The relative atomic mass of natural lithium is 6.95 it consist of two isotopes of relative masses 6.02 7.02 calculate the natural abundance of the isotopes
Fractional abundance of Isotope 1 = x
Fractional abundance of Isotope 2 = (1 - x)
The average mass in this case is 6.95
=> (Mass 1)*(Abundance 1) + (Mass 2)*(Abundance 2) = 6.95
=> 6.02*x + 7.02*(1-x) = 6.95
=> 7.02 - 6.95 = x
=> x = 0.07
=> 1- x = 0.93
Hence, Isotope 1 is 7% while Isotope 2 is 93%
To calculate the natural abundance of the isotopes, we need to use the weighted average formula. The formula is:
Average mass = (mass of isotope 1 * abundance of isotope 1) + (mass of isotope 2 * abundance of isotope 2)
Now, let's use the given information to calculate the natural abundance of the isotopes:
Relative atomic mass of lithium (average mass) = 6.95
Mass of isotope 1 = 6.02
Mass of isotope 2 = 7.02
Let the natural abundance of isotope 1 be x (in decimal form) and the natural abundance of isotope 2 be (1 - x) (as the total abundance will add up to 1).
Substituting the values into the formula:
6.95 = (6.02 * x) + (7.02 * (1 - x))
Simplifying the equation:
6.95 = (6.02x) + (7.02 - 7.02x)
6.95 = 6.02x + 7.02 - 7.02x
6.95 - 7.02 = -0.1x
-0.07 = -0.1x
Dividing both sides by -0.1:
-0.07 / -0.1 = -0.1x / -0.1
0.7 = x
Therefore, the natural abundance of isotope 1 is 0.7 or 70%, and the natural abundance of isotope 2 is (1 - 0.7) = 0.3 or 30%.