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# 4.3: Isotopes and Atomic Mass

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Explain the workings of a mass spectrometer and describe how this device is used to determine average atomic mass.
• Define atomic number and mass number.
• Define isotope.

## Lesson Vocabulary

• atomic number: The number of protons in the nucleus of each atom of an element.
• mass number: The total number of protons and neutrons in an atom.
• A-Z notation: The shorthand notation of the composition of any atom using the atomic number (Z) and the mass number (A).
• isotopes: Atoms that have the same atomic number but different mass numbers due to a difference in the number of neutrons.
• mass spectrometer: An instrument that determines the masses of atoms, molecules, and molecular fragments.
• percent abundance: The percentage of atoms of a particular isotope in a naturally occurring sample of the pure element.
• atomic mass: The weighted average of the atomic masses of the naturally occurring isotopes of an element.

• Describe the composition of an atom.
• What are the three subatomic particles and what are their properties?

## Introduction

Atoms are the fundamental building blocks of all matter and are composed of protons, neutrons, and electrons. Because atoms are electrically neutral, the number of positively charged protons must be equal to the number of negatively charged electrons. One of Dalton’s points in his atomic theory was that all atoms of a given element are identical in mass. In this section, we will see how this is not strictly true, due to variability in the number of neutrons that an atom may contain.

## Atomic Number

The atomic number of an element is the number of protons in the nucleus of each atom of that element. An atom can be classified as a particular element based solely on its atomic number. For example, any atom with an atomic number of 8 (its nucleus contains 8 protons) is an oxygen atom, and any atom with a different number of protons would be a different element. The periodic table (Figure below) displays all of the known elements and is arranged in order of increasing atomic number. In this table, an element’s atomic number is indicated above the elemental symbol. Hydrogen, at the upper left of the table, has an atomic number of 1. Every hydrogen atom has one proton in its nucleus. Next on the table is helium, whose atoms have two protons in the nucleus. Lithium atoms have three protons, beryllium atoms have four, and so on. Since atoms are neutral, the number of electrons in an atom is equal to the number of protons. Therefore, hydrogen atoms all have one electron occupying the space outside of the nucleus.

The periodic table of the elements.

## Mass Number

Rutherford’s experiment showed that the vast majority of the mass of an atom is concentrated in its nucleus, which is composed of protons and neutrons. The mass of an electron is very small compared to the mass of a neutron or proton, so the electrons in an element do not contribute much to the total mass. The mass number is defined as the total number of protons and neutrons in an atom. Remember that both protons and neutrons have a mass of approximately 1 amu. Knowing the mass number and the atomic number of an atom therefore allows you to determine the number of neutrons present in that atom by subtraction:

Number of neutrons = mass number - atomic number

The composition of any atom can be illustrated with a shorthand notation, sometimes called A-Z notation, using the atomic number (Z) and the mass number (A). The general form for this notation is as follows:

AZX\begin{align*}\mathrm{ ^{A}_{Z} X}\end{align*}

For example, a chromium atom that has 24 protons and 28 electrons could be written as:

5224Cr\begin{align*}{}_{24}^{52}\text{Cr}\end{align*}

Another way to refer to a specific atom is to write the mass number of the atom after the name, separated by a hyphen. The above atom would be written as chromium-52.

## Isotopes

As stated earlier, not all atoms of a given element are identical. Specifically, the number of neutrons in the nucleus can vary for many elements. As an example, naturally occurring carbon exists in three forms, which are illustrated in Figure below.

Nuclei of the three isotopes of carbon: Almost 99% of naturally occurring carbon is carbon-12, whose nucleus consists of six protons and six neutrons. Carbon-13 and carbon-14, with seven or eight neutrons, respectively, have a much lower natural abundance.

Each carbon atom has the same number of protons (6), which is equal to its atomic number. Each carbon atom also contains six electrons, allowing the atom to remain electrically neutral. However the number of neutrons varies from six to eight. Isotopes are atoms that have the same atomic number but different mass numbers due to a change in the number of neutrons. The three isotopes of carbon can be referred to as carbon-12 (12 6C\begin{align*}{}_{\ 6}^{12}\text{C}\end{align*}), carbon-13 (13 6C\begin{align*}{}_{\ 6}^{13}\text{C}\end{align*}), and carbon-14 (14 6C\begin{align*}{}_{\ 6}^{14}\text{C}\end{align*}). Naturally occurring samples of most elements are mixtures of isotopes. Carbon has only three natural isotopes, but some heavier elements have many more. Tin has ten stable isotopes, which is the most of any element. While the presence of isotopes affects the mass of an atom, it does not affect its chemical reactivity. Chemical behavior is governed by the number of electrons and the number of protons. Carbon-13 behaves chemically in exactly the same way as the more plentiful carbon-12.

