Question

silicon, which makes up about 25% of earths crust by mass, is used widely in the modern electronics industry. it has three naturally occurring isotopes, 28si, 29si, and 30si. calculate the atomic mass of silicon.
isotope
28si
29si
30si
isotopic mass (amu)
27.976927
28.976495
29.973770
abundance %
92.22
4.69
3.09
a) 29.2252 amu
b) 28.7260 amu
c) 28.0855 amu
d) 28.9757 amu
e) 27.9801 amu

Explanation:

Step1: Convert percentages to decimals

Multiply each isotopic mass by its abundance (in decimal form).
For \(^{28}\text{Si}\): \(27.976927\times0.9222\)
For \(^{29}\text{Si}\): \(28.976495\times0.0469\)
For \(^{30}\text{Si}\): \(29.973770\times0.0309\)

Step2: Calculate each product

\(27.976927\times0.9222 = 27.976927\times(1 - 0.0778)=27.976927-27.976927\times0.0778\approx27.976927 - 2.186 = 25.790927\)
\(28.976495\times0.0469 = 28.976495\times(0.04 + 0.0069)=28.976495\times0.04+28.976495\times0.0069 = 1.1590598+0.2009388 = 1.3599986\)
\(29.973770\times0.0309 = 29.973770\times(0.03+0.0009)=29.973770\times0.03 + 29.973770\times0.0009=0.8992131+0.0269764 = 0.9261895\)

Step3: Sum the products

\(25.790927+1.3599986 + 0.9261895=28.0771151\approx28.0855\)

Answer:

C. 28.0855 amu