Find the average atomic mass of silver if 51.83% of the silver atoms occurring in nature have mass 106.905 u and 48.17% of the atoms have mass 108.905 น.
The correct answer and explanation is :
To find the average atomic mass of silver ((Ag)), we use the formula for weighted average:
[
\text{Average Atomic Mass} = (\% \text{ abundance}_1 \times \text{mass}_1) + (\% \text{ abundance}_2 \times \text{mass}_2)
]
Given:
- Isotope 1: (106.905 \,u) (abundance = 51.83% or 0.5183)
- Isotope 2: (108.905 \,u) (abundance = 48.17% or 0.4817)
[
\text{Average Atomic Mass} = (0.5183 \times 106.905) + (0.4817 \times 108.905)
]
[
= 55.445 + 52.474
]
[
= 107.87 \,u
]
Explanation:
The atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes. Since silver exists in two stable isotopes, we calculate its atomic mass by multiplying the mass of each isotope by its fractional abundance and summing the values.
- Convert percentages to decimal form by dividing by 100.
- Multiply the decimal abundance by the respective isotope mass.
- Sum the products to obtain the average atomic mass.
The answer, 107.87 u, aligns with the periodic table value, confirming its correctness. This method applies to all elements with multiple isotopes and ensures an accurate representation of the element’s atomic weight in nature.
