Question

calculate based on the relative abundance of the three main isotopes of silicon the average tomic mass of Si and compare your results with the value in your table of elements ^28 Si (92.2%) , ^29 Si (4.7%), ^30 Si (3.1%)

Answer 1

Silicon-28 Isotope Mass= 27.98
Silicon-29 Isotope Mass=28.98
Silicon-30 Isotope Mass=29.97

Atomic Mass of silicon is 28.0855

Since the Average atomic mass of Si is 28.0855, you have a pretty good idea that most of the Silicon has to be the Si-28 isotope, which is close to the 28.0855 average mass.

In fact the percentages of Si-28 is 92.2%, while Si-29 is 4.67% and Si-30 is 3.10%.

Please be aware that these are ratios of Si found on earth. Studies of meteorites indicate that there is can be larger percentages of the two heavier isotopes from other sources.

Determining the three percentages from the information you provided is not possible. You need to know the percentages of two of the isotopes to derive the percentage of the third.

The way to calculate the average atomic mass would be to use the formula:

27.98x + 28.98y + 29.97z = 28.0855
where x, y, and z are the decimal values of the percentages of the three isotopes respectively (divide the % by 100).

Of course if you know x and y, all you need to do is add them together and subtract their sum from 100 to get the percentage of z. So you also know that x + y + z = 1.

All you need is one more formula with one or more variables in it to derive the values. For example if you know that Si-28 is 92.2% then you have the equation 0y +0z + x = 0.922.

With three equations now, you can derive the other two percentages using linear algebra
y = 0.0467

z = 0.031

percentages of Si-28 is 92.2%, while Si-29 is 4.67% and Si-30 is 3.10%.