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!
