To calculate the average atomic mass of the element with isotopes [tex]$X-24$[/tex], [tex]$X-25$[/tex], and [tex]$X-26$[/tex], we'll follow these steps:
1. Identify the mass and abundance of each isotope:
- Mass of [tex]$X-24$[/tex]: 24 atomic mass units (amu)
- Abundance of [tex]$X-24$[/tex]: 0.7870
- Mass of [tex]$X-25$[/tex]: 25 atomic mass units (amu)
- Abundance of [tex]$X-25$[/tex]: 0.1013
- Mass of [tex]$X-26$[/tex]: 26 atomic mass units (amu)
- Abundance of [tex]$X-26$[/tex]: 0.1117
2. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of [tex]$X-24$[/tex]: [tex]\( \text{Mass of } X-24 \times \text{Abundance of } X-24 \)[/tex]
- Contribution of [tex]$X-25$[/tex]: [tex]\( \text{Mass of } X-25 \times \text{Abundance of } X-25 \)[/tex]
- Contribution of [tex]$X-26$[/tex]: [tex]\( \text{Mass of } X-26 \times \text{Abundance of } X-26 \)[/tex]
3. Perform the calculations:
- Contribution of [tex]$X-24$[/tex]: [tex]\( 24 \times 0.7870 = 18.888 \)[/tex]
- Contribution of [tex]$X-25$[/tex]: [tex]\( 25 \times 0.1013 = 2.5325 \)[/tex]
- Contribution of [tex]$X-26$[/tex]: [tex]\( 26 \times 0.1117 = 2.9042 \)[/tex]
4. Sum the contributions to find the average atomic mass:
- Average atomic mass [tex]\( = 18.888 + 2.5325 + 2.9042 \)[/tex]
5. Calculate the final result:
- Average atomic mass [tex]\( = 24.3247 \, \text{amu} \)[/tex]
So, the average atomic mass of the element is 24.3247 atomic mass units (amu).
