Question

Silicon has three naturally occurring isotopes (Si-28, Si-29, and Si-30). The mass and natural abundance of Si-28 are 27.9769 amu and 92.2%, respectively. The mass and natural abundance of Si-29 are 28.9765 amu and 4.67%, respectively. Find the mass and natural abundance of Si-30 .

Answer 1

To find Si-30's natural abundance, subtract the abundances of Si-28 and Si-29 from 100%, yielding 3.13%. Then, use the average atomic mass of silicon (28.09 amu) and solve for Si-30's mass, which is approximately 29.9737 amu.

Step-by-step explanation:

The student's question is about calculating the mass and natural abundance of Si-30, the third isotope of silicon when the other two isotopes' masses and abundances are known. We know that the sum of the natural abundances of all isotopes must equal 100%. So, we can calculate the abundance of Si-30 by subtracting the known abundances of Si-28 and Si-29 from 100%. Using the masses and abundances for Si-28 and Si-29 provided:

• Si-28: Mass = 27.9769 amu, Abundance = 92.2%
• Si-29: Mass = 28.9765 amu, Abundance = 4.67%

The abundance of Si-30 is:

100% - 92.2% - 4.67% = 3.13%

To find the mass of Si-30, we use the average atomic mass of silicon, which is 28.09 amu, and the equation for average atomic mass:

28.09 amu = (0.922 × 27.9769 amu) + (0.0467 × 28.9765 amu) + (0.0313 × Mass of Si-30)

By solving the equation for Mass of Si-30, the mass is found to be approximately 29.9737 amu.