Final answer:
To find the isotopic mass of the least abundant isotope, one can use the weighted average formula, plugging in the given masses and abundances. After converting the relative abundance of the least abundant isotope to a decimal and performing calculations, the isotopic mass is found to be approximately 123.5 u.
Step-by-step explanation:
The student is asking how to calculate the isotopic mass of the least abundant isotope of a fictitious element X, given the average atomic mass of the element, the mass of the most abundant isotope, and its relative abundance. To solve this, we use the concept that the average atomic mass is the weighted average of the masses of its isotopes. The mass of the least abundant isotope can be calculated with the formula:
Average atomic mass = (abundance of isotope 1 × mass of isotope 1) + (abundance of isotope 2 × mass of isotope 2)
By converting the percentage of abundance to a decimal (by dividing by 100) and rearranging the formula, you can solve for the unknown mass:
Mass of isotope 2 = (Average atomic mass - (abundance of isotope 1 × mass of isotope 1)) / (1 - abundance of isotope 1)
Given:
- Average atomic mass = 122.118 u
- Mass of most abundant isotope (isotope 1) = 121.624 u
- Relative abundance of isotope 1 = 66.16%
We calculate the relative abundance of isotope 2 to be 100% - 66.16% = 33.84%, or 0.3384 in decimal form. Substituting these into the formula gives us:
Mass of isotope 2 = (122.118 u - (0.6616 × 121.624 u)) / (1 - 0.6616)
This calculation yields the mass of the least abundant isotope, which would be approximately 123.5 u, thus option B is correct.