On another planet, the isotopes of titanium have the following natural abundances. Isotope 46Ti 48Ti 50Ti Abundance 72% 11% 17% Mass (amu) 45.95263 47.94795 49.94479 What is the average atomic mass of titanium on that planet? mu
The Correct Answer and Explanation is:
To calculate the average atomic mass of titanium on this planet, we need to take the weighted average of the isotopes based on their natural abundances. The formula for the average atomic mass is:Average atomic mass=∑(mass of isotope×fractional abundance)\text{Average atomic mass} = \sum (\text{mass of isotope} \times \text{fractional abundance})Average atomic mass=∑(mass of isotope×fractional abundance)
We are given the following information about the isotopes of titanium:
- Isotope 46Ti: Mass = 45.95263 amu, Abundance = 72% = 0.72
- Isotope 48Ti: Mass = 47.94795 amu, Abundance = 11% = 0.11
- Isotope 50Ti: Mass = 49.94479 amu, Abundance = 17% = 0.17
Now, we apply the formula:Average atomic mass=(45.95263×0.72)+(47.94795×0.11)+(49.94479×0.17)\text{Average atomic mass} = (45.95263 \times 0.72) + (47.94795 \times 0.11) + (49.94479 \times 0.17)Average atomic mass=(45.95263×0.72)+(47.94795×0.11)+(49.94479×0.17)
Calculating each term:
- 45.95263×0.72=33.0668945.95263 \times 0.72 = 33.0668945.95263×0.72=33.06689
- 47.94795×0.11=5.2732947.94795 \times 0.11 = 5.2732947.94795×0.11=5.27329
- 49.94479×0.17=8.4906149.94479 \times 0.17 = 8.4906149.94479×0.17=8.49061
Now, summing these values:33.06689+5.27329+8.49061=46.8307933.06689 + 5.27329 + 8.49061 = 46.8307933.06689+5.27329+8.49061=46.83079
Therefore, the average atomic mass of titanium on this planet is approximately 46.83 amu.
Explanation:
The average atomic mass is the weighted average of the isotopes of an element, based on both their masses and their relative abundances. The more abundant isotopes contribute more to the overall average. In this case, isotope 46Ti contributes the most to the average due to its higher abundance of 72%, while isotope 48Ti and 50Ti contribute less due to their lower abundances. The result of this calculation, 46.83 amu, represents the average atomic mass of titanium on this particular planet.
