Step 1: Define atomic number.
The atomic number (Z) of a chemical element is defined as the number of protons found in the nucleus of every atom of that element. It uniquely identifies a chemical element.
Step 2: Evaluate each option based on the definition.
(1) Neutrons in the nucleus of its atom: The number of neutrons can vary for isotopes of the same element, so it does not define the atomic number.
(2) sum of the number of protons and Neutrons in the nucleus of its atom: This sum defines the mass number (or atomic mass number), not the atomic number.
(3) sum of the number of protons and electrons in the nucleus of its atom: Electrons are located outside the nucleus, not in it. Also, the sum of protons and electrons is not the definition of the atomic number. In a neutral atom, the number of electrons equals the number of protons, but the atomic number is fundamentally defined by protons.
(4) protons in the nucleus of its atom: This statement perfectly matches the definition of the atomic number.
Step 3: Conclude the correct statement.
The atomic number of an element is solely determined by the number of protons in the nucleus of its atom.
(4) protons in the nucleus of its atom.