Atomic Structure & Periodic Table

Isotopes and Relative Atomic Mass

5th Year · 6th Year (Leaving Cert)

✓By the end of this lesson students will be able to define isotopes and explain their properties.
✓By the end of this lesson students will be able to interpret and use isotopic notation.
✓By the end of this lesson students will be able to calculate the relative atomic mass of an element from isotopic masses and abundances.
✓By the end of this lesson students will be able to describe the principles and operation of a mass spectrometer (HL).
✓By the end of this lesson students will be able to interpret mass spectra to determine isotopic abundances and relative atomic mass (HL).

Key concepts

Isotopes

Isotopes are atoms of the same element that have the same number of protons (and thus the same atomic number, Z) but different numbers of neutrons (and thus different mass numbers, A). Because they have the same number of protons and electrons, isotopes of an element have identical chemical properties. However, due to their different masses, they exhibit slightly different physical properties.

Isotopic Notation

Isotopes are represented using isotopic notation, which shows the mass number (A) and the atomic number (Z) along with the element symbol (X). The mass number (A) is the total number of protons and neutrons in the nucleus. The atomic number (Z) is the number of protons in the nucleus. For a neutral atom, the number of electrons is equal to the number of protons. The number of neutrons is calculated as A - Z. An alternative notation is Element-A (e.g., Carbon-12).

^{A}_{Z}X

Relative Atomic Mass (

A_r

)

The relative atomic mass ( $A_r$ ) of an element is the weighted average of the masses of the isotopes of that element, taking into account their relative abundances, compared to 1/12th the mass of a carbon-12 atom. It is a weighted average because different isotopes occur in different proportions in nature. The unit for atomic mass is the atomic mass unit (u), where 1 u is defined as 1/12th the mass of a carbon-12 atom. Relative atomic mass itself has no units as it is a ratio.

A_r = \Sigma (\text{isotopic mass} \times \text{relative abundance})

Mass Spectrometer (HL)

A mass spectrometer is an instrument used to measure the mass-to-charge ratio (m/z) of ions. It is used to determine the exact masses of isotopes and their relative abundances, which allows for the calculation of relative atomic mass. The process involves five main stages: 1. **Vaporisation**: The sample is heated and converted into a gaseous state. 2. **Ionisation**: The gaseous atoms are bombarded with high-energy electrons, knocking off outer electrons to form positive ions (usually +1 charge). 3. **Acceleration**: The positive ions are accelerated by an electric field through a series of charged plates, giving them uniform kinetic energy. 4. **Deflection**: The accelerated ions pass through a strong magnetic field. The magnetic field deflects the ions according to their mass-to-charge ratio (m/z). Lighter ions and more highly charged ions are deflected more significantly. 5. **Detection**: The deflected ions hit a detector, which records the arrival of ions and generates an electric current proportional to their abundance. A mass spectrum is produced, showing relative abundance versus m/z ratio.

Key facts to remember

1Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.
2Isotopes have identical chemical properties but different physical properties due to their mass difference.
3Relative atomic mass ( $A_r$ ) is the weighted average of the masses of an element's isotopes, relative to 1/12th the mass of a carbon-12 atom.
4The standard for relative atomic mass is the carbon-12 isotope.
5A mass spectrometer separates ions based on their mass-to-charge (m/z) ratio (HL).
6The five stages of a mass spectrometer are vaporisation, ionisation, acceleration, deflection, and detection (HL).

Worked examples

Example 1

An atom of an isotope has a mass number of 39 and contains 19 protons. Determine the symbol for this isotope, and state the number of protons, neutrons, and electrons in a neutral atom of this isotope.

I1. Identify the atomic number (Z): The number of protons is 19, so Z = 19.

II2. Identify the element: An element with 19 protons is Potassium (K).

III3. Identify the mass number (A): Given as 39.

IV4. Write the isotopic symbol: Using the notation

^{A}_{Z}X

, the symbol is

^{39}_{19}K

V5. Determine the number of protons: Z = 19, so 19 protons.

VI6. Determine the number of electrons: For a neutral atom, number of electrons = number of protons = 19 electrons.

VII7. Determine the number of neutrons: Number of neutrons = A - Z = 39 - 19 = 20 neutrons.

Answer

The symbol for this isotope is $^{39}_{19}K$ . It contains 19 protons, 20 neutrons, and 19 electrons.

Example 2

Naturally occurring copper consists of two isotopes: copper-63 (mass 62.930 u) with an abundance of 69.17% and copper-65 (mass 64.928 u) with an abundance of 30.83%. Calculate the relative atomic mass of copper.

I1. Convert percentages to decimal abundances:

II Copper-63: 69.17% = 0.6917

III Copper-65: 30.83% = 0.3083

IV2. Apply the formula for relative atomic mass (

A_r

A_r = (\text{isotopic mass}_1 \times \text{abundance}_1) + (\text{isotopic mass}_2 \times \text{abundance}_2)

VI3. Substitute the values:

VII

A_r = (62.930 \text{ u} \times 0.6917) + (64.928 \text{ u} \times 0.3083)

VIII4. Perform the multiplication:

A_r = 43.529021 \text{ u} + 20.0270824 \text{ u}

105. Add the results:

A_r = 63.5561034 \text{ u}

126. Round to an appropriate number of significant figures (e.g., two decimal places, as often used for

A_r

values):

A_r \approx 63.55 \text{ u}

Answer

The relative atomic mass of copper is 63.55 u.

Remember that relative atomic mass has no units, but the isotopic masses are given in atomic mass units (u).

Example 3

(HL) A mass spectrum of an unknown element shows three peaks with the following relative intensities and m/z values: Peak 1: m/z = 24, relative intensity = 78.99%; Peak 2: m/z = 25, relative intensity = 10.00%; Peak 3: m/z = 26, relative intensity = 11.01%. Identify the element and calculate its relative atomic mass.

I1. Identify the isotopes from the m/z values: The isotopes have mass numbers 24, 25, and 26.

II2. Convert relative intensities to decimal abundances:

III Isotope 24: 78.99% = 0.7899

IV Isotope 25: 10.00% = 0.1000

V Isotope 26: 11.01% = 0.1101

VI3. Calculate the relative atomic mass (

A_r

) using the weighted average formula:

VII

A_r = (24 \times 0.7899) + (25 \times 0.1000) + (26 \times 0.1101)

VIII4. Perform the multiplications:

A_r = 18.9576 + 2.5000 + 2.8626

105. Add the results:

A_r = 24.3202

126. Round to an appropriate number of significant figures (e.g., two decimal places):

A_r \approx 24.32

147. Identify the element: The element with a relative atomic mass of approximately 24.32 is Magnesium (Mg).

Answer

The element is Magnesium (Mg), and its relative atomic mass is 24.32.

For simplicity, the m/z values are often taken as the exact isotopic masses in exam questions unless specified otherwise.

Common mistakes

✗Confusing atomic number (protons) with mass number (protons + neutrons).
✗Forgetting to convert percentage abundances to decimal fractions before calculating relative atomic mass.
✗Assuming that the relative atomic mass of an element must be a whole number.
✗Not understanding that a mass spectrometer measures mass-to-charge ratio (m/z), not just mass (HL).
✗Mixing up the order or function of the stages in a mass spectrometer (HL).

Exam tips

★Always show full step-by-step working for calculations of relative atomic mass, including the formula used.
★For mass spectrometry (HL), be able to clearly describe the purpose of each of the five stages.
★Remember that relative atomic mass is a weighted average, so it will be closer to the mass of the most abundant isotope.
★Practice interpreting isotopic notation to quickly determine the number of protons, neutrons, and electrons.

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