On another planet, the isotopes of titanium have the given natural abundances. Isotope 46TI Abundance Mass (u) 77.400% 45.95263 48TI 16.100% 47.94795 50TI 6.500% 49.94479 What is the average atomic mass of titanium on that planet? average atomic mass =
On another planet, the isotopes of titanium have the given natural abundances. Isotope 46TI Abundance Mass (u) 77.400% 45.95263 48TI 16.100% 47.94795 50TI 6.500% 49.94479 What is the average atomic mass of titanium on that planet? average atomic mass =
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![**Isotopes and Atomic Mass of Titanium on Another Planet**
On another planet, the isotopes of titanium have the following natural abundances:
| **Isotope** | **Abundance** | **Mass (u)** |
|-------------|---------------|----------------|
| ^46Ti | 77.400% | 45.95263 u |
| ^48Ti | 16.100% | 47.94795 u |
| ^50Ti | 6.500% | 49.94479 u |
**Problem Statement:**
What is the average atomic mass of titanium on that planet?
**Calculation:**
To calculate the average atomic mass of titanium, we use the formula for the weighted average:
\[ \text{average atomic mass} = (f_1 \times m_1) + (f_2 \times m_2) + (f_3 \times m_3) \]
where:
- \( f \) is the fractional abundance of each isotope.
- \( m \) is the mass of each isotope.
For the above isotopes, the calculation steps are:
1. Convert the abundance percentages to fractions:
- For ^46Ti: 77.400% = 0.77400
- For ^48Ti: 16.100% = 0.16100
- For ^50Ti: 6.500% = 0.06500
2. Multiply each fraction by the corresponding isotope mass:
- \( 0.77400 \times 45.95263 \)
- \( 0.16100 \times 47.94795 \)
- \( 0.06500 \times 49.94479 \)
3. Sum the results of these multiplications to find the average atomic mass.
**Fill in the calculations to complete the answer:**
\[ \text{average atomic mass} = \boxed{\phantom{XXX}} \ u \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcedd0880-65ed-4b01-a33f-975175ec858a%2F662513e3-cdab-4a53-b956-76d8aae6af60%2Fnrk6g49_processed.png&w=3840&q=75)
Transcribed Image Text:**Isotopes and Atomic Mass of Titanium on Another Planet**
On another planet, the isotopes of titanium have the following natural abundances:
| **Isotope** | **Abundance** | **Mass (u)** |
|-------------|---------------|----------------|
| ^46Ti | 77.400% | 45.95263 u |
| ^48Ti | 16.100% | 47.94795 u |
| ^50Ti | 6.500% | 49.94479 u |
**Problem Statement:**
What is the average atomic mass of titanium on that planet?
**Calculation:**
To calculate the average atomic mass of titanium, we use the formula for the weighted average:
\[ \text{average atomic mass} = (f_1 \times m_1) + (f_2 \times m_2) + (f_3 \times m_3) \]
where:
- \( f \) is the fractional abundance of each isotope.
- \( m \) is the mass of each isotope.
For the above isotopes, the calculation steps are:
1. Convert the abundance percentages to fractions:
- For ^46Ti: 77.400% = 0.77400
- For ^48Ti: 16.100% = 0.16100
- For ^50Ti: 6.500% = 0.06500
2. Multiply each fraction by the corresponding isotope mass:
- \( 0.77400 \times 45.95263 \)
- \( 0.16100 \times 47.94795 \)
- \( 0.06500 \times 49.94479 \)
3. Sum the results of these multiplications to find the average atomic mass.
**Fill in the calculations to complete the answer:**
\[ \text{average atomic mass} = \boxed{\phantom{XXX}} \ u \]
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