Silver occurs as two isotopes with atomic masses 106.9041 and 108.9047 amu: The first isotope represents 51.82% and the second 48.18%. Determine the average atomic mass of silver: Instructions: The number of significant figures is set to average atomic mass amu
The Correct Answer and Explanation is:
To calculate the average atomic mass of silver, we can use the weighted average formula for isotopes. The formula is:Average Atomic Mass=(m1×f1)+(m2×f2)\text{Average Atomic Mass} = (m_1 \times f_1) + (m_2 \times f_2)Average Atomic Mass=(m1×f1)+(m2×f2)
Where:
- m1m_1m1 and m2m_2m2 are the atomic masses of the two isotopes (106.9041 amu and 108.9047 amu),
- f1f_1f1 and f2f_2f2 are the fractional abundances of each isotope (51.82% or 0.5182 for the first, and 48.18% or 0.4818 for the second).
Now, let’s apply the values:Average Atomic Mass=(106.9041 amu×0.5182)+(108.9047 amu×0.4818)\text{Average Atomic Mass} = (106.9041 \, \text{amu} \times 0.5182) + (108.9047 \, \text{amu} \times 0.4818)Average Atomic Mass=(106.9041amu×0.5182)+(108.9047amu×0.4818)Average Atomic Mass=(55.4544 amu)+(52.4765 amu)\text{Average Atomic Mass} = (55.4544 \, \text{amu}) + (52.4765 \, \text{amu})Average Atomic Mass=(55.4544amu)+(52.4765amu)Average Atomic Mass=107.9309 amu\text{Average Atomic Mass} = 107.9309 \, \text{amu}Average Atomic Mass=107.9309amu
Since the given data has four significant figures, the result should be rounded to four significant figures:Average Atomic Mass=107.931 amu\text{Average Atomic Mass} = 107.931 \, \text{amu}Average Atomic Mass=107.931amu
Explanation:
In this calculation, the average atomic mass of silver is found by multiplying the atomic mass of each isotope by its relative abundance (in decimal form), and then summing the results. The result, 107.9309 amu, is rounded to 107.931 amu to match the precision of the given values.
This weighted average takes into account the contribution of each isotope to the overall atomic mass, reflecting the fact that silver naturally consists of a mixture of these two isotopes.
