Calculate the abundance of each isotope
Gallium consists of two naturally occurring isotopes with masses of 68.926 and 70.925 amu. The average atomic mass of Ga is 69.70 amu. Calculate the abundance of each isotope and identify them by mass number. (Remember significant figures!)
Let x = the fraction that has a mass of 70.925,
then (1-x) = fraction that has a mass of 68.926.
The sum of the two fractions times their masses will equation the average atomic mass which is given as 69.70
In equation form this is:
70.925 * x + 68.926 * (1-x) = 69.70
Solve for x:
70.925x + 68.926 - 68.926x = 69.70
1.99 x = 1.225
x = .6156
decimal fraction times 100 = %
.6156 * 100 = 61.56%, so 61.56% is Ga-70.92 and 38.44% is Ga-68.93.
The two elements with their mass numbers being:
Ga-71 and Ga-69