No, two atoms cannot have the same atomic number but different masses or charges. The atomic number of an atom is determined by the number of protons in its nucleus, and this number uniquely identifies the element. For example, an atom with 6 protons will always have an atomic number of 6, which corresponds to carbon (C).
While atoms of the same element must have the same atomic number, they can have different masses and charges due to the presence of different numbers of neutrons and electrons, respectively.
Isotopes are atoms of the same element that have different numbers of neutrons. These isotopes have the same atomic number (since they have the same number of protons) but different atomic masses due to the varying number of neutrons. For example, carbon-12 (12C) and carbon-14 (14C) are isotopes of carbon, both having an atomic number of 6 but different atomic masses.
As for charges, atoms can become ions by gaining or losing electrons. An atom that loses one or more electrons will have a positive charge and is called a cation, while an atom that gains one or more electrons will have a negative charge and is called an anion. However, the atomic number remains the same because it is based on the number of protons, which does not change during the formation of ions.
In summary, while atoms of the same element can have different masses and charges, they must have the same atomic number.