Respuesta :
Answer: One isotope has a percentage abundance of 75.75 % and the percentage abundance of another isotope is 24.24%.
Explanation:
We are given the two stable isotopes of chlorine with their respective masses. The average atomic mass of chlorine is also given.
Average atomic mass of chlorine = 35.45 amu.
Let us assume the fractional abundance of one isotope be 'x' and the fractional abundance for another isotope will be (1 - x) because the total fractional abundance is always equal to 1.
- For Chlorine-35 isotope:
Fractional abundance = x
Mass = 34.97 amu
- For Chlorine-37 isotope:
Fractional abundance = 1 - x
Mass = 36.95 amu
The formula for the calculation of average atomic mass is given by:
[tex]\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i[/tex]
Putting values in above equation, we get:
[tex]35.45=34.97(x)+36.95(1-x)\\\\35.45=34.97x+36.95-36.95\\\\-1.5=-1.98x\\\\x=\frac{-1.5}{-1.98}=0.7575[/tex]
[tex]1-x=1-0.7575=0.2424[/tex]
Converting these two fractional abundances into percentage abundances by multiplying it with 100.
[tex]x=0.7575\times 100=75.75\%\\\\1-x=0.2424\times 100=24.24\%[/tex]
Hence, one isotope has a percentage abundance of 75.75 % and the percentage abundance of another isotope is 24.24%.
