Gallium has two naturally occurring isotopes, 69Ga and 71Ga. If the atomic mass of gallium is 69.72 amu, which isotope is more abundant?

• A. 71Ga
• B. 69Ga

Answer: (B)

Verified step by step guidance

1. Understand that the atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes, weighted by their relative abundances.
2. Set up variables for the fractional abundances of the isotopes: let x be the fraction of 69Ga and (1 - x) be the fraction of 71Ga, since their total abundance must sum to 1.
3. Write the equation for the average atomic mass using the isotopic masses and their abundances: \(\text{Atomic mass} = x \times 69 + (1 - x) \times 71\).
4. Substitute the given atomic mass (69.72 amu) into the equation and solve for x to find the fractional abundance of 69Ga.
5. Interpret the value of x: if x is greater than 0.5, then 69Ga is more abundant; if less than 0.5, then 71Ga is more abundant.