To calculate the average atomic mass of titanium based on its isotopes and their abundances, you can use the following formula:
\[ \text{Average Atomic Mass} = \sum (\text{abundance} \times \text{mass of isotope}) \]
Where the abundance is expressed as a fraction (by dividing the percentage by 100).
Given the isotopes of titanium and their corresponding abundances:
- \( ^{46}\text{Ti} \) : 8.0% or 0.080
- \( ^{47}\text{Ti} \) : 73.4% or 0.734
- \( ^{49}\text{Ti} \) : 5.5% or 0.055
- \( ^{50}\text{Ti} \) : 5.3% or 0.053
Next, we can assume the atomic masses of the isotopes to be approximately equal to their mass number:
- Mass of \( ^{46}\text{Ti} \) = 46
- Mass of \( ^{47}\text{Ti} \) = 47
- Mass of \( ^{49}\text{Ti} \) = 49
- Mass of \( ^{50}\text{Ti} \) = 50
Now we can calculate the average atomic mass:
\[ \text{Average Atomic Mass} = (0.080 \times 46) + (0.734 \times 47) + (0.055 \times 49) + (0.053 \times 50) \]
Calculating each term individually:
- \( 0.080 \times 46 = 3.68 \)
- \( 0.734 \times 47 = 34.478 \)
- \( 0.055 \times 49 = 2.695 \)
- \( 0.053 \times 50 = 2.65 \)
Now summing these values:
\[ \text{Average Atomic Mass} = 3.68 + 34.478 + 2.695 + 2.65 = 43.503 \]
The average atomic mass of titanium is approximately \( 43.50 , \text{u} \).
However, it seems there might have been a slight misconception previously: the isotopes mentioned and their percentages do not add up to 100%. For the calculation, we used the provided percentages as they were. If you meant another percentage or scenario, please clarify!
The correct average atomic mass for naturally occurring titanium, considering that the common isotopes (mostly based on standard references) generally results in around \( 47.87 , \text{u} \).
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