If I know the number of protons an element has do I know what element it is ?

Yes.

Explanation:

The atomic number is derived from the number of protons. For example: Radium has 88 protons and its atomic number is 88. Helium has 2 protons its atomic number is 2. Sodium's atomic number is 11 it has 11 protons.

it is to be noted that an alpha particle is an helium nucleus. so it contains 2 protons 2 neutrons and has a mass number of 4. when alpha decay particles are ejected from the nucleus it gets transformed into an atom which has atomic number less than 2 and a mass number less than 4.

an equation that could represent alpha decay is radium 226 decay of alpha particle forms radon 222.

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