Calculating Atomic Number from Mass Number and Neutrons

The question asks us to determine the atomic number of an isotope given its mass number and the number of neutrons in its nucleus. Understanding the fundamental composition of an atom's nucleus is key to solving this problem.

Understanding Key Concepts: Atomic Structure

An atom is composed of a nucleus, which contains protons and neutrons, and electrons orbiting the nucleus. For any neutral atom, the number of electrons equals the number of protons. However, when discussing the nucleus and isotopes, the focus is on protons and neutrons.

• Atomic Number (Z): This is defined as the number of protons in the nucleus of an atom. The atomic number uniquely identifies an element. For example, all atoms with 6 protons are Carbon (C), and all atoms with 8 protons are Oxygen (O).
• Mass Number (A): This is the total number of protons and neutrons in the nucleus of an atom. It is the sum of the atomic number (number of protons) and the number of neutrons.
• Neutrons (N): These are neutral particles found in the nucleus. Isotopes of an element have the same atomic number (same number of protons) but different numbers of neutrons, leading to different mass numbers.

The Relationship Between Mass Number, Atomic Number, and Neutrons

The definition of the mass number provides the core relationship:

\text{Mass Number} = \text{Atomic Number} + \text{Number of Neutrons}

\(A = Z + N\)

We are given the mass number (A) and the number of neutrons (N) and need to find the atomic number (Z). We can rearrange the formula to solve for Z:

\(Z = A - N\)

Applying the Formula to Find the Atomic Number

Given:

• Mass number (A) = 298
• Number of neutrons (N) = 188

Using the rearranged formula:

\(Z = A - N\)

Substitute the given values into the formula:

\(Z = 298 - 188\)

Now, perform the subtraction:

\(Z = 110\)

The atomic number of the isotope is 110.

Conclusion

The atomic number of the isotope with a mass number of 298 and 188 neutrons is 110. The atomic number is always an integer representing the count of protons.

Revision Table: Atomic Structure

Additional Information: Isotopes and Elements

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the number of protons is the same, they have the same atomic number and are the same element. However, their different number of neutrons gives them different mass numbers. For example, Carbon-12 (\(_{6}^{12}\text{C}\)) has 6 protons and 6 neutrons (A=12), while Carbon-14 (\(_{6}^{14}\text{C}\)) has 6 protons and 8 neutrons (A=14). Both are isotopes of Carbon because they both have 6 protons (Z=6).

The element with atomic number 110 is Darmstadtium (Ds).