what subatomic particle is associted with the number that uniquely identifies an element? Why can the other subatomic particles not serve this purpose?

Answer 1

The atomic number (number of protons) uniquely identifies the element.

The other subatomic particles cannot serve this purpose because variations in these other particles (neutrons and electrons) doesn't change the identity of the element but will only change the mass or the charge. For example, a change in the number of neutrons only creates an isotope of the same element, but the identity of the element remains the same. A change in the number of electrons only changes the charge on that element but the identity of the element remains the same. Changing the number of protons however, changes the identity of the element.