boron has an average atomic mass of 10.81. one isotope of boron has a mass of 10.012938 and a relative…

Explanation:

Step1: Set up the formula for average atomic mass

The formula for average atomic mass ($A_{avg}$) is $A_{avg}=m_1x_1 + m_2x_2$, where $m_1$ and $m_2$ are the masses of the isotopes and $x_1$ and $x_2$ are their relative - abundances (in decimal form). Let $m_1 = 10.012938$, $x_1=0.1980$, $x_2 = 0.8020$, and $A_{avg}=10.81$. We need to find $m_2$.

Step2: Rearrange the formula to solve for $m_2$

Starting with $A_{avg}=m_1x_1 + m_2x_2$, we can isolate $m_2$: [m_2=\frac{A_{avg}-m_1x_1}{x_2}]

Step3: Substitute the values into the formula

[m_2=\frac{10.81-(10.012938\times0.1980)}{0.8020}] First, calculate $10.012938\times0.1980 = 10.012938\times\frac{198}{1000}=1.982561724$. Then, $10.81 - 1.982561724=8.827438276$. Finally, $m_2=\frac{8.827438276}{0.8020}\approx10.98$.

Answer:

$10.98$