Question

What is the average atomic mass of silicon?

Answer 1

Hint :We know that to find the solution of the first question, as the required data is already given, you need to only apply the direct formula for the average or relative atomic mass and for the second question, remember mass of one-gram atom is equal to the mass of one mole of atoms of an element.

Complete Step By Step Answer:
We know that the relative abundance of silicon with atomic number $ 28 $ is $ 98.25. $ The relative abundance of silicon with atomic number $ 29 $ is $ 4.65. $ The relative abundance of silicon with atomic number $ 30 $ is $ 3.10. $
We should know that, while doing any average mass calculations for an element, it should be equal to the sum of the masses of each isotope and each multiplied by its natural relative abundances. So, here the atomic number of each isotope of silicon will be equal to its atomic mass. Thus, the average atomic mass of an element having isotope equals the sum of mass of each isotope multiplied with abundance. So, the formula will be like,
We take the amu of each isotope, multiply it by the percentage of occurrence, and end up with a weighted average: $ \left( 27.9769\times .9218 \right)+\left( 28.9765\times .047 \right)+\left( 29.9738\times .0312 \right)~ $ (quick note - there is a bit of rounding in here - the abundance percentages add up to 1.01, so the number we calculate is going to be slightly off).
 $ Average\text{ }atomic\text{ }mass=\dfrac{\left( abundance\text{ }\times \text{ }atomic\text{ }mass \right)\text{ }of\text{ }{{1}^{st}}isotope\text{ }+\ldots }{100} $
Substituting the values;
 $ \Rightarrow \dfrac{\left( 28\times 92.25 \right)+\left( 29\times 4.65 \right)+\left( 30\times 3.1 \right)}{100}=\dfrac{2810.85}{100}=28.1 $ .

Note :
Remember that the average atomic mass for an element is calculated by summing the masses of the element’s isotopes, each multiplied by its natural abundance on earth. The mass of a one-gram atom equals the mass of one mole of elements in grams, which is its molar mass.