In isotopes of a given chemical element, how do the numbers of neutrons in the nuclei compare while the atomic number remains the same?

Introduction / Context:
The idea of isotopes is central to modern chemistry and nuclear science. Isotopes explain why atoms of the same element can have slightly different masses, why some forms are stable and others radioactive, and how techniques such as radiocarbon dating work. This question checks whether you remember the precise definition of isotopes in terms of protons and neutrons in the atomic nucleus. Understanding this distinction is also important for interpreting symbols like C 12 and C 14 in nuclear equations and mass spectrometry.

Given Data / Assumptions:

• We are talking about isotopes of the same chemical element.
• The atomic number, which is the number of protons, defines the element.
• Neutrons contribute to atomic mass but do not change the chemical identity of the element.
• We assume a basic understanding of subatomic particles: protons, neutrons and electrons.

Concept / Approach:
By definition, isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because they have the same number of protons, they have the same atomic number and very similar chemical properties. However, the different neutron counts give them different mass numbers and sometimes different nuclear stabilities. The approach is to recall that the chemical identity is tied to the proton count, while variation in neutron count leads to isotopic forms like hydrogen 1, hydrogen 2 and hydrogen 3.

Step-by-Step Solution:
Step 1: Note that the atomic number Z is defined as the number of protons in the nucleus and uniquely identifies the element. Step 2: Recognise that isotopes of a given element must all have the same atomic number, so they all have the same number of protons. Step 3: Understand that the mass number A equals the sum of protons and neutrons in the nucleus. Step 4: For isotopes of the same element, different mass numbers mean different numbers of neutrons, because the proton count is fixed. Step 5: Therefore, the defining feature of isotopes is that the number of neutrons differs while the number of protons remains the same.

Verification / Alternative check:
Consider hydrogen isotopes as a classic example. Protium has 1 proton and 0 neutrons, deuterium has 1 proton and 1 neutron, and tritium has 1 proton and 2 neutrons. All three have atomic number 1 because they each have one proton, yet they are isotopes due to their differing neutron counts. Similarly, carbon 12 has 6 protons and 6 neutrons, while carbon 14 has 6 protons and 8 neutrons. In each case, the element is the same (hydrogen or carbon), but the neutron number is different, confirming the correct definition.

Why Other Options Are Wrong:
Option A is wrong because if the number of neutrons were the same, the mass numbers would also be the same and the atoms would not be isotopes; they would be identical. Option C incorrectly suggests that both protons and neutrons change together, but changing proton number changes the element itself rather than giving an isotope. Option D is clearly incorrect because many isotopes, especially of heavier elements, contain neutrons, and only the lightest forms like ordinary hydrogen can have zero neutrons. Option E confuses isotopes with ions; ions differ in electron number, while isotopes differ in neutron number. Only option B correctly states that isotopes have different numbers of neutrons while the number of protons stays the same.

Common Pitfalls:
Students often confuse isotopes with ions or with entirely different elements. Another common mistake is to think that isotopes must always have different numbers of electrons, when in fact a neutral atom of any isotope still has the same number of electrons as protons. To avoid confusion, remember: isotopes differ in neutrons, ions differ in electrons and different elements differ in protons. Keeping these three comparisons clear will help in many nuclear chemistry and atomic structure problems.

Final Answer:
In isotopes of a given element, The number of neutrons is different while the number of protons stays the same, giving atoms of the same element but with different mass numbers.