Question

the average atomic mass of boron is 10.81 amu. based on the atomic mass of b-11 and the relative abundances of the boron isotopes, what is the atomic mass of b-10?

isotope	atomic mass (amu)	relative abundance (%)
b-10		19.9
b-11	11.009	80.1

a. 10.964 amu
b. 10.199 amu
c. 10.810 amu
d. 10.009 amu

Explanation:

Step1: Recall the formula for average atomic mass

The formula for average atomic mass $A_{avg}=\sum_{i}A_{i}x_{i}$, where $A_{i}$ is the atomic mass of isotope $i$ and $x_{i}$ is the relative abundance of isotope $i$ (in decimal form). Let the atomic mass of B - 10 be $x$. The relative abundance of B - 10, $x_1 = 0.199$ and the relative abundance of B - 11, $x_2=0.801$, the atomic mass of B - 11 is $A_2 = 11.009$ amu, and the average atomic mass $A_{avg}=10.81$ amu.

Step2: Substitute values into the formula

$10.81=x\times0.199 + 11.009\times0.801$.

Step3: First calculate the product of the atomic mass and relative - abundance of B - 11

$11.009\times0.801 = 8.818209$.

Step4: Rearrange the equation to solve for $x$

$x\times0.199=10.81 - 8.818209$.
$x\times0.199 = 1.991791$.
$x=\frac{1.991791}{0.199}$.

Step5: Calculate the value of $x$

$x = 10.009$ amu.

Answer:

D. 10.009 amu