Question

Gallium has two naturally occurring isotopes (Ga-69 and Ga-71) and has an atomic mass of 69.723 amu. The mass of Ga-71 is 70.925 amu, and its natural abundance is 39.892%.
Calculate the atomic mass (in amu) and natural abundance (in %) of the second isotope.

Answer 1

The answers are: 
- natural abundance: 60.108%
- atomic mass: 68.926 amu

The atomic mass of an element is the average of the atomic masses of its isotopes. The relative abundance of isotopes must be taken into consideration, therefore:
atomic mass of copper = atomic mass of isotope 1 * abundance 1 + atomic mass of isotope 2 * abundance 2

We know:
atomic mass of copper = 69.723 amu
The atomic mass of Ga-71 is: 70.925 amu
The abundance of Ga-69 is:  39.892% = 0.39892
The atomic mass of Ga-69 is: x
The abundance of Ga-69 is: 100% - 39.892% = 60.108% = 0.60108


Thus:
69.723 amu = 70.925 amu * 0.39892 + x * 0.60108
69.723 amu = 28.293 amu + 0.60108x
⇒ 69.723 amu - 28.293  amu = 0.60108x
⇒ 41.430 amu =  0.60108x
   ⇒ x = 41.430 amu ÷ 0.60108 = 68.926 amu