To determine the average relative atomic mass of titanium, given its three naturally occurring isotopes and their respective abundances, follow these steps:
1. Identify the mass and abundance of each isotope:
- Titanium-47 has a mass of 47 and an abundance of 43.5%.
- Titanium-48 has a mass of 48 and an abundance of 44.1%.
- Titanium-50 has a mass of 50 and an abundance of 12.4%.
2. Convert the percentages into decimal form:
- Titanium-47: 43.5% becomes 0.435.
- Titanium-48: 44.1% becomes 0.441.
- Titanium-50: 12.4% becomes 0.124.
3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of Titanium-47: [tex]\( 47 \times 0.435 \)[/tex].
- Contribution of Titanium-48: [tex]\( 48 \times 0.441 \)[/tex].
- Contribution of Titanium-50: [tex]\( 50 \times 0.124 \)[/tex].
4. Sum the contributions to find the average atomic mass:
[tex]\[
\text{Average atomic mass} = (47 \times 0.435) + (48 \times 0.441) + (50 \times 0.124)
\][/tex]
This simplifies to:
[tex]\[
\text{Average atomic mass} = 20.445 + 21.168 + 6.2
\][/tex]
5. Add the results:
[tex]\[
\text{Average atomic mass} = 47.813
\][/tex]
Therefore, the average relative atomic mass of titanium is approximately 47.813.
Given the answer choices:
A. 21.168
B. 47.8
C. 2.23
D. 20.445
The closest answer to our calculated value is:
B. 47.8.
