To find the average atomic mass of an element with multiple isotopes, you can use the formula for weighted averages. The formula involves multiplying the atomic mass of each isotope by its relative abundance (as a decimal), then summing these values. Let's solve it step-by-step.
1. Convert the percentage abundances into decimal form:
- For X-63: [tex]\( 69.15\% = \frac{69.15}{100} = 0.6915 \)[/tex]
- For X-65: [tex]\( 30.85\% = \frac{30.85}{100} = 0.3085 \)[/tex]
2. Multiply the atomic mass of each isotope by its relative abundance:
- For X-63: [tex]\( 62.9296 \, \text{amu} \times 0.6915 \)[/tex]
- For X-65: [tex]\( 64.9278 \, \text{amu} \times 0.3085 \)[/tex]
3. Perform the multiplications:
- [tex]\( 62.9296 \times 0.6915 = 43.5112732 \)[/tex]
- [tex]\( 64.9278 \times 0.3085 = 20.0347715 \)[/tex]
4. Add the results together to find the average atomic mass:
- [tex]\( 43.5112732 + 20.0347715 = 63.5460447 \, \text{amu} \)[/tex]
5. Round the result to the nearest hundredth:
- [tex]\( 63.5460447 \rightarrow 63.55 \, \text{amu} \)[/tex]
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \, \text{amu} \)[/tex].
