This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 ^71Ga. If the abundance of ^69Ga is x\%, then the abundance of ^71Ga is the remaining percentage. Abundance of ^71Ga = (100 - x)\% The expression for the abundance of ^71Ga is (100 - x)\%. b) Step 1: Write the formula for Relative Atomic Mass (RAM). The Relative Atomic Mass (RAM) is calculated using the formula: RAM = (mass of isotope 1 × abundance of isotope 1) + (mass of isotope 2 × abundance of isotope 2)100 Step 2: Substitute the given values into the formula. Given: RAM = 69.72 Mass of ^69Ga = 69 Mass of ^71Ga = 71 Abundance of ^69Ga = x\% Abundance of ^71Ga = (100 - x)\% 69.72 = ((69 × x) + (71 × (100 - x)))/(100) Step 3: Solve for x. Multiply both sides by 100: 69.72 × 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 = (128)/(2) x = 64 The percentage abundance of the ^69Ga isotope is 64\%. Send me the next one 📸