Final answer:
The isotopic mass of the second isotope 13M is calculated using the given natural abundances and isotopic mass of the first isotope 11M with the average atomic mass of the element. After solving the equation, the isotopic mass of 13M is found to be 12.87 amu, which is option (b).
Step-by-step explanation:
To find the isotopic mass of the second isotope 13M, we use the information provided about the natural abundances and isotopic masses of the two isotopes of element M. We know that:
- 11M has an isotopic mass of 11.01 amu and a natural abundance of 65%.
- The average atomic mass of element M is 11.66 amu.
- The natural abundance of 13M is 35% (since the sum of percentages of isotopic abundances must be 100%).
We can use the average atomic mass formula, which states that the average atomic mass of an element is the sum of the products of the isotopic masses and their respective natural abundances:
Average atomic mass = (isotopic mass of isotope 1 × its abundance) + (isotopic mass of isotope 2 × its abundance)
Substituting the known values:
11.66 amu = (11.01 amu × 0.65) + (isotopic mass of 13M × 0.35)
Solve for the isotopic mass of 13M:
11.66 amu = 7.1565 amu + (isotopic mass of 13M × 0.35)
4.5035 amu = (isotopic mass of 13M × 0.35)
Isotopic mass of 13M = 4.5035 amu ÷ 0.35
Isotopic mass of 13M = 12.87 amu
Therefore, the second isotope 13M has an isotopic mass of 12.87 amu, which corresponds to option (b).