a sample of sulfur contains sulfur-32, sulfur-33, sulfur-34, and sulfur-36 atoms. why these atoms can have different mass number but they must have the same atomic number?​

These atoms belong to the same element (sulfur, atomic number .) Hence, the atomic number of each atom would be equal to the atomic number of sulfur: .

Each of these isotopes contains a different number of neutrons. Hence, the mass number (number of neutrons and protons in the atom) differ.

Explanation:

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

The mass number of an atom is the number of protons in this atom, plus the number of neutrons in this atom.

The exact element (e.g., sulfur) that an atom belongs to depends on the atomic number of that atom. For example, an atom with atomic number belongs to sulfur, while an atom with atomic number belongs to argon.

All four types of atoms in this sample belongs to the element sulfur. The atomic number of sulfur is . Hence, the atomic number of all four types of atoms must also be . Otherwise, these atoms would belong to other elements and won't be named after "sulfur".

Hence, all atoms in this sample would have the same atomic number: . Each of these atoms would contain protons.

While the number of protons in each of these atoms is fixed, the number of neutrons in each of these atoms could still vary. Because the mass number of an atom accounts for both protons and neutrons, the mass number of these atoms would not be the same.

For example, sulfur- (mass number ) contains neutrons, whereas sulfur- (mass number ) contains neutrons. (The in the left-hand side is the number of protons in each of these atoms.) Hence, these types of atoms have different mass numbers even though they share the same proton number.

since the atomic number is the number of protons in the nucleus, as we move to the left on the periodic table, the electrostatic pull between the nucleus and the valence electron shell decreases. as we move down a group (vertical column), the valence shell energy level gets further and further from the nucleus.