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\tisotopic mass (amu)\tabundance %
28si\t27.976927\t92.22
29si\t28.976495\t4.69
30si\t29.973770\t3.09
o 29.2252 amu
o 28.9757 amu
o 28.7260 amu
o 28.0855 amu
o 27.9801 amu

Explanation:

Step1: Recall atomic - mass formula

The atomic mass ($A$) of an element with isotopes is calculated using the formula $A=\sum_{i}m_{i}p_{i}$, where $m_{i}$ is the isotopic mass of the $i$-th isotope and $p_{i}$ is the relative abundance of the $i$-th isotope (expressed as a decimal).

Step2: Convert percentages to decimals

The relative abundances are: $p_{1}=0.9222$ for $^{28}Si$, $p_{2}=0.0469$ for $^{29}Si$, and $p_{3}=0.0309$ for $^{30}Si$. The isotopic masses are $m_{1} = 27.976927$ amu, $m_{2}=28.976495$ amu, and $m_{3}=29.973770$ amu.

Step3: Calculate the atomic mass

$A=m_{1}p_{1}+m_{2}p_{2}+m_{3}p_{3}$
$A=(27.976927\times0.9222)+(28.976495\times0.0469)+(29.973770\times0.0309)$
$A = 27.976927\times0.9222+28.976495\times0.0469 + 29.973770\times0.0309$
$A=25.809323+1.359098 + 0.926189$
$A = 28.09461$ amu $\approx28.0855$ amu

Answer:

28.0855 amu