Bromine has two naturally occurring isotopes. Bromine-79 has a mass of 78.9183 amu and an abundance of 50.69%, and bromine-81 has a mass of 80.92 amu and an abundance of 49.31%. What is the average atomic mass of Bromine? Select one: a. 99.91 amu b. 79.91 amu c. 112.00 amu d. 79.00 amu
The Correct Answer and Explanation is:
The correct answer is b. 79.91 amu.
Here is the explanation for how to arrive at this answer:
The average atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes. This means that the mass of each isotope is multiplied by its relative abundance, and the results are then added together. The calculation is not a simple average; it must account for how common each isotope is.
The formula for calculating the average atomic mass is:
Average Atomic Mass = (Mass of Isotope 1 × Fractional Abundance of Isotope 1) + (Mass of Isotope 2 × Fractional Abundance of Isotope 2) + …
Step 1: Convert percentage abundances to fractional abundances.
To use the abundances in the formula, you must first convert them from percentages to decimal form by dividing by 100.
- Fractional abundance of Bromine-79 = 50.69% / 100 = 0.5069
- Fractional abundance of Bromine-81 = 49.31% / 100 = 0.4931
Step 2: Multiply each isotope’s mass by its fractional abundance.
This step calculates the contribution of each isotope to the overall average atomic mass.
- Contribution from Bromine-79 = 78.9183 amu × 0.5069 = 40.0025 amu
- Contribution from Bromine-81 = 80.92 amu × 0.4931 = 39.8997 amu
Step 3: Add the contributions together.
The sum of the contributions from all isotopes gives the average atomic mass of the element.
- Average Atomic Mass of Bromine = 40.0025 amu + 39.8997 amu = 79.9022 amu
Step 4: Compare the result to the given options.
The calculated average atomic mass is 79.9022 amu. Looking at the choices:
a. 99.91 amu
b. 79.91 amu
c. 112.00 amu
d. 79.00 amu
The value 79.9022 amu is closest to 79.91 amu. The slight difference is likely due to rounding in the values provided in the question or the answer options. The result is logical because the two isotopes are present in almost equal amounts, so the average mass should fall almost exactly between their individual masses (78.9183 and 80.92)
