Silicon has three naturally occurring isotopes: Si-28 with mass 27.9769 amu and a natural abundance of 92.21%, Si-29 with mass 28.9765 amu and a natural abundance of 4.69%, and Si-30 with mass 29.9737 amu and a natural abundance of 3.10%. Calculate the atomic mass of silicon.

Solution 102P

Here, we are going to calculate the atomic mass of silicon.

Step 1:

Atomic mass can be defined as the average mass of the isotopes of that element. If an element has no isotopes, then the mass of its atom would be the same as the sum of protons and neutrons in it. But if an element occurs in isotopic forms, then we have to know the percentage of each isotopic form and then the average mass is calculated.

The general formula for calculating the atomic mass of an element having n number of isotopes is given below:

Atomic mass = (fraction of isotope n) x (mass of isotope n) ----(1)

Step 2:

Given, percentage abundance of Si-28 isotope = 92.21 %

Therefore, fraction of Si-28 isotope = 92.21 / 100 = 0.9221

Mass of Si-28 isotope = 27.9769 amu

Percentage abundance of Si-29 isotope = 4.69 %

Therefore, fraction of Si-29 isotope = 4.69 / 100 = 0.0469

Mass of Si-29 isotope = 28.9765 amu

Percentage abundance of Si-30 isotope = 3.10 %

Therefore, fraction of Si-30 isotope = 3.10 / 100 = 0.0310

Mass of Si-30 isotope = 29.9737 amu