Example 4.1

Silver has two known isotopes, one with 60 neutrons and the other with 62 neutrons. What are the mass numbers and symbols of these isotopes?

## Atomic Mass and the Mass Spectrometer

Beginning in the early part of the twentieth century, scientists were approaching a new understanding of the composition of the atom. Several major discoveries demonstrated that the atom contained a nucleus, where protons and neutrons are situated. It was discovered that electrons surrounded the nucleus and it was later determined that electrons primarily determine the chemical properties of elements. Several devices were created during this time which demystified the inner workings of the atom and the composition of elements. One such device was the mass spectrometer, which was developed in 1918 by Arthur Jeffrey Dempster. The mass spectrometer is an instrument for determining the masses of atoms, molecules, and molecular fragments. The Figure below illustrates a modern mass spectrometer.

An electron is removed from an atom to yield a positive ion (such as H+, O+, or N+). The ions are then accelerated and deflected by a magnetic field. The degree of deflection directly relates to the mass of the ion: the lighter the ion, the greater the deflection and the heavier the ion, the lesser the deflection. The beam of ions is then detected and the relative abundance of each isotope of an element can then be determined.

If we were to place a sample of carbon into a mass spectrometer and analyze its mass, we would find that some of the carbon atoms have a relative mass of 12, while other atoms have a relative mass of 13, and still others have a relative mass of 14. The mass spectrometer measures the percent abundance of these carbon isotopes. Percent abundance is the percentage of atoms in a naturally occurring sample of the pure element that are a particular isotope. We can represent the percent abundance of carbon with what is known as a mass spectrogram, shown in the Figure below.

Mass spectrogram for carbon.

The spectrogram reveals the percent abundances of the variants of carbon atoms consists of 98.9% 12C, 1.1% 13C, and << 0.1% 14C. Because we generally deal with very large amounts of atoms, it is more practically useful to know the average mass of each atom in a large sample as determined by the percent abundance of each isotope. The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element.

Example 4.2

Using the percent abundances for each carbon isotope as given above, calculate the weighted average for the atomic mass of carbon.

We calculate average atomic mass by taking the percent abundance of each isotope and multiplying this by the atomic mass of the isotope.

12C

0.989 × 12 = 11.868

13C

0.011 × 13 = 0.143

Then, add these values together to get the relative atomic mass:

11.868 + 0.143 = 12.011

Therefore, the average atomic mass of carbon is calculated to be 12.011. This is the same number that is listed on the periodic table.

## Lesson Summary

• The atomic number (Z) of an element is equal to the number of protons in its nucleus.
• The mass number (A) of an element is equal to the sum of the protons and the neutrons in its nucleus.
• Isotopes are atoms of the same element that have a different mass number (A) but the same atomic number (Z).
• Isotopes have the same number of protons and electrons, but a different number of neutrons.
• The mass spectrometer measures the percent abundance of different isotopes in a given sample.
• The average atomic mass of an element can be calculated from the atomic mass and percent abundance of each naturally occurring isotope.

## Review Questions

1. Describe in general terms how a mass spectrometer functions.
2. Complete Table below:
1H 2H 3H 23Na 35Cl 14C 12C
protons
electrons
neutrons
1. What is the mass number of a tin atom that has 69 neutrons? Write its full symbol.
2. How many neutrons are there in an atom of platinum with a mass number of 195?
3. What is the mass number of a copper atom with 34 neutrons?
4. How many protons, neutrons, and electrons are there in a 5928Ni\begin{align*}\mathrm{ ^{59}_{28} Ni}\end{align*} atom?
5. Silicon has three isotopes with 14, 15, and 16 neutrons, respectively. What are the mass numbers and symbols of these three isotopes?
6. A natural sample of boron consists of two isotopes. One has an exact mass of 10.0129 amu and its percent abundance is 19.91. The other isotope, of mass 11.0093 amu, has a percent abundance of 80.09. Calculate the average atomic mass.

## Points to Consider

• In this chapter, we discussed the structure of the atom and saw that it contains a nucleus that consists of protons and neutrons. The nucleus is surrounded by negatively charged particles called electrons. How do you think electrons might be arranged around the nucleus?

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