# How do I calculate the approximate percent abundance of gallium's isotopes (69Ga, 71Ga) in a sample of gallium metal.  This is how I tried to solve the equation 69Ga=x   71Ga=(1-x)...

1. How do I calculate the approximate percent abundance of gallium's isotopes (69Ga, 71Ga) in a sample of gallium metal.

This is how I tried to solve the equation

69Ga=x   71Ga=(1-x)

69x+(1-x)71=68.92

69x+71-71x=68.92

-2x+71=68.92

71=68.92+2x

2.08=2x

divide by 2 on both sides

x=1.04

How can this be if this is the percentage of 69Ga?

Does it not have to be a number less than 1?

justaguide | Certified Educator

The mass of gallium which is the weighted average mass of its isotopes is 69.723. Using this approximate percentage of the isotopes 69Ga and 71Ga can be estimated as follows.

Let the percentage of 69Ga be x. The percentage of the 71Ga isotope is 1 - x.

69*x + 71*(1 - x) = 69.723

=> 69x + 71 - 71x = 69.723

=> 2x = 71 - 69.723

=> 2x = 1.277

=> x = 0.6385

This gives x = 63.85%

The percentage of 69Ga is 63.85% and that of 71Ga is 36.15%.

[The atomic mass of gallium you had used was 68.92 which is less than the mass of the lighter isotope that has a mass of 69. This gave the erroneous value of x greater than 1]