Question

Silver has an atomic mass of 107.9 amu. If 51.84% of Ag exists as Ag-107 (106.9051 amu), what is the identity and the atomic mass of the other isotope?

Answer 1

Mass of Ag as 107.9
This must be a combination of these two isotopes. So the % of the other isotope must be 48.16%.
To work with these percentages in an equation I'll use them as decimals.
So now I can start putting them into an equation:
107.9=(106.905⋅0.5184)+(x⋅0.4816)
Because both of the isotope masses, multiplied by their percentage, would give us the overall average mass.
107.9=55.419552⋅(x⋅0.4816)
Worked out the brackets that we can work out, and then rearrange to give:
107.9−55.419552=(x⋅0.4816)
Again rearrange:
52.480448=(x⋅0.4816)
And final rearranging:
x=52.480448/0.4816
x=108.9710 (using same sig figs as given in question)