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The sum of protons, electrons, and neutrons equals the atomic number (Z) due to the fundamental principles of atomic structure and the way atoms are composed.

Protons are positively charged subatomic particles found in the nucleus of an atom. Each proton has a charge of +1.

Electrons are negatively charged subatomic particles that orbit the nucleus in specific energy levels or electron shells. Each electron has a charge of -1.

Neutrons are electrically neutral subatomic particles also found in the nucleus of an atom. Neutrons have no charge.

In a neutral atom, the number of protons is equal to the number of electrons. This balance of positive protons and negative electrons ensures that the atom as a whole has no net charge.

The atomic number (Z) of an element represents the number of protons in the nucleus of its atoms. It defines the identity of the element since each element has a unique number of protons.

The sum of protons and electrons in a neutral atom is equal to the atomic number (Z). This balance ensures that the positive charge of the protons cancels out the negative charge of the electrons, resulting in a net charge of zero for the atom.

Neutrons, on the other hand, do not significantly contribute to the atomic charge since they are electrically neutral. They primarily influence the mass of the atom but not its overall charge.

Therefore, by summing up the protons and electrons in an atom, we obtain the atomic number (Z), which defines the element, while neutrons contribute to the overall mass but not the atomic number or charge.

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