Lesson Explainer: Isotopes Chemistry

In this explainer, we will learn how to define and identify isotopes of an element, list some of their properties and uses, and calculate the relative atomic mass of an element from isotopic abundances.

The nucleus of an atom contains protons and neutrons. All atoms of a given element will have the same number of protons in their nucleus. The number of protons is represented by the atomic number on the periodic table.

Definition: Atomic Number

Atomic number is the number of protons in the nucleus of an atom. It is also the number of an element on the periodic table, and it ranges from 1 to 118.

Therefore, all atoms of oxygen will have eight protons and all atoms of boron will have five protons. However, all atoms of a given element will not necessarily have the same number of neutrons in their nucleus.

If we were to sample all the atoms of boron that naturally occur, we would find two types of boron atoms, shown below.

At first glance, these atoms appear to be the same; however, the atom on the left contains six neutrons, whereas the atom on the right contains five neutrons. Atoms that contain the same number of protons but a different number of neutrons are called isotopes.

Definition: Isotopes

Isotopes are atoms that have the same number of protons but a different number of neutrons.

The word isotope comes from the Greek ísos meaning same and tópos meaning place or position. The term was first suggested by Scottish doctor Margaret Todd to describe an idea proposed by chemist Frederick Soddy, which is that several types of atoms may share the same position (atomic number) on the periodic table.

Isotopes of an element share nearly identical chemical properties. This is because chemical properties such as reactivity are determined primarily by the number of protons and electrons in an atom. However, isotopes do differ in their nuclear stability.

Inside the nucleus, the positively charged protons repel one another strongly; however, there are also many short-range attractive forces that occur between two protons, two neutrons, or a proton and a neutron. The nucleus is stable when the attractive forces outweigh the repulsive forces. When the repulsive forces prevail, the nucleus is unstable and will emit particles and/or radiation to improve its stability. Too few or too many neutrons in the nucleus can tip the balance of forces causing the isotope to be unstable and radioactive.

Radioactive isotopes have many useful applications both in medicine and in different industries. Iodine-131, which has 78 neutrons, is used to treat thyroid disorders. Cobalt-33, which has 33 neutrons, and cesium-137 are used as a cancer treatment. Americium-241, which has 146 neutrons, is found in smoke detectors. Uranium-235 powers nuclear reactors, and nickel-63 is used to detect explosives.

Example 1: Definition of Isotopes

Fill in the blank: Isotopes are atoms with the same number of protons but a different number of .

Answer

Atoms that have a different number of protons are different elements. Atoms that have the same number of protons but a different number of electrons are called ions. Atoms that have the same number of protons but a different number of neutrons are called isotopes. We should fill in the blank with the word neutrons.

In addition to having a different number of neutrons, isotopes of an element will also have a different mass number.

Definition: Mass Number

Mass number is the sum of the protons and neutrons in the nucleus.

We can quickly distinguish between isotopes by representing each isotope using nuclide notation, where the top-left number is the mass number and the bottom-left number is the atomic number: 105115BB

We can also distinguish between them using simplified nuclide notation: 1011BB

Moreover, this can also be done using hyphen notation: boron-10boron-11

Example 2: Classifying Isotopes by Mass from Nuclide Notation

Which of the following isotopes is the heaviest?

  1. 4018Ar
  2. 4119K
  3. 4020Ca
  4. 3919K
  5. 4418Ar

Answer

In nuclide notation, the number written in the top left is the mass number (𝐴). The mass number is the sum of the number of protons and neutrons in an atom and represents the approximate mass of the atom. The number written on the bottom left is the atomic number (𝑍). The atomic number represents the number of protons in the atom.

We need to compare the mass numbers to find the largest value. The largest mass number is 44. This means that answer choice E is the heaviest isotope.

Example 3: Identifying Isotopes Based on Isotope Names

Which of the following is an isotope of carbon-12?

  1. Boron-11
  2. Carbon-14
  3. Oxygen-12
  4. Oxygen-16
  5. Nitrogen-15

Answer

Isotopes are atoms that have the same number of protons but a different number of neutrons. Carbon, which has the atomic number six, has six protons. In the hyphen notation carbon-12, the 12 represents the mass number of this carbon atom. The mass number is the sum of the protons and neutrons. We can substitute the mass number and number of protons into the mass number equation massnumbernumberofprotonsnumberofneutrons=+ and solve for the number of neutrons as follows: 12=6+6=.numberofneutronsnumberofneutrons

This isotope of carbon has six neutrons. To be an isotope of carbon-12, the atom must have six protons but not six neutrons. Atoms of the same element will have the same number of protons. This means that the only potential isotope of carbon-12 is answer choice B as only the element carbon will have six protons.

We can verify that answer choice B has a different number of neutrons by substituting the mass number (14) and the number of protons (6) into the mass number equation as follows: massnumbernumberofprotonsnumberofneutronsnumberofneutronsnumberofneutrons=+14=6+8=.

With six protons and eight neutrons, answer choice B is an isotope of carbon-12.

Each isotope of an element has a different number of neutrons, a different mass number, and a different exact mass. The given table shows the approximate masses of a proton, a neutron, and an electron.

ParticleApproximate Mass (kg)Approximate Mass (u)
Proton1.6726×101.0073
Neutron1.6749×101.0087
Electron9.1094×105.4858×10

We can calculate the mass of each isotope of boron in kilograms or unified atomic mass units by adding the masses of the subatomic particles.

