No, not all atoms in an element necessarily have the same number of protons or electrons. The atomic number of an element corresponds to the number of protons in the nucleus of an atom of that element, and it defines the identity of the element. In a neutral atom, the number of electrons is equal to the number of protons, maintaining electrical neutrality.
However, atoms can exist in different forms called isotopes, which have the same number of protons but different numbers of neutrons in the nucleus. Isotopes of an element have the same atomic number (since it is determined by the number of protons), but they have different mass numbers due to the varying number of neutrons.
Isotopes can have different physical properties, such as varying atomic masses and nuclear stability. Some isotopes are stable, while others may undergo radioactive decay, resulting in the emission of radiation.
To summarize, while all atoms of a given element have the same atomic number (number of protons), they can have different numbers of neutrons, leading to the existence of isotopes.