What is the percent abundance of the heaviest isotope?

Question

A newly discovered element has an average atomic mass of 552.6209 amu. The element is found to have three isotopes. The first isotope has a mass of 551.1 amu and an abundance of 37.55 %. The second isotope has a mass of 552.1 amu and the third isoptope has a mass of 554.1 amu

Answer 1

The heaviest has a mass of 554.1 amu, and the abundance would be the difference between the sum of the other 2 isotopes and 100%.  Without knowing the abundance of the second isotope (mass of 551.1 amu), you can't determine the abundance of the heaviest isotope.

Answer 2

I will set this up for you, but YOU do the calculations.

 

m = 552.6209 amu

 

A₁ = abundance of 1st isotope = 37.55%

A₃ = abundance of 3rd isotope = ? (what you want to solve for)

A₂ = abundance of 2nd isotope = 100 - (A₁ + A₃)

 

m₁ = mass of 1st isotope = 551.1 amu

m₂ = mass of 2nd isotope = 552.1 amu

m₃ = mass of 3rd isotope = 554.1 amu

 

m = (A₁m₁ + A₂m₂ + A₃m₃)/(A₁ + A₂ + A₃)

 

We know that  A₁ + A₂ + A₃ must equal 100%, so 

 

m = {A₁m₁ + [100 - (A₁ + A₃)]m₂ + A₃m₃} / 100

 

In the last equation above, you know m, A₁, m₁, m₂, and m₃.  The only unknown is A₃.  Do the algebra to solve for A₃, plug in the values of m, A₁, m₁, m₂, and m₃, evaluate, and get the value of A₃.