The atomic mass of lithium is 6.94, the naturally occurring isotopes are 6Li = 6.015121 amu, and 7Li = 7.016003 amu. Determine the percent abundance of each isotope.
To determine the percent abundance of each isotope, you need to know the atomic masses and the overall abundance of the isotopes present in lithium.
Let's denote the percent abundance of 6Li as x% and the percent abundance of 7Li as y%.
Since the sum of the percentages must equal 100%, we can say that x + y = 100.
Now, let's establish the relationship between the atomic masses and the percent abundances.
The atomic mass of lithium (6.94 amu) can be calculated using the following formula:
Atomic mass = (6Li atomic mass * percent abundance of 6Li) + (7Li atomic mass * percent abundance of 7Li)
Substituting the given atomic masses and unknown percent abundances into the formula:
6.94 amu = (6.015121 amu * x%) + (7.016003 amu * y%)
Now, we have two variables (x and y) and two equations:
x + y = 100 (equation 1)
6.015121x + 7.016003y = 6.94 (equation 2)
We can solve this system of equations to find the values of x and y.
First, multiply equation 1 by -6.015121:
-6.015121x - 6.015121y = -601.5121 (equation 3)
Next, add equation 3 to equation 2:
-6.015121x + 6.015121x - 6.015121y + 7.016003y = -601.5121 + 6.94
0x + 0y = -594.5721
0 = -594.5721
This equation is not possible, which means there is an error in the given data or calculations. Please double-check the data provided and try again.
amu is atomic mass unit or the proportion of the isotope existing in nature expressed in percentage. i.e. 6Li exist approximately 6.015% while 7Li exist 7.016%.
hope that helps.