The element rhenium (Re, atomic number 75) has two naturally occurring isotopes, Re-185 (mass = 184.935 amu) and Re-187 (mass = 186.956 amu). Calculate the percent abundances of the isotopes of rhenium.

Answer:

Let Y be the percent abundance of isotope Re-185 , then the percentage abundance of Re-187 is (1-Y)

Average atomic mass of Re is 186.2 units

Average atomic mass = Sum of the product of the masses of the isotope with their percentage abundance

                                 = ( Atomic mass of Re-185 x its percent abundance) + ( Atomic mass of Re-187 x its percent abundance)

                   186.2   = ( 184.935 x Y ) + ( 186.956 x(1-Y))

                                 = 184.935Y + 186.956 - 186.956Y

                             Y = 0.374

So percent abundance of Re-185 is = Y = 0.375 x 100 = 37.4 %

Percent abundance of Re-187 is 100 - 37.4 = 62.6 %