Question

boron has the average atomic mass of 10.81 and has two naturally occurring isotopes (boron - 10 and boron - 11). which isotope of boron is more abundant? boron - 10 and boron - 11 have the same abundance. boron - 11 is more abundant. there is not enough information to make that determination. boron - 10 is more abundant.

Explanation:

Step1: Set up the formula for average atomic mass

The formula for average atomic mass \(M\) is \(M = M_1x_1+M_2x_2\), where \(M_1\) and \(M_2\) are the masses of the isotopes, and \(x_1\) and \(x_2\) are their fractional abundances (\(x_1 + x_2=1\)). Let \(x\) be the fractional abundance of boron - 10 (\(M_1 = 10\)), then the fractional abundance of boron - 11 (\(M_2 = 11\)) is \(1 - x\). The average atomic mass of boron \(M=10.81\).
So, \(10.81=10x + 11(1 - x)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(10.81=10x+11 - 11x\).
Combine like terms: \(10.81=11 - x\).
Rearrange to solve for \(x\): \(x = 11 - 10.81=0.19\).
The fractional abundance of boron - 11 is \(1 - x=1 - 0.19 = 0.81\).

Answer:

Boron - 11 is more abundant.