Boron IsotopesCalculated Mass (kg)Calculated Mass (u)
5 protons, 5 neutrons, 5 electrons1.6742×10 kg10.083
5 protons, 6 neutrons, 5 electrons1.8415×10 kg11.091

We can also determine the relative mass of each isotope of boron by comparing the mass of each boron isotope to the mass of 112 of a carbon atom 1.660539×10kg.

Boron IsotopesCalculated Mass
(kg)
Calculated Mass
(u)
Relative MassMass Number
5 protons, 5 neutrons, 5 electrons1.6742×10 kg10.08310.08310
5 protons, 6 neutrons, 5 electrons1.8415×10 kg11.09111.09111

The calculated mass in kilograms is a very small value and is difficult to work with. The calculated mass in unified atomic mass units and the relative mass of each atom are values that are much easier to use. Notice that the mass in unified atomic mass units and the relative mass are very close to the mass number of each isotope. It is common to use the mass number to refer to the mass of an isotope as a simplification, but we must recognize that the mass number is not the true mass of the isotope.

The two isotopes of boron have approximate masses of 10 and 11; however, if we look at the periodic table, we do not find either of these values for boron. Instead, we see the value 10.8 written below the chemical symbol.

The 10.8 represents the average atomic mass of the two isotopes of boron.

To calculate the mass shown on the periodic table, we may imagine that we could average the masses of the two boron isotopes. The mass number is frequently used in these calculations as an estimate of the relative mass to simplify the process. Thus, Averagemassofboron=(10+11)2=10.5.

However, this procedure gives us a value of 10.5 and not 10.8. What we neglected to consider is how common each boron isotope is. If we examined all of the naturally occurring atoms of boron, we would find that approximately 80% of them are boron-11 and 20% are boron-10.

These percentages represent the abundance, the relative amount of each naturally occurring isotope of an element. The sum of the abundances should always equal 100%.

Definition: Abundance

Abundance is the percentage that represents the relative amount of an isotope of an element.

We must consider the abundance of each isotope when determining the average mass. We call the result of this weighted average the relative atomic mass.

Equation: Calculating Relative Atomic Mass

Relativeatomicmassisotopeabundanceisotopemassnumberisotopeabundanceisotopemassnumber=(1×1)+(2×2)+.

The dots in the equation indicate that we should continue adding the isotope abundance times the isotope mass number for each isotope of that particular element. It is important to remember that the abundance percentage must be in decimal form when solving.

We can substitute the abundance and mass number for each of the two isotopes of boron into the relative atomic mass equation and solve for the relative atomic mass of boron as follows: relativeatomicmass=(0.2×10)+(0.8×11)=10.8.

This gives us the value of 10.8, a unitless value, which is the average atomic mass shown on many periodic tables for boron, depending on the accuracy of the table. While all elements have isotopes, not every element has a relative atomic mass on the periodic table. The man-made elements do not occur naturally and therefore do not have abundances. The mass of their most stable isotope is often shown in parenthesis in lieu of a relative atomic mass.

Example 4: Calculating the Relative Atomic Mass of Chlorine from Isotopic Abundances

Chlorine has two stable isotopes, chlorine-35 and chlorine-37. A sample of chlorine was analyzed using a mass spectrometer, and the following isotopic abundances were calculated.

IsotopeAbundance (mol%)
Chlorine-3575.8%
Chlorine-3724.2%

What is the relative atomic mass of chlorine in the sample?

Answer

First, we must recognize that 35 is the mass number of an atom of chlorine-35 and 37 is the mass number of an atom of chlorine-37. We are given the abundance of each of these isotopes in a sample. We can substitute the abundance and mass number of each isotope into the relative atomic mass equation to calculate the relative atomic mass of chlorine in the sample using the following equation: relativeatomicmassisotopeabundanceisotopemassnumberisotopeabundanceisotopemassnumber=(1×1)+(2×2).

We must convert the percentages into decimal notation before solving. This can be done by dividing each percentage by 100. Thus, 75.8% is 0.758 in decimal notation, and 24.2% is 0.242 in decimal notation. This gives us relativeatomicmass=(0.758×35)+(0.242×37)=35.5.

The relative atomic mass of the chlorine in the sample is 35.5.

Example 5: Calculating the Relative Atomic Mass of Magnesium from Isotopic Abundances

Magnesium exists as three isotopes: magnesium-24, magnesium-25, and magnesium-26. Their isotopic abundances are 79%, 10%, and 11% respectively. What is the relative atomic mass of magnesium to 1 decimal place?

Answer

First, we must recognize that in the notation magnesium-24, the 24 represents the mass number of this isotope of magnesium. We can organize the information given in the question so that we have a mass number and abundance for each isotope. We can also convert the percent abundance into decimal form by dividing the percent by 100.

IsotopeMass NumberAbundanceAbundance in Decimal Form
Magnesium-242479%0.79
Magnesium-252510%0.1
Magnesium-262611%0.11

We can use the following relative atomic mass equation: relativeatomicmassisotopeabundanceisotopemassnumberisotopeabundanceisotopemassnumberisotopeabundanceisotopemassnumber=(1×1)+(2×2)+(3×3).

We can substitute the mass number and abundance in decimal form for each isotope into the equation as follows: relativeatomicmass=(0.79×24)+(0.1×25)+(0.11×26)=24.32.

The relative atomic mass of magnesium rounded to one decimal place is 24.3.

Key Points

  • Atoms that have the same number of protons but a different number of neutrons are called isotopes.
  • Isotopes of an element have similar chemical properties but differ in their radioactivity.
  • The mass shown on the periodic table for each element is the relative atomic mass.
  • The equation for relative atomic mass is relativeatomicmassisotopeabundanceisotopemassnumberisotopeabundanceisotopemassnumber=(1×1)+(2×2)+.

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