To determine the percentage abundance of the isotopes of gallium, we can use the relative atomic mass (RAM) and the masses of the isotopes.
Let x represent the percentage abundance of the isotope with mass number 69, and (100 - x) represent the percentage abundance of the isotope with mass number 71.
The formula for calculating the relative atomic mass is:
RAM = (mass of isotope 1 × abundance of isotope 1) + (mass of isotope 2 × abundance of isotope 2)
Given that the RAM is 70.59 and the masses of the isotopes are 69 and 71 (rounded to the nearest whole number), we can set up the following equation:
70.59 = (69 × x) + (71 × (100 - x))
Simplifying the equation:
70.59 = 69x + 7100 - 71x 70.59 - 7100 = -2x -7029.41 = -2x x = -7029.41 / -2 x = 3514.705
The percentage abundance of the isotope with mass number 69 is approximately 3514.705%.
To find the percentage abundance of the other isotope, we can subtract the value of x from 100:
100 - x = 100 - 3514.705 = 96485.295
The percentage abundance of the isotope with mass number 71 is approximately 96485.295%.
Please note that the calculated percentage abundances have been rounded for simplicity.