Rhenium has two naturally occurring isotopes, Re-185 and Re-187. The relative atomic mass of rhenium is 186.2. What are the natural abundances of these isotopes

The natural abundance of Re-185 is 40% and of Re-187 is 60%

Explanation:

Relative atomic mass is defined as the sum of the mass of each isotope times its relative abundances.

Is Rhenium has only 2 isotopes and the abundances are X and Y we can write:

X + Y = 1 (1)

And:

185X + 187Y = 186.2 (2)

Where X is abundance of Re-185 and Y abundance of Re-187

Replacing (1) in (2):

185X + 187(1-X) = 186.2

185X + 187-187X = 186.2

-2X = -0.8

X = 0.4 = 40%

And Y = 100% - 40% = 60%

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