Question

1. calculate the atomic mass of silicon. the three silicon isotopes have atomic masses and relative abundances of 27.9769 amu (92.2297%), 28.9765 amu (4.6832%) and 29.9738 amu (3.0872%).

Explanation:

Step1: Convert percentages to decimals

For the first isotope: \( 92.2297\% = 0.922297 \)
For the second isotope: \( 4.6832\% = 0.046832 \)
For the third isotope: \( 3.0872\% = 0.030872 \)

Step2: Calculate the contribution of each isotope

First isotope: \( 27.9769 \times 0.922297 \approx 25.80 \)
Second isotope: \( 28.9765 \times 0.046832 \approx 1.357 \)
Third isotope: \( 29.9738 \times 0.030872 \approx 0.925 \)

Step3: Sum the contributions

\( 25.80 + 1.357 + 0.925 = 28.082 \)

Answer:

The atomic mass of silicon is approximately \( 28.09 \) amu (more precise calculation: \( 27.9769\times0.922297 + 28.9765\times0.046832 + 29.9738\times0.030872 = 27.9769\times0.922297+28.9765\times0.046832 + 29.9738\times0.030872\approx25.801 + 1.357+0.925 = 28.083\approx28.09 \) amu)