Question

The atomic masses of 10B and 11B are 10.012938 and 11.009305 amu, respectively. The average atomic mass of boron is 10.811 amu. Calculate the natural abundances of these two isotopes.

Answer 1

19.9% 10B and 80.1% 11B

Step-by-step explanation:

The average atomic mass of boron is calculated using the weighted average of the atomic masses of 10B and 11B.

A system of two equations can be written, where x represents the percentage (in decimal form) of 10B and where y represents the percentage (in decimal form) of 11B.

1.
`10.012938x + 11.009305y = 10.811`

2.
`x + y = 1` >>
`y = 1 - x`

Inserting Equation 2 into Equation 2 gives:

`10.012938x + 11.009305(1 - x) = 10.811`

Solving for x gives:

`x = 0.199`

Substituting this value of x into Equation 2 above gives:

`y = 1 - x = 1 - 0.199 = 0.801`