Silver has only two naturally occurring isotopes: Ag-107 and Ag-109.
Why isn’t the average atomic mass of silver given on the periodic table simply 108?
The correct answer and explanation is :
The average atomic mass of silver is not exactly 108 because the element has two naturally occurring isotopes—Ag-107 and Ag-109—each with a different atomic mass and a different relative abundance. The atomic mass listed on the periodic table is a weighted average of the masses of these isotopes, taking into account both their individual masses and the relative abundance in nature.
Here’s a breakdown of how this works:
- Isotopes of Silver:
- Ag-107 has an atomic mass of approximately 106.905 u and an abundance of about 51.84%.
- Ag-109 has an atomic mass of approximately 108.905 u and an abundance of about 48.16%.
- Weighted Average:
The average atomic mass of silver is calculated by multiplying the mass of each isotope by its respective abundance (expressed as a fraction), and then summing these values: [
\text{Average atomic mass} = ( \text{Mass of Ag-107} \times \text{Abundance of Ag-107} ) + ( \text{Mass of Ag-109} \times \text{Abundance of Ag-109} )
] Substituting the values: [
\text{Average atomic mass} = (106.905 \, \text{u} \times 0.5184) + (108.905 \, \text{u} \times 0.4816)
] This gives an average atomic mass of approximately 107.868 u. - Why Not 108?
If the average atomic mass were simply 108, it would imply that both isotopes have the same mass and abundance, which is not the case. The average atomic mass of 107.868 u reflects the fact that Ag-107 is slightly lighter and more abundant than Ag-109, which means the weighted average is closer to 107 than 109.
Thus, the average atomic mass is not simply 108 because of the difference in isotopic masses and their respective abundances. This nuanced value accurately reflects the natural composition of silver.