Isotopes are atoms of the same chemical element that have different values of which important quantity?

Introduction / Context:
The concept of isotopes is essential in chemistry, nuclear physics, and many applications such as medical imaging and radiocarbon dating. Isotopes involve atoms of the same element that differ in certain properties. This question asks which quantity is different among isotopes of a given element.

Given Data / Assumptions:
- All isotopes of an element share the same atomic number.
- Atomic number equals the number of protons in the nucleus.
- Isotopes are defined by differences in their neutron count and therefore in their mass.

Concept / Approach:
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the total number of nucleons (protons plus neutrons) changes, the mass number changes as well. Atomic number and nuclear charge remain constant, so the chemical identity is preserved, even though nuclear properties and some physical properties can change. The quantity that captures this change is the mass number, not the atomic number or position in the periodic table.

Step-by-Step Solution:
Step 1: Recall that atomic number is equal to the number of protons and defines the element. Step 2: Recognise that isotopes must have the same atomic number to remain the same element. Step 3: Note that isotopes differ in the number of neutrons in the nucleus. Step 4: Understand that mass number equals the sum of protons and neutrons. Step 5: Conclude that isotopes of an element have different mass numbers because of different neutron counts.

Verification / Alternative check:
Consider carbon 12 and carbon 14. Both have 6 protons, so their atomic numbers are 6, and both are carbon. Carbon 12 has 6 neutrons, mass number 12, while carbon 14 has 8 neutrons, mass number 14. This pattern appears for many elements with multiple isotopes, confirming that mass number, not atomic number, is the distinguishing feature. Because atomic number does not change, nuclear charge and periodic table position also remain the same.

Why Other Options Are Wrong:
- Atomic numbers because they contain different numbers of protons: If the atomic number changed, we would not have isotopes but entirely different elements.
- Nuclear charges and therefore different elements: Nuclear charge is determined by proton number, which does not change among isotopes.
- Positions in the periodic table: These are fixed by atomic number, so isotopes occupy the same place in the periodic table.
- Numbers of electrons in a neutral atom: In a neutral atom, electrons equal protons, so for isotopes of a given element, that number is the same. Only ions change electron count.

Common Pitfalls:
A common confusion is between isotopes, ions, and isobars. Isotopes differ in neutrons, ions differ in electrons, and isobars share the same mass number but are different elements. Keeping these definitions distinct helps prevent mixing up mass number and atomic number or thinking that periodic table position changes for isotopes.

Final Answer:
Isotopes of the same element have different Mass numbers because they contain different numbers of neutrons.