5.6 Atomic Mass

The development of modern atomic theory revealed much about the inner structure of atoms. It was learned that an atom contains a very small nucleus composed of positively charged protons and uncharged neutrons, surrounded by a much larger volume of space containing negatively charged electrons. The nucleus contains the majority of an atom’s mass because protons and neutrons are much heavier than electrons, whereas electrons occupy almost all of an atom’s volume. The diameter of an atom is on the order of 10 −10 m, whereas the diameter of the nucleus is roughly 10 −15 m—about 100,000 times smaller. For a perspective about their relative sizes, consider this: If the nucleus were the size of a blueberry, the atom would be about the size of a football stadium (Figure 5.6a).

The diagram on the left shows a picture of an atom that is 10 to the negative tenth power meters in diameter. The nucleus is labeled at the center of the atom and is 10 to the negative fifteenth power meters. The central figure shows a photograph of an American football stadium. The figure on the right shows a photograph of a person with a handful of blueberries.

Video Source: TED-Ed. (2012, April 16). Just how small is an atom? [Video]. YouTube.

Atoms—and the protons, neutrons, and electrons that compose them—are extremely small. For example, a carbon atom weighs less than 2 × 10 −23 g, and an electron has a charge of less than 2 × 10 −19 C (coulomb). When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu) and the fundamental unit of charge (e). The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which are assigned masses of exactly 12 amu. (This isotope is known as “carbon-12”). Thus, one amu is exactly [latex]\frac[/latex] of the mass of one carbon-12 atom: 1 amu = 1.6605 × 10 −24 g. (The Dalton (Da) and the unified atomic mass unit (u) are alternative units that are equivalent to the amu.) The fundamental unit of charge (also called the elementary charge) equals the magnitude of the charge of an electron (e) with e = 1.602 × 10 −19 C.

A proton has a mass of 1.0073 amu and a charge of 1+. A neutron is a slightly heavier particle with a mass 1.0087 amu and a charge of zero; as its name suggests, it is neutral. The electron has a charge of 1− and is a much lighter particle with a mass of about 0.00055 amu (it would take about 1800 electrons to equal the mass of one proton). The properties of these fundamental particles are summarized in Table 5.6a. (An observant student might notice that the sum of an atom’s subatomic particles does not equal the atom’s actual mass. The total mass of six protons, six neutrons, and six electrons is 12.0993 amu, slightly larger than 12.00 amu. This “missing” mass is known as the mass defect, which you can learn about it if you study nuclear chemistry.)

Table 5.6a: Properties of Subatomic Particles
Name Location Charge (C) Unit Charge Mass (amu) Mass (g)
electron outside nucleus −1.602 × 10 −19 1− 0.00055 0.00091 × 10 −24
proton nucleus 1.602 × 10 −19 1+ 1.00727 1.67262 × 10 −24
neutron nucleus 0 0 1.00866 1.67493 × 10 −24

Atomic Mass

Because each proton and each neutron contribute approximately one amu to the mass of an atom, and each electron contributes far less, the atomic mass of a single atom is approximately equal to its mass number (a whole number). However, the average masses of atoms of most elements are not whole numbers because most elements exist naturally as mixtures of two or more isotopes, each with their own slightly different masses due to the different number of neutrons they contain.

The mass of an element shown in a periodic table or listed in a table of atomic masses is a weighted, average mass of all the isotopes present in a naturally occurring sample of that element. This is equal to the sum of each individual isotope’s mass multiplied by its fractional abundance.

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For example, the element boron is composed of two isotopes: About 19.9% of all boron atoms are 10 B with a mass of 10.0129 amu, and the remaining 80.1% are 11 B with a mass of 11.0093 amu. The average atomic mass for boron is calculated to be:

It is important to understand that no single boron atom weighs exactly 10.8 amu; 10.8 amu is the average mass of all boron atoms, and individual boron atoms weigh either approximately 10 amu or 11 amu.

Exercise 5.6a

Calculating Average Atomic Mass

5.6a – Calculating Average Atomic Mass (Text version)

A meteorite found in central Indiana contains traces of the noble gas neon picked up from the solar wind during the meteorite’s trip through the solar system. Analysis of a sample of the gas showed that it consisted of 91.84% 20 Ne (mass 19.9924 amu), 0.47% 21 Ne (mass 20.9940 amu), and 7.69% 22 Ne (mass 21.9914 amu). What is the average mass of the neon in the solar wind?

STEP 1 – List known quantities and identify what you are asked to find

Known information: Isotopes of neon – 91.84% 20 Ne (mass 19.9924 amu), 0.47% 21 Ne (mass 20.9940 amu), and 7.69% 22 Ne (mass 21.9914 amu).

What am I asked to Find: average mass of the neon in the solar wind

Step 2 – Determine how you will solve the problem

Use the following formula to solve problem:

Step 3 – Solve the Problem

The average mass of a neon atom in the solar wind is 20.15 amu. (The average mass of a terrestrial neon atom is 20.1796 amu. This result demonstrates that we may find slight differences in the natural abundance of isotopes, depending on their origin.)

Step 4 – Does the answer make sense?