Problem:  how do I know if isotope AU-173 decays by beta or alpha emission?  What are the clues/steps/concepts that I need to tell me how this isotope decays?

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Alpha decay occurs with an atomic number of 83+, s it's got to be either beta decay or electron capture. Now, we know that the ratio of protons and neutrons in this gold isotope is 1/1.18. Now beta decay is when we lose neutrons to gain more protons and electrons. We definitely don't want that because it already is under the ratio of protons and neutrons in these heavy metals. Therefore, we want to have more neutrons and less protons by using electrons from the electron shells and collide them with the protons to form new neutrons, hence making it more stable.   This is why Au-173 decays through electron capture.