In elementary chemistry, atoms of the same element can differ in which fundamental quantity while still representing the same chemical element?

Introduction / Context:
This question tests the core idea behind isotopes in atomic structure. Atoms of the same element must share certain properties, yet they can still be different from one another. Understanding which property can change, while the element remains the same, is crucial for topics such as nuclear chemistry, radioactivity, and mass spectroscopy.

Given Data / Assumptions:
- We are dealing with atoms of the same chemical element.
- The element identity is determined by its atomic number, which is the number of protons in the nucleus.
- The options list several possible atomic properties, but only one can vary without changing the element itself.

Concept / Approach:
Atoms of the same element can have different numbers of neutrons while having the same number of protons. These variants are called isotopes. Changing the number of neutrons changes the mass of the atom and therefore its mass number, but does not change its atomic number or its place in the periodic table. Thus, isotopes of an element differ in mass number but share atomic number and nuclear charge.

Step-by-Step Solution:
Step 1: Recall that atomic number equals the number of protons in the nucleus and defines the element. Step 2: Recognise that changing the atomic number would change the element completely, so that cannot be the correct answer. Step 3: Remember that isotopes have the same protons but different neutrons, which changes the total number of nucleons. Step 4: The total number of protons and neutrons is called the mass number. Step 5: Therefore, atoms of the same element can differ in mass number while still being the same element.

Verification / Alternative check:
Consider simple examples such as carbon 12 and carbon 14. Both have 6 protons (same atomic number, same element) but different numbers of neutrons, giving mass numbers 12 and 14. They remain carbon but differ in mass. Similarly, chlorine has common isotopes with mass numbers 35 and 37. In each case the periodic table position and chemical symbol remain unchanged, confirming that the distinctive property that varies is mass number, not atomic number or nuclear charge.

Why Other Options Are Wrong:
- Atomic number: If this changed, the number of protons would change and the atom would no longer be the same element.
- Number of protons in the nucleus: This is directly tied to atomic number, so it must remain fixed for a given element.
- Nuclear charge: Nuclear charge depends on the number of protons, so for the same element it is constant.
- Position in the periodic table: This is determined by atomic number and therefore does not change between isotopes of the same element.

Common Pitfalls:
Students sometimes confuse mass number with atomic mass or assume that any atomic property can vary independently. Another common error is believing that changing electrons alone defines isotopes, but that actually describes ions. Isotopes concern neutrons and mass number, while ions concern electrons and charge. Keeping these distinctions clear makes many later topics in chemistry easier to understand.

Final Answer:
Atoms of the same element can differ in their Mass number while remaining the same chemical element.