The mass number of an isotope of an element is 298. If its nucleus contains 189 neutrons, what is the atomic number of this element, that is, the number of protons in its nucleus?

Introduction / Context:
This numerical chemistry question tests understanding of basic nuclear terminology, specifically the relationship between mass number, atomic number, and the number of neutrons in an atomic nucleus. Being able to calculate one of these quantities from the other two is essential in nuclear chemistry, radioactivity, and isotopic notation. Here we are given the mass number and the number of neutrons and asked to determine the atomic number.

Given Data / Assumptions:

• Mass number of the isotope, A = 298.
• Number of neutrons in the nucleus, N = 189.
• Atomic number Z is defined as the number of protons in the nucleus.
• Mass number A = Z + N for any nuclide.

Concept / Approach:
The central concept is that mass number A is the sum of the number of protons and neutrons in the nucleus. In symbols, A = Z + N. The atomic number Z represents the number of protons and defines the identity of the element. If we know A and N, we can rearrange the formula to find Z using Z = A - N. This straightforward relationship allows us to calculate the atomic number directly from the provided data.

Step-by-Step Solution:

Verification / Alternative check:
As a check, add the computed atomic number back to the given number of neutrons and confirm that the result equals the mass number. Using Z = 109 and N = 189 gives A = 109 + 189 = 298, which matches the original mass number. This confirms that the calculation is correct. In addition, an atomic number of 109 corresponds to a very heavy, artificially produced element in the transactinide region, which is reasonable for such a high mass number.

Why Other Options Are Wrong:

• 298: This is the mass number, not the atomic number. It represents the total number of protons and neutrons, not just the number of protons.
• 189: This is the number of neutrons, not the atomic number.
• 487: This is the result of adding rather than subtracting the numbers (298 + 189), which is not how mass number is defined.
• 199: This is an arbitrary number with no simple relation to the given data and does not satisfy A = Z + N.

Common Pitfalls:
Students sometimes confuse mass number with atomic number and may select 298 by mistake. Another common error is to add instead of subtracting when rearranging the formula. It is important to remember that mass number already includes both protons and neutrons, so to obtain the number of protons you must subtract the number of neutrons. Writing the formula A = Z + N clearly and checking units can help avoid such errors.

Final Answer:
The atomic number of the element is 109, which means its nucleus contains 109 protons.