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 ??
the setup of the answer is correct. however calculations are wrong
To calculate the percent abundance of 153 Eu, we need to use the atomic masses and the given atomic mass of Eu.
The atomic mass of 151 Eu is 150.9198 u.
The atomic mass of 153 Eu is 152.9212 u.
The given atomic mass of Eu is 151.9640 u.
Let x be the percent abundance of 153 Eu.
The formula to calculate the average atomic mass (given) is:
atomic mass (given) = (isotope 1 atomic mass * percent abundance 1) + (isotope 2 atomic mass * percent abundance 2)
Plugging in the values:
151.9640 u = (150.9198 u * (100 - x)) + (152.9212 u * x)
Let's simplify the equation and solve for x:
151.9640 = 150.9198 - 150.9198x + 152.9212x
151.9640 = 150.9198 + 2.0014x
Rearranging the equation:
2.0014x = 151.9640 - 150.9198
2.0014x = 1.0442
Dividing both sides by 2.0014:
x = 1.0442 / 2.0014
Calculating the value of x:
x = 0.521
Therefore, the percent abundance of 153 Eu is approximately 0.521%, or 0.521/100 = 0.00521.
To calculate the percent abundance of an isotope, you can use the following formula:
Percent abundance = (Number of atoms of the isotope / Total number of atoms of all isotopes) * 100
In this case, we know the atomic mass of Europium is given as 151.9640 u, which is a weighted average of the atomic masses of both isotopes, taking into account their abundance. Let's assign x as the percent abundance of the isotope 151 Eu and (100 - x) as the percent abundance of 153 Eu.
We can set up the following equation based on the atomic masses and percent abundances:
(151 Eu atomic mass * x/100) + (153 Eu atomic mass * (100 - x)/100) = 151.9640 u
Now, we can solve for x to find the percent abundance of 153 Eu.
(150.9198 * x/100) + (152.9212 * (100 - x)/100) = 151.9640
Simplifying the equation:
(150.9198x + 152.9212(100 - x))/100 = 151.9640
Expanding and rearranging:
150.9198x + 152.921200 - 152.9212x = 151.9640
-1.0014x = 151.9640 - 152.921200
-1.0014x = -0.9572
Dividing both sides by -1.0014:
x = -0.9572 / -1.0014
x ≈ 0.9556
Since x represents the percent abundance of 151 Eu, the percent abundance of 153 Eu is (100 - x):
Percent abundance of 153 Eu = 100 - 0.9556
Percent abundance of 153 Eu ≈ 99.0444 %
Therefore, the percent abundance of 153 Eu is approximately 99.0444%.
151.9640 = (150.9198 + x) + (152.9212 + y)
= 150.9198x + (152.92 (1-x))
= 150.9198x + 152.92 -152.92x
= -1.922x + 152.92
151.9640-152.92 = -1.922x = 152.92-152.92
-0.956 = -1.922x
-.0956/-1.922x = -1.922x/-1.922x
0.49739... = x
x = 49.73%
Eu-151 = 49.73%
Eu-153 = 50.27%(since 100%-49.73% = 50.27%)