Question

The average atomic mass of silver (Ag) is 107.87 u. Which of the following mass spectra could correspond to an average sample of Ag?

a. Ag-105 with 20% abundance, Ag-109 with 80% abundance.

b. Ag-106 with 50% abundance, Ag-108 with 50% abundance.

c. Ag-107 with 40% abundance, Ag-110 with 60% abundance.

d. Ag-104 with 30% abundance, Ag-111 with 70% abundance.

Answer 1

The mass spectrum corresponding to the average atomic mass of silver, 107.87 u, is option (b) with Ag-106 at 50% abundance and Ag-108 at 50% abundance, yielding a calculated average mass of 107 u.

Step-by-step explanation:

To determine which mass spectrum corresponds to the average atomic mass of silver (Ag), we need to calculate the weighted average of the given isotopes and compare that to the provided average atomic mass of 107.87 u.

1. For option (a): Ag-105 with 20% abundance, Ag-109 with 80% abundance.
   
   The weighted average is: (105 × 0.20) + (109 × 0.80) = 21 + 87.2 = 108.2 u.
   
2. For option (b): Ag-106 with 50% abundance, Ag-108 with 50% abundance.
   
   The weighted average is: (106 × 0.50) + (108 × 0.50) = 53 + 54 = 107 u.
   
3. For option (c): Ag-107 with 40% abundance, Ag-110 with 60% abundance.
   
   The weighted average is: (107 × 0.40) + (110 × 0.60) = 42.8 + 66 = 108.8 u.
   
4. For option (d): Ag-104 with 30% abundance, Ag-111 with 70% abundance.
   
   The weighted average is: (104 × 0.30) + (111 × 0.70) = 31.2 + 77.7 = 108.9 u.
   

Comparing the calculated weighted averages with the known average atomic mass of silver (107.87 u), option (b) is the closest and, hence, the most likely corresponding mass spectrum for a sample of silver.