Answer:
The estimated atomic of silicon is 28.082 a.m.u.
Explanation:
The estimated atomic mass of silicon ([tex]M_{Si, est}[/tex]), in a.m.u., is equal to the weighted average of atomic masses of silicon available in nature and in terms of their abundances:
[tex]M_{Si, est} = r_{1}\cdot M_{Si-28} + r_{2} \cdot M_{Si-29} + r_{3}\cdot M_{Si-30}[/tex] (1)
Where:
[tex]r_{1}[/tex], [tex]r_{2}[/tex], [tex]r_{3}[/tex] - Relative abundance of each isotope, no unit.
[tex]M_{Si-28}[/tex], [tex]M_{Si-29}[/tex], [tex]M_{Si-30}[/tex] - Atomic mass of each isotope, in a.m.u.
If we know that [tex]M_{Si-28} = 27.976\,a.m.u.[/tex], [tex]M_{Si-29} = 28.976\,a.m.u.[/tex], [tex]M_{Si-30} = 29.974\,a.m.u.[/tex], [tex]r_{1} = \frac{92.22}{100}[/tex], [tex]r_{2} = \frac{4.68}{100}[/tex] and [tex]r_{3} = \frac{3.09}{100}[/tex], then the estimated atomic mass of silicon is:
[tex]M_{Si, est} = r_{1}\cdot M_{Si-28} + r_{2} \cdot M_{Si-29} + r_{3}\cdot M_{Si-30}[/tex]
[tex]M_{Si,est} = \left(\frac{92.22}{100} \right)\cdot (27.976\,a.m.u.) + \left(\frac{4.68}{100} \right)\cdot (28.976\,a.m.u.) + \left(\frac{3.09}{100} \right)\cdot (29.974\,a.m.u.)[/tex]
[tex]M_{Si, est} = 28.082\,a.m.u.[/tex]
The estimated atomic of silicon is 28.082 a.m.u.
