Name: average atomic mass and isotopes
Uploaded: 2020-09-03T13:38:25.000Z
Duration: 1 min 52 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.2.1

Atomic Mass

The mass of a single atom is very small, so it is not practical to measure the mass in grams or kilograms. The mass of atoms and molecules are measured in units called Daltons, abbreviated Da, or atomic mass units, abbreviated amu, or sometimes just u.

The mass of an atom in amu is approximately equal to the sum of the number of protons and the number of neutrons; however, most elements have several naturally occurring isotopes. Each of these isotopes has a different number of neutrons and, therefore, a different mass.

For each element, its average mass is calculated by summing the masses of the element&#8217;s isotopes, each multiplied by its natural fractional abundance on Earth. 

The mass and relative abundance of various isotopes of an element can be determined using mass spectrometry. The isotopes are separated by mass, and the mass spectrum of a sample shows the relative abundance of the isotopes.

These values are used to calculate the average atomic mass that appears on the periodic table.

The mass spectrum of a representative sample of boron shows that 19.9% of this sample is boron-10 with a mass of 10.0129 amu. The rest is boron-11 with a mass of 11.0093 amu. 

The mass of boron-10 and boron-11 are each multiplied by their fractional abundance, 19.9 per 100 for boron-10 and 80.1 per 100 (the remainder) for boron-11. These values are then summed to find the average atomic mass of boron.

atomic mass

Atoms &#8212; and the protons, neutrons, and electrons that compose them &#8212; are extremely small. For example, a carbon atom weighs less than 2 &#215; 10&#8722;23 g. When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu). 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. Thus, one amu is exactly 1/12 of the mass of one carbon-12 atom: 1 amu = 1.6605 &#215; 10&#8722;24 g. The Dalton (Da) and the unified atomic mass unit (u) are alternative units that are equivalent to the amu. 

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 sum of protons and neutrons in the atom). For example, the mass number of a single nitrogen atom is 14 (7 protons + 7 neutrons). 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. Isotopes are atoms of the same element with the same proton number but a different number of neutrons. 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. The average mass is equal to the sum of each individual isotope&#8217;s mass multiplied by its fractional abundance.

<img alt="Average mass equation, &#931;(fractional abundance &#215; isotope mass), chemistry formula diagram." src="/files/core/CDNSource/lessons/807/807_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

For example, the element chlorine (atomic number 17) is composed of two isotopes: 35Cl and chlorine 37Cl. About 75.78% of all chlorine atoms are 35Cl with a mass of 34.969 amu, and the remaining 24.22% are 37Cl with a mass of 36.966 amu. The average atomic mass for chlorine is calculated to be:

<img alt="Chlorine isotopic average mass calculation formula; static, educational chemistry concept." src="/files/core/CDNSource/lessons/807/807_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

It is important to understand that no single chlorine atom weighs exactly 35.45 amu; This value is the average mass of all chlorine atoms, and individual chlorine atoms weigh either approximately 35 amu or 37 amu. Also, because naturally occurring chlorine contains more 35Cl atoms than 37Cl atoms, the weighted average mass of chlorine is closer to 35 amu than to 37 amu.

The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer. Mass spectrometry (MS) is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. In a typical mass spectrometer, the sample is vaporized and exposed to a high-energy electron beam that causes the sample&#8217;s atoms or molecules to become electrically charged, typically by losing one or more electrons. These cations then pass through a variable magnetic field that deflects each cation&#8217;s path to the extent that depends on both its mass and charge. Finally, the ions are detected, and a plot of the relative number of ions generated versus their mass-to-charge ratios, a mass spectrum, is made. The height of each vertical feature or peak in a mass spectrum is proportional to the fraction of cations with the specified mass-to-charge ratio. Since its first use during the development of modern atomic theory, MS has evolved to become a powerful tool for chemical analysis in a wide range of applications.

Text adapted from <a href="https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism">Openstax Chemistry 2e, Section 2.3: Atomic Structure and Symbolism.</a>

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Education

JoVE Core

Atoms and Elements

KEY TERMS AND CONCEPTS

average atomic mass and isotopes

Average atomic mass explains why many elements on the periodic table have decimal values. Atoms are extremely small, so scientists use the atomic mass unit, or amu, to measure them. A carbon atom weighs less than 2 × 10−23 g, and the amu is defined from carbon-12. One amu is exactly 1/12 the mass of one carbon-12 atom, which is 1.6605 × 10−24 g. The dalton (Da) and the unified atomic mass unit (u) mean the same thing as the amu.

For a single atom, atomic mass is usually close to its mass number. The mass number is the total of protons and neutrons in the atom. Each proton and neutron contributes about 1 amu, while each electron adds far less. For example, a nitrogen atom has a mass number of 14 because it has 7 protons and 7 neutrons.

Most elements do not have a whole-number atomic mass because they exist as mixtures of isotopes. Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. The atomic mass listed for an element in the periodic table is a weighted average of the masses of all naturally occurring isotopes. This average is found by multiplying each isotope’s mass by its fractional abundance and then adding the results.

Chlorine is a good example. It has two isotopes, chlorine-35 and chlorine-37. About 75.78% of chlorine atoms are chlorine-35 with a mass of 34.969 amu, and 24.22% are chlorine-37 with a mass of 36.966 amu. The average atomic mass of chlorine is 35.45 amu. No single chlorine atom has exactly that mass. Individual chlorine atoms are closer to 35 amu or 37 amu, depending on the isotope.

Scientists can measure isotopes and their natural abundance with a mass spectrometer. Mass spectrometry, or MS, is used in chemistry, forensics, medicine, environmental science, and other fields to identify substances in a sample. In a mass spectrometer, the sample is vaporized and hit with a high-energy electron beam. This makes the atoms or molecules become charged, usually by losing one or more electrons. The cations then move through a magnetic field, which bends their paths based on mass and charge. The detector records them and creates a mass spectrum, a graph of ion count versus mass-to-charge ratio. Each peak shows how many ions have a given mass-to-charge ratio. Since its early use in modern atomic theory, MS has become a powerful tool for chemical analysis.

Average Atomic Mass and Isotopes

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Average atomic mass explains why many elements on the periodic table have decimal values. Atoms are extremely small, so scientists use the atomic mass unit, or amu, to measure them. A carbon atom weighs less than 2 × 10−23 g, and the amu is defined from carbon-12. One amu is exactly 1/12 the mass of one carbon-12 atom, which is 1.6605 × 10−24 g. The dalton (Da) and the unified atomic mass unit (u) mean the same thing as the amu. For a single atom, atomic mass is usually close to its mass...

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Learn how isotopes, fractional abundance, and mass spectrometry explain average atomic mass values on the periodic table for high school chemistry.

Average Atomic Mass and Isotopes | JoVE K12

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ohios-learning-standards-and-model-curriculum

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Physical Science

Study Of Matter

Atoms

Structure And Properties Of Matter

Quantifying matter

Physical Geology

Minerals

Atoms and elements

Virginia  Standards of Learning

HIgh School

CH.2

CH.2.a

CH.4

CH.4.a

PS.4

PS.4.a

Texas Essential Knowledge and Skills

High School

CHEM.8

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CHEM.11

CHEM.11.E

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Average Atomic Mass and Isotopes

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