a) Step 1: Define the total percentage abundance. The total percentage abundance of all isotopes of an element is $100\%$. Step 2: Express the abundance of $^{71}\text{Ga}$. If the abundance of $^{69}\text{Ga}$ is $x\%$, then the abundance of $^{71}\text{Ga}$ is the remaining percentage. $$ \text{Abundance of } ^{71}\text{Ga} = (100 - x)\% $$ The expression for the abundance of $^{71}\text{Ga}$ is $\boxed{(100 - x)\%}$. b) Step 1: Write the formula for Relative Atomic Mass (RAM). The Relative Atomic Mass (RAM) is calculated using the formula: $$ \text{RAM} = \frac{(\text{mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{abundance of isotope 2})}{100} $$ Step 2: Substitute the given values into the formula. Given: RAM = 69.72 Mass of $^{69}\text{Ga}$ = 69 Mass of $^{71}\text{Ga}$ = 71 Abundance of $^{69}\text{Ga}$ = $x\%$ Abundance of $^{71}\text{Ga}$ = $(100 - x)\%$ $$ 69.72 = \frac{(69 \times x) + (71 \times (100 - x))}{100} $$ Step 3: Solve for $x$. Multiply both sides by 100: $$ 69.72 \times 100 = 69x + 71(100 - x) $$ $$ 6972 = 69x + 7100 - 71x $$ Combine like terms: $$ 6972 = (69 - 71)x + 7100 $$ $$ 6972 = -2x + 7100 $$ Rearrange the equation to solve for $x$: $$ 2x = 7100 - 6972 $$ $$ 2x = 128 $$ $$ x = \frac{128}{2} $$ $$ x = 64 $$ The percentage abundance of the $^{69}\text{Ga}$ isotope is $\boxed{64\%}$. Send me the next one 📸