Mass number and isotopes — AQA A-Level Chemistry
Test yourself on Mass number and isotopes with AQA A-Level practice questions.
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Mass number and isotopes explained
The atomic number Z is the number of protons in the nucleus, and it alone fixes which element you have; change it and you have a different element.
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The mass number A counts the protons and the neutrons together, so the number of neutrons is simply A − Z. In the standard notation the mass number sits above the atomic number to the left of the symbol. A is always a whole number because you cannot have a fraction of a nuclear particle, which is why a time of flight calculation that ends at 84.04 is reported as mass number 84. Relative atomic mass is a different quantity, an abundance-weighted mean across isotopes, and it is usually not a whole number.
Students should be able to: determine the number of fundamental particles in atoms and ions using mass number, atomic number and charge explain the existence of isotopes.
Counting particles is a three-step routine. Protons equal the atomic number. Neutrons equal mass number minus atomic number. Electrons equal protons minus the charge, so a 2⁺ ion has lost two electrons and a 1⁻ ion has gained one; subtracting the signed charge handles both cases in one step. Isotopes exist because the number of neutrons in a nucleus can vary while the proton count stays fixed, so the element is unchanged but the mass number differs. Because isotopes have the same number of electrons and therefore the same electron configuration, they react in exactly the same way; the mark scheme credits same electron configuration and ignores answers based only on the proton count.
The principles of a simple time of flight (TOF) mass spectrometer, limited to ionisation, acceleration to give all ions constant kinetic energy, ion drift, ion detection, data analysis.
A time of flight spectrometer separates ions by mass in five stages. The sample is vaporised and ionised, usually by electron impact for an element. An electric field then accelerates every ion through the same potential difference, so each ion leaves with the same kinetic energy. Since kinetic energy is ½mv², equal energy means a heavier ion must be slower. The ions then drift through a field-free flight tube of known length, so the flight time t = d/v separates them by mass. At the detector each ion gains an electron from the negatively charged plate, producing a current whose size is proportional to the abundance of that ion. Data analysis converts flight times into mass-to-charge ratios and plots abundance against them.
The mass spectrometer gives accurate information about relative isotopic mass and also about the relative abundance of isotopes.
A mass spectrum reports two things for each isotope. The position of a peak on the mass-to-charge axis gives the relative isotopic mass, the mass of one atom of that isotope compared with one-twelfth the mass of an atom of carbon-12, and for a singly charged mononuclear ion that reading is the isotopic mass itself. The height of the peak gives the relative abundance, which comes physically from the size of the current generated as those ions arrive at the detector. Because the technique resolves individual isotopes rather than averaging them, it is far more precise than any bulk measurement, and it lets you work backwards: given the relative atomic mass and all but one isotopic mass, the missing value can be calculated.
Mass spectrometry can be used to identify elements.
Every element produces a characteristic pattern of peaks, so a mass spectrum acts as a fingerprint. Two features identify the element: the mass-to-charge values, which tell you which isotopes are present, and the ratio of the peak heights, which is fixed for that element. Chlorine, for example, gives peaks at 35 and 37 in a ratio close to 3:1, and bromine gives peaks at 79 and 81 in a ratio close to 1:1. Combining the isotopic masses with their abundances gives a relative atomic mass that can be matched against the Periodic Table. The identification must use the whole pattern, because a single peak could belong to several different elements or to a multiply charged ion.
Mass spectrometry can be used to determine relative molecular mass.
For a molecular sample, the peak at the highest mass-to-charge value that is not an isotope satellite is the molecular ion peak, formed when the whole molecule loses a single electron. For a singly charged ion its mass-to-charge value equals the relative molecular mass, so reading that peak gives the relative molecular mass directly. The tallest peak, the base peak, is usually a fragment and must not be used. A small peak one mass unit higher comes from the roughly one per cent of carbon present as carbon-13, and it is ignored when quoting relative molecular mass but can be used to estimate the number of carbon atoms.
Students should be able to: interpret simple mass spectra of elements calculate relative atomic mass from isotopic abundance, limited to mononuclear ions.
