Answer
Protons: 15
Neutrons: 17
Work Step by Step
The atomic number of phosphorous is 15, meaning that there are 15 protons (the atomic number is the number of protons). Because it is Phosphorous-32, the atomic mass number of this isotope is 32 amu. Both protons and neutrons weigh one amu while electrons are essentially weightless, so this means that there must be 17 neutrons (15 protons+17 neutrons= 32 amu).