Silicon has 3 isotopes - Si-28, Si-29, Si-30. If 92.23% is Si-28, 4.67% is Si-29, and 3.10% is Si-30, calculate the average atomic mass of silicon. Show your work.

Steps to Solve

1. Identify the Isotopes and Their Abundances
   List the isotopes of silicon and their respective atomic masses and abundances. For example:

   • $^{28}\text{Si}$: atomic mass = $27.97693 , \text{u}$, abundance = $98.89% = 0.9889$
   • $^{29}\text{Si}$: atomic mass = $28.97649 , \text{u}$, abundance = $1.11% = 0.0111$
   • $^{30}\text{Si}$: atomic mass = $29.97377 , \text{u}$, abundance = $0.00% = 0.0000$

2. Calculate Each Isotope's Contribution
   Multiply the atomic mass of each isotope by its corresponding abundance:

   • For $^{28}\text{Si}$:
     Contribution = $27.97693 , \text{u} \times 0.9889$
   • For $^{29}\text{Si}$:
     Contribution = $28.97649 , \text{u} \times 0.0111$
   • For $^{30}\text{Si}$:
     Contribution = $29.97377 , \text{u} \times 0.0000$

3. Sum the Contributions
   Add all the contributions calculated in the previous step to find the average atomic mass of silicon: $$ \text{Average Atomic Mass} = \text{Contribution of } ^{28}\text{Si} + \text{Contribution of } ^{29}\text{Si} + \text{Contribution of } ^{30}\text{Si} $$

4. Compute the Final Average
   Carry out the arithmetic calculations and sum them up. The final average atomic mass will be approximately.