Reading a spectrum of an element means listing each isotopic mass with its abundance, then taking an abundance-weighted mean. Multiply each relative isotopic mass by its abundance, add the products, and divide by the total abundance, which is 100 only when the data are percentages. The same expression solves in reverse: if the relative atomic mass and one isotopic mass are known, the unknown mass can be found. For rhenium with peaks at 185 and an unknown mass in abundances 10 and 17, setting 186.3 equal to (185 × 10 + x × 17) ÷ 27 gives 187.1. Only mononuclear singly charged ions are examined, so each peak corresponds to one atom.
Your focus
- Deduce the number of neutrons in a nuclide from its mass number and atomic number.
- Explain why a mass number must be a whole number whereas a relative atomic mass usually is not.
- Identify an element from its atomic number alone and justify why the neutron count does not change that identification.
Show all 21 objectives
- Determine the numbers of protons, neutrons and electrons in a given ion by subtracting the signed charge from the proton count.
- Explain why two nuclides of the same element differ in mass number but not in chemistry.
- Justify, in terms of electron configuration rather than nuclear composition, why isotopes react identically.
- Calculate the speed of an ion from its kinetic energy and mass, then the flight time from the length of the drift region.
- Explain why two ions of different mass given identical kinetic energy arrive at the detector at different times.
- Describe what happens at the detector and how the current produced relates to isotopic abundance.
- Calculate an unknown relative isotopic mass from the relative atomic mass and the abundances of the other isotopes.
- Explain how the height of a peak is generated physically inside the instrument.
- Convert a set of relative abundances into fractions of the total before using them in a mean.
- Deduce the identity of an element from the mass-to-charge values and relative heights of the peaks in its spectrum.
- Explain why one peak alone is insufficient evidence to name an element.
- Predict the number and relative heights of the peaks expected from a sample of chlorine atoms.
- Identify the molecular ion peak in a spectrum and use it to state the relative molecular mass of the compound.
- Explain why the base peak cannot be used to obtain relative molecular mass.
- Account for the small peak one mass unit above the molecular ion peak.
- Calculate the relative atomic mass of an element from a table of isotopic masses and abundances.
- Rearrange the weighted-mean expression to find a missing isotopic mass from a known relative atomic mass.
- Check a calculated relative atomic mass against the abundances by confirming it lies closest to the most abundant isotope.
Mass number and isotopes exam tips
Marking Points
- one mark for the atomic number given as the number of protons
- one mark for the mass number given as the total number of protons and neutrons
- one mark for neutrons obtained as mass number minus atomic number
- one mark for the mass number quoted as a whole number
- one mark for number of protons taken directly from the atomic number
- one mark for number of neutrons calculated as mass number minus atomic number
- one mark for the electron count adjusted correctly for the charge on the ion
- one mark for isotopes defined as atoms with the same number of protons but different numbers of neutrons
- one mark for the same electron configuration explaining identical chemical properties
- one mark for the accelerating electric field giving all the ions the same kinetic energy
- one mark for using kinetic energy = ½mv² to obtain the speed of the ion
- one mark for the flight time related to tube length by speed = distance ÷ time
- one mark for the ion gaining an electron at the detector
- one mark for the size of the current being proportional to the abundance of that isotope
- one mark for reading the relative isotopic mass from the mass-to-charge value of the peak
- one mark for reading the relative abundance from the height of the peak
- one mark for stating that abundance is measured from the size of the current at the detector
- one mark for a correct weighted-mean expression linking isotopic masses, abundances and relative atomic mass
- one mark for identifying the isotopes present from the mass-to-charge values of the peaks
- one mark for using the relative abundances to calculate a relative atomic mass
- one mark for matching that relative atomic mass to an element in the Periodic Table
- one mark for using the characteristic ratio of peak heights as supporting evidence
- one mark for identifying the molecular ion peak as the peak at the highest mass-to-charge value
- one mark for stating that its mass-to-charge value equals the relative molecular mass when the ion is singly charged
- one mark for ignoring the small peak one mass unit above the molecular ion, which arises from carbon-13
- one mark for distinguishing the molecular ion peak from the base peak or fragment peaks
- one mark for a correct weighted-mean expression with each isotopic mass multiplied by its abundance
- one mark for dividing by the total abundance rather than by the number of isotopes
- one mark for the correct value of the relative atomic mass or of the unknown isotopic mass
- one mark for an answer quoted to an appropriate number of significant figures rather than rounded to a whole number
Examiner Tips
- 💡Write A − Z under the symbol as soon as you meet it; the neutron count is needed more often than you expect.
