There are two isotopes of boron: boron-10 and boron-11. Explain, in terms of weighted average atomic mass, the difference in percent abundance of each of the isotopes of boron.

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