Nitrogen has two naturally occurring isotopes, N-14 and N-15. Its atomic mass is 14.007. Which isotope is more abundant?

N-14 is more abundant.

assume N-14 has mass = 14

and N-15 has mass = 15

and since that 14.007 is the weighted average mass over all the isotopes, it is equal to

fraction N-14 x 14 + fraction N-15 x 15 = 14.007

now.. if the fractions were =, that is if fraction N-14 = fraction N-15 = 0.5, then...

0.5 x 14 + 0.5 x 15 = 14.5.. right?  

more N-15 would make that number larger..

0.3 x 14 + 0.7 x 15 = 14.7.. right?  

to make it < 14.5, you need more N-14 than N-15.  Do you see that?  And in fact if we let x = abundance of N-14, then (1-x) = abundance of N-15, and we could solve for x.

(X)x14 + (1-X)x 15 = 14.007.. right?  

14X + 15 - 15X = 14.007

X = 0.993

the relative abundance of N-14 = 99.3%

the relative abundance of N-15 = 0.7%

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