- 💡If a calculation gives a non-integer mass number, round it and say so; examiners want a whole number.
- 💡Use the Periodic Table to check the atomic number matches the element named in the question.
- 💡Write protons, neutrons and electrons as three labelled lines; a table earns the process marks even if one value slips.
- 💡Answer the isotope chemistry question with the words same electron configuration, then add same number of electrons as support.
- 💡Never write same number of neutrons in an isotope answer; that statement is explicitly refused.
- 💡Set out the five stages as five labelled lines; description questions are marked stage by stage.
- 💡Convert units before substituting: centimetres to metres, grams to kilograms.
- 💡Finish a mass calculation by multiplying the mass of one ion in grams by the Avogadro constant to reach a molar mass.
- 💡Add up the abundances first; that total is the denominator of every weighted mean you write.
- 💡Label each peak with isotopic mass and abundance before doing any arithmetic.
- 💡When solving for an unknown isotopic mass, write the weighted-mean equation in full before rearranging.
- 💡Always calculate the relative atomic mass to at least one decimal place before naming the element.
- 💡Check whether the number of peaks matches the number of isotopes the element is known to have.
- 💡If a peak sits at an unexpectedly low value, test whether it is a 2⁺ ion by doubling it.
- 💡Read the spectrum from the right-hand end; the molecular ion is the last significant peak you meet.
- 💡State that the ion is singly charged when you quote relative molecular mass from the axis.
- 💡Use the size of the peak one mass unit above the molecular ion only when the question asks about the number of carbon atoms.
- 💡Write the full fraction before substituting; the expression itself carries a mark even if the arithmetic fails.
- 💡Add the abundances first and write the total down so you cannot forget to divide by it.
- 💡Sense-check the answer: it must lie between the smallest and largest isotopic masses, nearer the most abundant.
Common Mistakes
- quoting a relative atomic mass such as 186.3 as the mass number
- leaving a calculated mass number as a decimal instead of rounding to the nearest whole number
- swapping the positions of A and Z in the symbol notation
- saying that atomic number changes between isotopes of the same element
- adding electrons for a positive ion instead of removing them
- explaining identical chemistry by saying isotopes have the same number of protons, which examiners ignore
- saying isotopes have different chemical properties because their masses differ
- forgetting the charge entirely and giving an ion the same electron count as the atom
- saying heavier ions are given less kinetic energy rather than the same kinetic energy and a lower speed
- leaving the flight tube length in centimetres when the kinetic energy equation needs metres
- using the mass in grams rather than kilograms in the kinetic energy equation
- dividing by the Avogadro constant when converting the mass of one ion to a molar mass, instead of multiplying
- saying the detector counts the ions directly without describing the transfer of an electron
- reading the tallest peak as the relative atomic mass of the element
- assuming abundances must be percentages when the axis is labelled relative abundance
- forgetting that a 2⁺ ion appears at half its true mass on the mass-to-charge axis
- rounding a calculated relative isotopic mass to a whole number when the question says calculate
- naming the element from the largest peak alone and ignoring the other isotopes
- forgetting that a 2⁺ ion appears at half the mass-to-charge value of the 1⁺ ion
- treating the mass-to-charge axis as a mass in grams
- quoting the relative atomic mass as a whole number so that two neighbouring elements cannot be told apart
- using the tallest peak instead of the peak at the highest mass-to-charge value
- quoting the peak one mass unit above the molecular ion as the relative molecular mass
- forgetting that the reading equals relative molecular mass only for a singly charged ion
- treating a fragment peak as evidence of a second compound in the sample
- dividing by the number of isotopes instead of by the sum of the abundances
- assuming the abundances add to 100 when they are relative rather than percentage values
- rounding the relative atomic mass to a whole number so it no longer matches the Periodic Table value
- multiplying abundance by atomic number rather than by relative isotopic mass