Isotopes, Mass Spectrometry, and Average Atomic Mass

Vasily Kandinsky

Composition 8

1923 

Vocabulary

• isotope
• relative abundance
• mass spectrum
• average atomic mass

AP Topics

Topic 1.2: Mass Spectra of Elements

Learning Objective: Explain the quantitative relationship between the mass spectrum of an element and the masses of the element’s isotopes.

Essential Knowledge:

• The mass spectrum of a sample containing a single element can be used to determine the identity of the isotopes of that element and the relative abundance of each isotope in nature.
• The average atomic mass of an element can be estimated from the weighted average of the isotopic masses using the mass of each isotope and its relative abundance.

Quick Review

Protons

• have positive charge
• located in the nucleus (Rutherford)
• have a mass of 1 amu
• determine the identity of element.
• all atoms of the same element must have the same number of protons.
• the atomic number is equal to the number of protons…always!

Quick Review

Neutrons

• have no charge
• located in the nucleus (Chadwick)
• have a mass of 1 amu
• Atoms of the same element can have different number of neutrons
• These atoms with different numbers of neutrons make up the different isotopes of the element.

Quick Review

Electrons

• have a negative charge
• located in energy levels around the nucleus (Bohr)
• have a mass ~1800x less than protons and neutrons so have a mass ~0 amu
• Neutral atoms have the same number of protons and electrons
• Atoms can gain or lose electrons to become ions (charged atoms)
• Losing electrons creates positive ions (cations) and gaining electrons creates negative ions (anions).

Quick Review

Atomic number (Z)

• Number of protons
• Identifies the element
• Found on periodic table

Mass number (A)

• Number of protons + number of neutrons
• Identifies the isotope of an element
• Not found on the periodic table

Isotopes

• Isotopes are variations of atoms of the same element (same numbers of protons) with different numbers of neutrons.
• Each of the isotopes of the same element have the same atomic number (protons) but different mass numbers (protons + neutrons)
• Almost all elements have multiple naturally occurring isotopes

Example

oxygen-16

Remember what this number means?

Isotopes

• Isotopes are variations of atoms of the same element (same numbers of protons) with different numbers of neutrons.
• Each of the isotopes of the same element have the same atomic number (protons) but different mass numbers (protons + neutrons)
• Almost all elements have multiple naturally occurring isotopes

Example

oxygen-16

oxygen-17

Isotopes

• Isotopes are variations of atoms of the same element (same numbers of protons) with different numbers of neutrons.
• Each of the isotopes of the same element have the same atomic number (protons) but different mass numbers (protons + neutrons)
• Almost all elements have multiple naturally occurring isotopes

Example

oxygen-16

oxygen-17

oxygen-18

Relative abundance:

The percentage of

each isotope that

occurs naturally

Example

A lump of carbon is shown to the left. If you analyzed the carbon atoms in it, you would find three different isotopes of carbon:

• carbon-12
• carbon-13
• carbon-14

Example

How many protons, neutrons, and electrons are located in atoms of each of the following isotopes of carbon?

• carbon-12
• carbon-13
• carbon-14

6, 6, 6

6, 7, 6

6, 8, 6

Identifying Isotopes

So How Do We Know That �Elements Have Different Isotopes?

Overview of Mass Spectrometry

Mass Spectrometry is an analytic technique that utilizes the degree of deflection of charged particles by a magnetic field to find the relative masses of atomic and molecular ions and fragments. It is a powerful method because it provides a great deal of information and can be conducted on tiny samples.

What properties of a particle do you think affect how it deflects as it passes through a magnetic field?

• Mass
• Charge

Prediction

In the diagram below, which path of particles passing through the magnetic separator do you think shows particles with the least mass assuming all of the particles have the same charge?

A

B

C

Prediction

In the diagram below, which path of particles passing through the magnetic separator do you think shows particles with the least mass assuming all of the particles have the same charge?

C

Applications

Mass spectrometry has a number of applications in organic chemistry, including:

• Determining molecular mass
• Finding out the structure of an unknown substance
• Verifying the identity and purity of a known substance
• Providing data on isotopic abundance

Example

A mass spectrum is shown below for a sample of zirconium.

Each line represents an isotope of zirconium and the height of each line is proportional to the relative abundance of each isotope.

Which isotope of Zr is most abundant? Least?

Which isotope has the greatest mass?

Average Atomic Mass

The periodic table shows the average atomic mass of each element. This is the weighted average mass of all the atoms of that element. It is calculated using the following formula:

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Avg Atomic Mass = %₁ x mass₁ + %₂ x mass₂ + %₃ x mass₃ + …

must be % as decimal!!!

Example

Let’s calculate the average atomic mass of zirconium based on its mass spectrum.

Atomic Weight = %₁ x mass₁ + %₂ x mass₂ + %₃ x mass₃ + …

= 0.5285 x 90. + 0.1172 x 91 + 0.1715 x 92 + 0.1708 x 94 + 0.0120 x 96

= 91.2 amu

Example 2

Magnesium has three naturally occurring isotopes. 78.70% of magnesium atoms exist as magnesium-24, 10.03% exist as magnesium-25, and 11.17% exist as magnesium-26. What is the average atomic mass of magnesium?

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Avg atomic mass = 0.7870 x 24 + 0.1003 x 25 + 0.1117 x 26

​

Answer: 24.30 amu

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