Question

| The element gallium has two stable isotopes: 69 Ga with an atomic mass of 68.92 u and 71 Ga with an atomic mass of 70.92 u. A periodic table shows that the chemical atomic mass of gallium is 69.72 u. What is the percent abundance of 69 Ga?

Short answer

Calculate the percent abundance of nucleus ⁶⁹Ga.

Consider x₁ and x₂are the fractions of nuclei ⁶⁹Ga and ⁷¹Ga respectively. The total fraction of two isotopes is equal to one. That is,

x₁+x₂=1

Rearrange the equation forx₂

x₂ =1-x₁

Step-by-step solution

The chemical atomic mass of gallium is equal to the x1 times of atomic mass of 69Ga plus x2times of atomic mass of 71Ga

That is,

$x_1\left(68.92\right)+x_2\left(70.92u\right)=69.72u$

Substitute 1-x₂ for x₂ in the above equation and solve for x₁

$$\begin{gathered} x_1\left(68.92u\right)+\left(1-x_1\right)\left(70.92u\right)=69.72u \\ {x}_1=60\% \end{gathered}$$

Therefore, the abundance percentage of nucleus ⁶⁹Ga is 60 %.