Lithium has 2 isotopes. The relative atomic masses are 6.02 and 7.02. The average relative atomic mass of lithium is 6.94. What is the calculated relative abundance of the lighter isotope?
Say you have 1 gram of Lithium. If x grams have mass 6.02, then
6.02x + 7.02(1-x) = 6.94
x = .08
so, 8% of Li is the lighter isotope. Makes sense, since 6.94 is so much closer to the heavier value.
To calculate the relative abundance of the lighter isotope of lithium, we need to consider the average atomic mass of lithium as well as the relative atomic masses of its isotopes.
Let's denote the relative abundance of the lighter isotope as x (in decimal form) and the relative abundance of the heavier isotope as (1 - x).
According to the given information, the relative atomic mass of the lighter isotope is 6.02 and the relative atomic mass of the heavier isotope is 7.02.
The average relative atomic mass is calculated as the weighted average of the isotopes' relative atomic masses, using their respective relative abundances:
Average atomic mass = (Relative atomic mass of the lighter isotope * Relative abundance of the lighter isotope) + (Relative atomic mass of the heavier isotope * Relative abundance of the heavier isotope)
Using the given values, we can write this equation as:
6.94 = (6.02 * x) + (7.02 * (1 - x))
Now, we can solve this equation to find the value of x, which represents the relative abundance of the lighter isotope.
6.94 = 6.02x + 7.02 - 7.02x
6.94 = 0.9999999999999998x + 7.02 - 7.02x
6.94 - 7.02 = -0.020000000000000018x
-0.07999999999999996 = -0.020000000000000018x
x = (-0.07999999999999996) / (-0.020000000000000018)
x = 3.999999999999998
Rounding the answer to an appropriate number of decimal places, we can say that the calculated relative abundance of the lighter isotope of lithium is approximately 4.0%.