Question

estimate the atomic mass of silicon based on the following information:

the natural abundance of si-28 is 92.23%. for si-29, it is 4.67%, and for si-30, it is 3.10%.

○ a. 25.8 amu

○ b. 28.1 amu

○ c. 29.0 amu

○ d. 87.0 amu

Explanation:

Step1: Recall the formula for atomic mass

The atomic mass is calculated as the weighted average of the masses of its isotopes, using the formula:
Atomic Mass = (Mass of Isotope 1 × Abundance of Isotope 1) + (Mass of Isotope 2 × Abundance of Isotope 2) + (Mass of Isotope 3 × Abundance of Isotope 3)

Assume the masses of the isotopes are approximately their mass numbers (Si - 28 ≈ 28 amu, Si - 29 ≈ 29 amu, Si - 30 ≈ 30 amu).

Step2: Convert abundances to decimals

• Abundance of Si - 28: \( 92.23\% = \frac{92.23}{100} = 0.9223 \)
• Abundance of Si - 29: \( 4.67\% = \frac{4.67}{100} = 0.0467 \)
• Abundance of Si - 30: \( 3.10\% = \frac{3.10}{100} = 0.0310 \)

Step3: Calculate the weighted sum

\[

$$\begin{align*} \text{Atomic Mass} &= (28 \times 0.9223) + (29 \times 0.0467) + (30 \times 0.0310) \\ &= 25.8244 + 1.3543 + 0.93 \\ &= 25.8244 + 2.2843 \\ &= 28.1087 \approx 28.1 \text{ amu} \end{align*}$$

\]

Answer:

B. 28.1 amu