Question

(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 amu. Explain.

Short answer

(a) The isotope used as the standard in establishing the atomic mass scale is Carbon-12 (${}^{12}$C). (b) The atomic weight of boron is reported as 10.81 amu because it represents the weighted average mass of boron atoms based on the natural abundances of its stable isotopes, Boron-10 (${}^{10}$B) and Boron-11 (${}^{11}$B).

Step-by-step solution

Answering (a): Identifying the standard isotope for atomic mass scale

The isotope used as the standard in establishing the atomic mass scale is Carbon-12 (${}^{12}$C), where 1 atomic mass unit (amu) is defined as $\frac{1}{12}$ of the mass of a Carbon-12 atom.

Answering (b): Explaining the atomic weight of boron

The atomic weight (or relative atomic mass) of boron is reported as 10.81 amu. This is because the atomic weight is a weighted average of the masses of the isotopes of an element, taking into consideration their natural abundance. Boron has two stable isotopes, Boron-10 (${}^{10}$B) and Boron-11 (${}^{11}$B), which have atomic masses of approximately 10 amu and 11 amu, respectively. To calculate the atomic weight of boron, we consider the natural abundance of each isotope and their respective atomic masses: Atomic weight of Boron = (% abundance of Boron-10 × mass of Boron-10) + (% abundance of Boron-11 × mass of Boron-11) Boron-10 has a natural abundance of approximately 19.8% and Boron-11 has a natural abundance of approximately 80.2%. Therefore, we can calculate the atomic weight of boron as follows: Atomic weight of Boron = (0.198 × 10) + (0.802 × 11) = 1.98 + 8.82 = 10.80 amu (rounded to 10.81 amu) No atom of boron has a mass of exactly 10.81 amu, but this value represents the weighted average mass of boron atoms based on the natural abundances of its isotopes.

Key concepts

Isotopes

Isotopes are fascinating variants of elements that have the same number of protons but differ in the number of neutrons. This means they have the same atomic number but different mass numbers. For example, Boron has two stable isotopes: Boron-10 and Boron-11. Both have 5 protons since they are both Boron, but Boron-10 has 5 neutrons while Boron-11 has 6 neutrons.

Isotopes are crucial in various applications, from medical diagnostics to understanding the age of fossils through radiocarbon dating. They have unique properties due to their different masses. Identifying and understanding isotopes help scientists determine the atomic weight of elements, which is a key component in chemistry and physics.

Some key features of isotopes include:

• Same chemical properties due to identical proton counts.
• Different physical properties because of their varying masses.
• Important role in calculating relative atomic masses of elements.

Atomic Mass Unit (amu)

The Atomic Mass Unit (amu) is a standard unit used to express atomic and molecular weights, making it easier to compare different elements and molecules. By definition, 1 amu is precisely $\frac{1}{12}$ of the mass of a Carbon-12 atom. This choice is primarily because Carbon-12 is a stable and common isotope.

Using amu provides a convenient way to convey the mass of atoms without resorting to unwieldy and large numbers. It simplifies calculations and interpretations in chemistry and physics, making it easier for scientists and students to work with atomic masses.

Remember, the atomic mass of a single proton or neutron is approximately 1 amu. However, because nucleons (protons and neutrons) bind together with a slight loss of mass due to binding energy, which Einstein's equation $E=m{c}^2$ can explain, the mass of Carbon-12's total nucleons slightly differs from 12 amu.

Relative Atomic Mass

The concept of relative atomic mass is essential for understanding the average mass of atoms in a chemical element. It is essentially a weighted average that considers the masses and natural abundances of an element's isotopes. Unlike a simple average, it accounts for how common each isotope is.

For example, with boron, the relative atomic mass is calculated using its two isotopes, Boron-10 and Boron-11. Boron-10 makes up about 19.8% of natural boron, while Boron-11 accounts for about 80.2%. The calculated relative atomic mass of boron is about 10.81 amu, which represents this weighted average and not any single atom's exact mass.

• Helps with determining molar masses used in chemical equations.
• Represents the average mass of atoms of an element.
• Important in the calculation of chemical reactions and formulas.

While no individual atom may have a mass exactly equal to the relative atomic mass, this concept is vital for working with macroscopic amounts of elements.