Answer:
Percent abundance of B¹⁰ is 19.9% and B¹¹ is 80.1%.
The weighted average atomic mass of boron is 10.811 amu.
Explanation:
We know that average atomic mass of Boron is 10.811 amu and there are two isotopes of boron B¹⁰ (10.012938) and B¹¹ (11.009305)
We will determine the percent abundance of each isotopes.
First of all we will set the fraction for both isotopes B¹⁰ and B¹¹.
X for the isotopes having mass 11.009305 amu.
1-x for isotopes having mass 10.012938 amu.
The average atomic mass of Boron is 10.811 amu
we will use the following equation,
11.009305x + 10.012938 ( 10.012938 -x) = 10.811
11.009305x + 10.012938 - 10.012938 x = 10.811
11.009305x - 10.012938 x = 10.811 - 10.012938
0.996367x = 0.798062
x= 0.798062 / 0.996367
x= 0.800972
Percent abundance of B¹¹.
0.800972 × 100 = 80.1 %
80.1 % is abundance of B¹¹ because we solve the fraction x.
now we will calculate the abundance of B¹⁰.
(1-x)
1-0.800972 =0.199
Percent abundance of B¹⁰.
0.199 × 100= 19.9%
19.9% for B¹⁰.
Now we can calculate the average atomic mass of boron.
Formula:
Average atomic mass = [mass of isotope× its abundance] + [mass of isotope× its abundance] +...[ ] / 100
Now we will put the values in formula.
Average atomic mass = [19.9 × 10.012938] + [80.1 × 11.009305] / 100
Average atomic mass = 199.2575 + 881.8453 / 100
Average atomic mass = 10.811 amu
