Answer: The percentage abundance for
isotope is 3.09 %.
Explanation:
The average atomic mass of an element is calculated by taking the sum of the masses of all isotopes weighted by their respective natural fractional abundances.
To compute average atomic mass, the following formula is applied:
.....(1)
From the information provided:
Let the fractional abundance for
isotope be 'x'
- For
isotope:
Mass of
isotope = 27.9769 amu
Percentage abundance of
isotope = 92.22 %
Fractional abundance for
isotope = 0.9222
- For
isotope:
Mass of
isotope = 28.9764 amu
Percentage abundance for
isotope = 4.68%
Fractional abundance of
isotope = 0.0468
- For
isotope:
Mass of
isotope = 29.9737 amu
Fractional abundance for
isotope = x
- The average atomic mass of silicon is 28.084 amu
By inserting these values into equation 1, we derive:
![28.084=[(27.9769\times 0.9222)+(28.9764\times 0.0468)+(29.9737\times x)]\\\\x=0.0309](https://tex.z-dn.net/?f=28.084%3D%5B%2827.9769%5Ctimes%200.9222%29%2B%2828.9764%5Ctimes%200.0468%29%2B%2829.9737%5Ctimes%20x%29%5D%5C%5C%5C%5Cx%3D0.0309)
To convert this fractional abundance into a percentage, multiply by 100:

This shows that the percentage abundance for
isotope is 3.09 %.