Rhenium has two naturally occurring isotopes: Re-185 with a natural abundance of 37.40% and Re-187 with a natural abundance of 62.60%. The sum of the masses of the two isotopes is 371.9087 amu. Find the masses of the individual isotopes.
The atomic weight of Rhenium (Re) as found on the periodic table of the elements is 186.207. Let x = the atomic weight of Re-185 and (371.9087 - x) = the atomic weight of Re-187.
atomic weight of Re = 186.207 amu
x = atomic weight of Re-185 in amu
(371.9087 - x) = atomic weight of Re-187 in amu
abundance of Re-185 = 37.40% = 0.3740
abundance of Re-187 = 62.60% = 0.6260
atomic masses of Re-185 and Re-187
Note: In order to reduce rounding errors, I will include guard digits and round to the proper number of significant figures at the end.
Multiply x times the abundance of Re-185 and multiply (371.9087 - x) times the abundance of Re-187.
Re-185: (0.3740)(x) = 0.3740x
Re-187: (0.6260)(371.9087 - x) = 232.8148462 - 0.6260x