Silicon is widely used in the semi-conductor industry. Its isotopes and their atomic masses are: Si-28 ( \(27.9769 \mathrm{amu}\) ), Si-29 ( \(28.9765 \mathrm{amu}\) ), and Si-30 ( \(29.9794\) amu). Which is the most abundant?

We will first find the atomic mass of Silicon. According to periodic table, the atomic mass of Silicon is approximately \(28.0855\) amu. This value is a weighted average of the masses of its isotopes.

To represent the weighted average, let the fraction of each isotope (Si-28, Si-29 and Si-30) be represented by x, y, and z, respectively. We can set up the equation: $$28.0855 = 27.9769x + 28.9765y + 29.9794z$$ Since x, y, and z are fractions of the isotopes, their sum will be equal to 1: $$x+y+z=1$$

We will solve for one of the variables in terms of the others. Let's solve for z: $$z = 1-x-y$$ Now, substitute z into the weighted average equation: $$28.0855 = 27.9769x + 28.9765y + 29.9794(1-x-y)$$

Rearrange the equation in order to group terms with x and y: $$1.0026x - 0.9779y = 0.1061$$

From the rearranged equation, we can see that if the value of x (Si-28 fraction) is more significant than the value of y (Si-29 fraction), then the value of 1.0026x would be greater than 0.9779y. Similarly, if y is more significant than x, then 0.9779y would be greater than 1.0026x. Now, if Si-30 was the most abundant, increasing its fraction (increasing z) value would decrease both x and y. However, this would decrease the right side of the equation, which is a fixed value (0.1061). This means that an increased fraction of Si-30 would not conform to the equation. Hence, Si-30 cannot be the most abundant isotope. Now, let's compare Si-28 and Si-29. To satisfy the equation, increasing x (increasing Si-28 fraction) and decreasing y (decreasing Si-29 fraction) would make the left side of the equation greater, while increasing y (increasing Si-29 fraction) and decreasing x (decreasing Si-28 fraction) would make the left side of the equation smaller. Therefore, Si-28 (having a higher fraction) would have a higher contribution to the atomic mass and thus be the most abundant isotope. #Conclusion# The most abundant isotope of Silicon is Si-28.