Question

silver has two naturally occurring isotopes; ag-107 and ag-109. the relative atomic mass of silver is 107.87 g. determine the percent abundance of ag-107. round your answer to one decimal place. * (0.5 points) enter your answer

Explanation:

Step1: Let the percent abundance of Ag - 107 be $x$.

Then the percent abundance of Ag - 109 is $1 - x$.

Step2: Set up the equation for relative atomic mass.

The relative atomic mass of silver is calculated as the weighted - average of the masses of its isotopes. So, $107.87=107x + 109(1 - x)$.

Step3: Expand and simplify the equation.

$107.87=107x+109 - 109x$. Combine like terms: $107.87=109 - 2x$.

Step4: Solve for $x$.

First, move the terms around: $2x = 109 - 107.87$. So, $2x=1.13$. Then $x=\frac{1.13}{2}=0.565$.

Step5: Convert $x$ to a percentage.

Multiply $x$ by 100 to get the percent abundance: $0.565\times100 = 56.5\%$.

Answer:

$56.5\%$