The atomic mass of silver is 107.87. Silver has two very abundant isotopes occurring in almost equal proportions, along with a number of very rare isotopes. Which are most likely to be the atomic masses of the two most abundant isotopes of silver?
The Correct Answer and Explanation is:
To determine the most likely atomic masses of the two most abundant isotopes of silver (Ag), we first note that the atomic mass of silver is given as 107.87 amu (atomic mass units). The two most abundant isotopes of silver are typically silver-107 (Ag-107) and silver-109 (Ag-109), which are found in almost equal proportions.
Given the atomic mass of silver, the masses of these isotopes can be inferred as follows:
- Ag-107: The mass of this isotope is approximately 106.905 amu.
- Ag-109: The mass of this isotope is about 108.904 amu.
To verify these numbers, we can use the concept of weighted averages to see how they contribute to the atomic mass. The average atomic mass (107.87 amu) can be calculated based on the relative abundances of these isotopes:
[
\text{Average Atomic Mass} = (f_{107} \times m_{107}) + (f_{109} \times m_{109})
]
Assuming ( f_{107} ) and ( f_{109} ) are the fractions of each isotope and considering they are nearly equal in abundance, we can assign:
- ( f_{107} \approx 0.5 )
- ( f_{109} \approx 0.5 )
Substituting the approximate masses into the equation gives:
[
\text{Average Atomic Mass} \approx (0.5 \times 106.905) + (0.5 \times 108.904)
]
Calculating this yields:
[
\text{Average Atomic Mass} \approx 53.4525 + 54.452 = 107.9045 \text{ amu}
]
This average is consistent with the atomic mass of silver, 107.87 amu, when accounting for rounding and the presence of very rare isotopes that have minimal effect on the overall atomic mass.
Thus, the most likely atomic masses of the two most abundant isotopes of silver are approximately 106.905 amu for Ag-107 and 108.904 amu for Ag-109.