# Question 7b209

Jul 1, 2017

$28.085$ $\text{amu}$

#### Explanation:

We're asked to calculate the relative atomic mass of silicon, in units of $\text{amu}$.

With all the known isotopic abundances and masses, this process is straightforward; we simply multiply (for all three isotopes) the percent abundance by the atomic mass of the isotope, and sum te total of all 3.

We can change each percentage into a fraction, and the process goes like this:

Isotope 1: overbrace((27.9769color(white)(l)"amu"))^"isotopic mass"overbrace((0.922297))^"fractional abundance" = color(red)(25.8030 color(red)("amu"

Isotope 2: overbrace((28.9765color(white)(l)"amu"))^"isotopic mass"overbrace((0.046832))^"fractional abundance" = color(blue)(1.3570 color(blue)("amu"

Isotope 3: overbrace((29.9738color(white)(l)"amu"))^"isotopic mass"overbrace((0.030872))^"fractional abundance" = color(green)(0.9254 color(green)("amu"

Total = atomic mass of silicon:

$\textcolor{red}{25.8030}$ $\textcolor{red}{\text{amu}}$ + color(blue)(1.3570 color(blue)("amu" + color(green)(0.9254 color(green)("amu"

= color(purple)(28.085 color(purple)("amu"#

Which is nearly the exact value if you were to look it up!