Final answer:
The average atomic mass of silver is calculated by using the relative abundances and masses of its isotopes. After converting the abundances to decimal form and multiplying by the respective isotope mass, the result is approximately 107.86 amu.
Step-by-step explanation:
To calculate the average atomic mass of silver, we take into account the different mass numbers of its naturally occurring isotopes and their relative abundances. We use the following formula to calculate the average atomic mass:
Average atomic mass = (Fraction of isotope 1 × Mass of isotope 1) + (Fraction of isotope 2 × Mass of isotope 2)
For silver:
- Isotope Ag-107 has a relative abundance of 51.35% and a mass of 106.905092 amu.
- Isotope Ag-109 has a relative abundance of 48.65% (100% - 51.35%) and a mass of 108.9044757 amu.
First, let's convert the percentages to fractions:
- 51.35% = 0.5135
- 48.65% = 0.4865
Now, we can calculate the average atomic mass:
Average atomic mass of Ag = (0.5135 × 106.905092 amu) + (0.4865 × 108.9044757 amu)
We perform the multiplication:
- (0.5135 × 106.905092 amu) = 54.86869102 amu
- (0.4865 × 108.9044757 amu) = 52.995235305 amu
Then we add the two products together:
Average atomic mass of Ag = 54.86869102 amu + 52.995235305 amu = 107.863926325 amu
The average atomic mass of naturally occurring silver is therefore approximately 107.86 amu.