Question

Silicon has three naturally occurring isotopes: Si-28 (27.977 amu) with an abundance of \(92.23 \%\), Si-29 (28.976 amu) with a \(4.68 \%\) abundance, and Si-30 (29.974 amu) with a 3.09\% abundance. What is the atomic mass of silicon?

Short answer

The atomic mass of silicon is approximately 28.074 amu.

Step-by-step solution

- Convert Percentages to Decimal Form

Convert the natural abundance percentages of each isotope to decimal form by dividing by 100. Si-28: \(92.23\text{ %} \rightarrow 0.9223\)Si-29: \(4.68\text{ %} \rightarrow 0.0468\)Si-30: \(3.09\text{ %} \rightarrow 0.0309\)

- Multiply Each Isotope's Mass by Its Decimal Abundance

Calculate the contribution of each isotope to the atomic mass by multiplying the mass of each isotope by its corresponding decimal abundance:\[ \text{Contribution of Si-28} = 27.977 \times 0.9223 = 25.7908 \text{ amu} \]\[ \text{Contribution of Si-29} = 28.976 \times 0.0468 = 1.3570 \text{ amu} \]\[ \text{Contribution of Si-30} = 29.974 \times 0.0309 = 0.9261 \text{ amu} \]

- Sum the Contributions

Add the contributions from each isotope to find the weighted average atomic mass of silicon:\[ \text{Atomic mass of Si} = 25.7908 + 1.3570 + 0.9261 = 28.0739 \text{ amu} \]

Key concepts

isotopes

Atoms of the same element can have varying numbers of neutrons. These variations are known as isotopes. Different isotopes of an element share the same number of protons but differ in their numbers of neutrons. For silicon, isotopes like Si-28, Si-29, and Si-30 only differ in the neutrons they possess. This variance leads to slightly different atomic masses for each isotope. Isotopes are crucial in scientific calculations and applications, from understanding nuclear reactions to measuring the age of ancient artifacts.

natural abundance

Natural abundance refers to the relative percentage of each isotope of an element found in nature. For any given element, different isotopes will be present in varying proportions. Take silicon, for example: Si-28 is the most abundant isotope, making up 92.23% of natural silicon. In contrast, Si-29 has a 4.68% abundance, and Si-30 only 3.09%. These percentages influence how we compute the average atomic mass of the element, highlighting the importance of considering natural abundance in chemical calculations.

weighted average

Calculating the atomic mass of an element involves finding a weighted average of its isotopes' masses. Each isotope's mass is multiplied by its decimal form abundance. This process accounts for the relative contributions of each isotope to the total atomic mass. For silicon:

• Si-28 contributes about 25.7908 amu.
• Si-29 contributes about 1.3570 amu.
• Si-30 contributes about 0.9261 amu.

Summing these contributions gives a weighted average atomic mass of 28.0739 amu. This precise calculation reflects the collective influence of all naturally occurring silicon isotopes.