Let's denote the relative % abundance of the first isotope (with atomic mass 62.93) as x, and the relative % abundance of the second isotope (with atomic mass 64.928) as 100 - x.
To find the values of x and (100 - x), we can set up an equation using the given average relative atomic mass:
(x/100) * 62.93 + ((100 - x)/100) * 64.928 = 63.546
Simplifying the equation:
0.6293x + 64.928 - 0.64928x = 63.546 0.01998x = 63.546 - 64.928 0.01998x = -1.382 x = -1.382 / 0.01998 x ≈ 69.1
Therefore, the relative % abundance of the first isotope (with atomic mass 62.93) is approximately 69.1%, and the relative % abundance of the second isotope (with atomic mass 64.928) is approximately 30.9%.
Please note that the negative value of x in the intermediate step is due to the subtraction involved and doesn't have physical meaning. The final result for x represents the relative % abundance.