Question

Question #7b209

Answer 1

`28.085` `"amu"`

Explanation:

We're asked to calculate the relative atomic mass of silicon, in units of `"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:

`color(red)(25.8030)` `color(red)("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!