Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Spectrometry Detective

Age 16 to 18
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Why do this problem?

This problem gives practice in mathematical reasoning in a genuine scientific context. It involves reasonably basic mathematics of combinatorics but requires more advanced inductive reasoning. It might prove an interesting context for the prospective mathematician and will definitely be useful for those interested in studying chemistry at university.

Possible approach

As this problem does not fit directly into the typical chemistry or mathematics classroom it could be used as an end of term activity in which the focus is to encourage some clear mathematical thinking in a cross-curricular context.

Suggest that students interested in both chemistry and mathematics try the problem, either individually or in small groups. The basic chemical knowledge required is simply that of isotopes and atomic mass. The mass spectrometer might be unfamiliar, but should be simple to grasp in essence.

The focus throughout the problem should be on clarity in the mathematical explanations, and there will be an element of convincing others of the soundness of any resulting analysis.

When this problem was created it caused a great deal of discussions amongst students. Hopefully some of this discussion might be replicated amongst your students.

Finally, note that this problem is of an industrial, real world sort. It gives a flavour of the types of real questions which might be asked to professional scientists and mathematicians, where errors in mathematical reasoning can be highly costly . It gives great practice in such thinking.

Key questions

Have you understood the chemical terms?

Which numbers seem to stand out, when compared with the periodic table?

Are you clear as to which aspects of you calculations are mathematically certain?

Possible extension

Extension is built into this problem directly.

Possible support

To make this problem more straightforward, provide copies of the periodic table. Suggest that students write down all the diatomic gasses that they know and start from these.

For a more straightforward foray into combinatoric chemistry, try the problem Heavy Hydrocarbons.

You may also like

Teams

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

Crossing the Bridge

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo