Answer:
isotope 1: 37.6%
isotope 2: 62.4%
Explanation:
As the element has only two naturally occurring isotopes, we can name them as:
x = mass of isotope 2; so x = 47.000amu
(1-x) = mass of isotope 1; so (1-x) = 44.000amu
Then the average atomic mass of the element must be:
[tex]45.873=(47.000x)+(44.000(1-x))[/tex]
Solving for x, we have:
[tex]45.873=47.000x+44.000-44.000x[/tex]
[tex]45.873=44.000+3.000x[/tex]
[tex]45.873-44.000=3.000x[/tex]
[tex]1.873=3.000x[/tex]
[tex]x=\frac{1.873}{3.000}[/tex]
[tex]x=0.624[/tex]
So, with x we can find (1-x):
[tex]1-x=1-0.624[/tex]
[tex]1-x=0.376[/tex]
So, the abundance of isotope 1 is 37.6% and isotope 2 has an abundance of 62.4%.
