Which isotope of an element is the most abundant if you know the elements average atomic mass

Question

Deternine which isotope of an element is the most abundant if you know the elements average atomic mass

 

Answer 1

for an element which has two isotopes, the procedure follows

let us use Copper 63 and Copper 65

1. find the value of Cu from the Periodic Table, which, in this case, is 63.546

2. find the value of Cu63 = 62.9296

3. find the value of Cu65 = 64.9278

 

let x = abundance of Cu63; then the abundance of Cu65 will be 1 - x

 

4. our equation will be x(62.9596) + [(1-x)64.9278] = 63.546

then 62.9296x + 64.9278 - 64.9278x = 63.546

5. combining, 64.9278 - 63.546 = 64.9278x - 62.9296x

which yields 1.3318 = 1.9982x

6. solving for 1.3318/1.9982 = x

7. 0.6915 = x; then 1 - x = 0.308

8. multiplying by 100%, we get 69.15% and 30.8%