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The atomic number is the number of protons in the nucleus of an atom.

(Note: that in a neutral atom the number of protons in the nucleus is also equal to the number of electrons the atom has)

The Atomic Mass is the mass (weight) of all the components of the atom but is dominated by the nucleus composed of protons and neutrons. Basically atomic mass is how many times an atom of an element is heavier than an atom of hydrogen, (whose atomic mass is taken as unity [1]).

(Note: atoms with the same atomic number [ie an element] may have slightly differing atomic masses. This is because atoms can have differing numbers of neutrons in their nucleus. These variations in atomic mass are called "isotopes" of that element)

I have made a related link below showing you a Periodic Table of the Elements. The numbers on the table are the atomic numberof the element.
An element's atomic number represents the number of protons that are present in the nucleus of an atom in that element.
The atomic number represents the number of protons there is in that element. It also represents the number of electrons for that particular element only if the atom is atomically neutral and is not electrically charged. Typically, an atom does not lose protons so it is reliable to base this number on the number of protons in an atom as opposed to the number of electrons, seeing that electrons can be easily lost.

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