To find the relative atomic abundance of each isotope, we can set up a system of equations using the given information. Let's denote the relative atomic abundance of the isotope with mass number 63 as x, and the relative atomic abundance of the isotope with mass number 65 as y.
The relative atomic mass (RAM) of the element Y is given as 63.5, which is the weighted average of the isotopes' masses, considering their relative atomic abundances:
RAM = (mass of isotope 1 × relative atomic abundance of isotope 1) + (mass of isotope 2 × relative atomic abundance of isotope 2)
Using the values provided:
63.5 = (63 × x) + (65 × y)
Since the relative atomic abundances should add up to 1, we also have the equation:
x + y = 1
Now we have a system of equations:
63.5 = 63x + 65y
x + y = 1
We can solve this system to find the values of x and y.
Multiplying the second equation by 63, we get:
63x + 63y = 63
Subtracting this equation from the first equation:
63.5 - 63 = 63x + 65y - (63x + 63y) 0.5 = 2y y = 0.5/2 y = 0.25
Substituting the value of y back into the second equation:
x + 0.25 = 1 x = 1 - 0.25 x = 0.75
Therefore, the relative atomic abundance of the isotope with mass number 63 is 0.75, and the relative atomic abundance of the isotope with mass number 65 is 0.25.