Europium has two stable isotopes, 151 Eu (150.9198 u) and 153 Eu (152.9212 u). The atomic mass given for Eu is 151.9640 u. What is the percent abundance of 153 Eu ??
y = fraction Eu 151
then 1-y = fraction Eu 153
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y(150.9198) + (1-y)(152.9212) = 151.9640
Solve for y and 1-y.
To find the percent abundance of 153 Eu, we need to compare the masses of the isotopes and use the given atomic mass of Europium.
Let's denote the percent abundance of 151 Eu as x and the percent abundance of 153 Eu as (100 - x), since the sum of the percent abundances should be 100%.
We can set up the following equation based on the atomic masses:
(x/100) * 150.9198 + ((100 - x)/100) * 152.9212 = 151.9640
To solve this equation, we can simplify it:
(150.9198x + 152.9212(100 - x)) / 100 = 151.9640
Now let's solve for x:
150.9198x + 152.9212(100 - x) = 151.9640 * 100
150.9198x + 152.9212 * 100 - 152.9212x = 151.9640 * 100
-1.0014x = (151.9640 * 100) - (152.9212 * 100)
-1.0014x = 15196.40 - 15292.12
-1.0014x = -95.72
Now, divide both sides by -1.0014:
x = - (-95.72) / 1.0014
x ≈ 95.63
So, the percent abundance of 153 Eu is approximately 95.63%.