<u>Answer:</u> The percentage abundance for
isotope is 3.09 %.
<u>Explanation:</u>
Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.
Formula used to calculate average atomic mass follows:
.....(1)
We are given:
Let the fractional abundance for
isotope be 'x'
- <u>For
isotope:</u>
Mass of
isotope = 27.9769 amu
Percentage abundance of
isotope = 92.22 %
Fractional abundance of
isotope = 0.9222
- <u>For
isotope:</u>
Mass of
isotope = 28.9764 amu
Percentage abundance of
isotope = 4.68%
Fractional abundance of
isotope = 0.0468
- <u>For
isotope:</u>
Mass of
isotope = 29.9737 amu
Fractional abundance of
isotope = x
- Average atomic mass of silicon = 28.084 amu
Putting values in equation 1, we get:
![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)
Converting this fractional abundance into percentage abundance by multiplying it by 100, we get:

Hence, the percentage abundance for
isotope is 3.09 %.