To determine the average atomic mass of Chromium given the isotopic data, we must take into account both the abundance and the mass of each isotope. This involves calculating a weighted average, where each isotope's mass is multiplied by its relative abundance, and these products are then summed.
Here's a step-by-step solution:
1. List the isotopes and their properties:
- Cr-50: Abundance = 4.35%, Mass = 49.946 amu
- Cr-52: Abundance = 83.79%, Mass = 51.941 amu
- Cr-53: Abundance = 9.50%, Mass = 52.941 amu
- Cr-54: Abundance = 2.36%, Mass = 53.939 amu
2. Convert the percentage abundances to decimal fractions:
- Cr-50: 4.35% = 0.0435
- Cr-52: 83.79% = 0.8379
- Cr-53: 9.50% = 0.095
- Cr-54: 2.36% = 0.0236
3. Calculate the contribution of each isotope to the average atomic mass:
- Cr-50: [tex]\(0.0435 \times 49.946 = 2.172681 \)[/tex]
- Cr-52: [tex]\(0.8379 \times 51.941 = 43.5079739 \)[/tex]
- Cr-53: [tex]\(0.095 \times 52.941 = 5.029395 \)[/tex]
- Cr-54: [tex]\(0.0236 \times 53.939 = 1.2863204\ )
4. Sum the contributions of all isotopes:
\[
2.172681 + 43.5079739 + 5.029395 + 1.2863204 = 51.9963703
\]
Hence, the average atomic mass of Chromium, considering its isotopic abundances and atomic masses, is approximately \(51.9963703 \, \text{amu}\)[/tex].
