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Chapter 2: Problem 33

(a) What isotope is used as the standard in establishing the atomic mass scale? (b) The atomic weight of boron is reported as \(10.81,\) yet no atom of boron has the mass of \(10.81 \mathrm{u}\). Explain.

Short Answer

Expert verified
(a) The isotope used as the standard for establishing the atomic mass scale is Carbon-12 (\(^{12}\textrm{C}\)). (b) The atomic weight of boron is reported as 10.81 u because it is the weighted average of its isotopes' atomic masses (boron-10 and boron-11) based on their natural abundances (19.9% and 80.1%, respectively). The atomic weight represents an average value for all naturally occurring boron atoms, not the mass of one specific atom.

Step by step solution

01

Part (a) - Identifying the standard isotope for atomic mass scale

To establish the atomic mass scale, a standard is needed to provide a reference point for all other elements. The isotope used as the standard for the atomic mass scale is Carbon-12 (\(^{12}\textrm{C}\)). Carbon-12 was chosen because it is the most abundant isotope of carbon and has 6 protons and 6 neutrons in its nucleus. In this atomic mass scale, one atomic mass unit (u) is defined as exactly \(1/12\)th of the mass of one Carbon-12 atom.
02

Part (b) - Explaining the atomic weight of boron

Boron has two stable isotopes: boron-10 (\(^{10}\textrm{B}\)) with about 19.9% natural abundance and boron-11 (\(^{11}\textrm{B}\)) with about 80.1% natural abundance. The atomic weight of an element is determined by taking the weighted average of the atomic masses of its isotopes based on their natural abundances. First, find the weighted average of boron isotopes: Weighted average of boron = (% abundance of boron-10 × atomic mass of boron-10) + (% abundance of boron-11 × atomic mass of boron-11)
03

- Convert the abundance percentages to decimal values

Percentage abundance values must be converted into decimal values for calculations. Decimal abundance of boron-10 = 19.9% = 0.199 Decimal abundance of boron-11 = 80.1% = 0.801
04

- Calculate the weighted average of boron isotopes

Now, calculate the weighted average using the decimal abundance values and the atomic masses of the isotopes. Weighted average of boron = (0.199 × 10 u) + (0.801 × 11 u) Weighted average of boron = 1.990 u + 8.811 u Weighted average of boron = 10.801 u The atomic weight of boron is reported as 10.81 u because it's the weighted average of its isotopes' atomic masses based on their natural abundances, even though no single atom of boron has a mass equal to 10.81 u. It's important to note that the atomic weight represents an average value for all naturally occurring boron atoms, not the mass of one specific atom.

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