Step 1: Understanding the Concept
Phosphorus has atomic number \(Z=15\) and mass number \(A=31\).
Step 2: Protons and neutrons
Protons \(=Z=15\). Neutrons \(=A-Z=31-15=16\).
Step 3: Electrons
A neutral atom has \(15\) electrons. The ion \(\text{P}^{3-}\) gains \(3\) electrons, so electrons \(=15+3=18\).
Step 4: Compare the options
Protons, electrons and neutrons are \(15,18\) and \(16\), option (C).
Final Answer:
The ion has 15 protons, 18 electrons and 16 neutrons.
\[ \boxed{\text{(C) }\text{15, 18 and 16}} \]