Final answer:
The atomic weight is the weighted average mass of all isotopes of an element, whereas the mass number is the sum of protons and neutrons in the nucleus for each isotope. Therefore, option b is correct.
Step-by-step explanation:
The relationship between atomic weight and mass number is often misunderstood. The correct statement that describes their relationship is: 'b) Atomic weight is the weighted average mass of all isotopes of an element.'
Mass number is the sum of the number of protons and neutrons in the nucleus of an atom, which is always a whole number for any given isotope. On the other hand, the atomic weight of an element is a weighted average that takes into account the variation in mass and relative abundance of each naturally occurring isotope.
For instance, the atomic weight of carbon is calculated from the isotopes 12C and 13C. Although the mass number of 12C is 12, the atomic mass of carbon is approximately 12.011 because it includes the minor contribution of the heavier isotope 13C, which has a slightly higher atomic mass than its mass number due to the presence of extra neutrons.
In summary, option b is the correct choice because the atomic weight reflects the average mass of all isotopes, while the mass number is specific to each isotope and does not represent an average.