosphorus. It is possible to determine the number of neutrons in one atom of an element by subtracting the number of protons in the element from the atom's atomic mass.
One atom of phosphorus has 15 protons and an atomic mass of 30.97 amu, according to the Royal Society of Chemistry. Phosphorus also has two isotopes, which are atoms of an element that have the same number of protons but different atomic masses and different numbers of neutrons. P-32 has 15 protons and 17 neutrons, while P-33 has 15 protons and 18 neutrons.