The ratio of the number of atoms of the isotopes Ga 69 and Ga 71 in eight sample

Question

The ratio of the number of atoms of the isotopes Ga 69 and Ga 71 in eight samples from different sources was measured in an effort to understand differences in reported values of the atomic mass of gallium. Sample 1- 1.5260, Sample 2- 1.52992, Sample 3-1.52592, Sample 4- 1.52731, Sample 5- 1.52894, Sample 6- 1.52804, Sample 7- 1.52685, and Sample 8- 1.52793. For the data of 4-3, find the % natural abundance for the two isotopes of gallium, including error estimates based on the mean and standard deviation of the ratio from 4-3. Hint, this is a two equation/two unknown problem.

Explanation / Answer

There are 8 Samples

Mean of 8 Samples = 1/8 * (1.5260 + 1.52992 + 1.52592 + 1.52731 + 1.52894 + 1.52804 + 1.52685 + 1.52793) = 1.52761375

Let the percentage of Ga-71 be x%

then percentage of Ga-69 be 1.52761375x%

1.52761375x% + x% = 100

x = 39.563%

Percentage of Ga-69 = 100 - 39.653 = 60.347%

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