Answer
24.62 amu is the atomic mass of hypothetical element X.
Work Step by Step
Strategy: The atomic mass of the element is found by multiplying each isotopic mass by its abundance fraction, and then add all of them. The picture of the report with isotopes X-23 and X-25, will help us to find abundance fraction for each isotope.
We are given isotopic mass of each isotopes: X- 23 with 23.02 amu and x-25 with 25.147 amu.
We can find the abundance fraction of isotopes.
we count in the picture that there are 5 brown colored atoms of isotope X - 23.
There are 15 green colored atoms of isotope X - 25.
In total there are 20 isotopes of element X.
So we can calculate:
the abundance fraction of isotope X - 23: $\frac{5}{20}$ = $\frac{1}{4}$ = 0.250
the abundance fraction of isotope X - 25: $\frac{15}{20}$ = $\frac{3}{4}$ = 0.750
Now we can find the atomic mass by multiplying each isotopic mass by its abundance fraction
23.02 amu x 0.250 = 5.7550 amu
25.147 amu x 0.750 = 18.8603 amu
____________________________
Sum: 24.6153 amu
So the atomic mass of element X would be 24.6153 amu or 24.62 amu.
To check our answer we see that this number is near the mass of isotope X-25 ( with 25.147 amu) that has the greatest abundance of 0.750.
