Calculate the relative abundance of the europium isotopes??

Question

The element exists in nature as 2 isotopes.

^153Eu the mass is 152.9209
^151Eu the mass is 150.9196

The average atomic mass of europium is 151.96 amu.

Calculate the relative abundance of the europium isotopes.
pleaseee

give me the equation so i could understand

Answer 1

The observed average atomic mass is the appropriate arithmetic average. If a fraction y is 153Eu, then (1-y) is 151Eu, and

y x exact mass of 153Eu + (1-y) x exact mass of 151Eu = average atomic mass of Eu

and all that is left to do is the fiddly arithmetic, which I leave to you. Just looking at the numbers, y must be a little bit more than 0.5.

Actually, the question gets things backwards. The way we determine relative atomic masses these days is by mass spectrometry, determining the mass and relative abundance of each isotope, and using this to get the appropriate average.