Chromium has four isotopes. Chromium-50 (mass of 49.946 amu and 4.35% abundance), chromium-52 (mass of 51.941 amu and 83.79% abundance), chromium-53 (mass of 52.941 amu and 9.50% abundance), and chromium-54 (mass of 53.939 amu and 2.36% abundance). Calculate the average atomic mass of chromium
The correct answer and explanation is :
To calculate the average atomic mass of chromium, we use the concept of a weighted average based on the masses and abundances of the different isotopes. Each isotope contributes to the overall atomic mass according to its relative abundance. The formula for the average atomic mass is:
[
\text{Average atomic mass} = \sum \left( \text{isotope mass} \times \text{abundance} \right)
]
Here, the abundance is given as a percentage, so we must first convert it to a decimal by dividing by 100.
Step 1: Convert abundances to decimals
- Chromium-50: 4.35% → 0.0435
- Chromium-52: 83.79% → 0.8379
- Chromium-53: 9.50% → 0.0950
- Chromium-54: 2.36% → 0.0236
Step 2: Multiply isotope mass by its corresponding abundance
- Chromium-50: ( 49.946 \, \text{amu} \times 0.0435 = 2.173 \, \text{amu} )
- Chromium-52: ( 51.941 \, \text{amu} \times 0.8379 = 43.523 \, \text{amu} )
- Chromium-53: ( 52.941 \, \text{amu} \times 0.0950 = 5.034 \, \text{amu} )
- Chromium-54: ( 53.939 \, \text{amu} \times 0.0236 = 1.272 \, \text{amu} )
Step 3: Sum the contributions from each isotope
Now, we add the contributions from all isotopes to get the average atomic mass:
[
\text{Average atomic mass} = 2.173 \, \text{amu} + 43.523 \, \text{amu} + 5.034 \, \text{amu} + 1.272 \, \text{amu} = 51.002 \, \text{amu}
]
Final Answer:
The average atomic mass of chromium is approximately 51.002 amu.
Explanation:
The concept behind calculating the average atomic mass is based on the isotopic distribution of elements in nature. Each isotope of an element has a specific mass and a relative abundance. The relative abundance tells us how common or rare each isotope is, and the mass of each isotope represents its contribution to the element’s total mass. By multiplying each isotope’s mass by its relative abundance and summing the results, we get a weighted average that accurately represents the average atomic mass of the element. This is why the average atomic mass of chromium is slightly different from any individual isotope mass, reflecting the mixture of isotopes found in nature.