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Isotopes and Relative Atomic Mass

High schoolChemistryTwo-isotope weighted neutral mass and equal-voltage positive-ion semicircular magnetic separation

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About this experiment

Mix isotopes of one element, calculate the average atomic mass and launch ions through a magnetic sector. Separate changes in abundance from changes in mass, ion charge and instrument geometry.

Learning goals

  • Calculate an abundance-weighted mean mass.
  • Relate mass-to-charge ratio to a mass spectrum.
  • Test how accelerating voltage and magnetic field affect an ion path.

How to use it

  1. 1Record the representative chlorine mixture and compare its mean mass with 35 and 37.
  2. 2Increase the lighter fraction to one and predict the remaining spectrum peak.
  3. 3Launch the ions and compare their radii and arrival times.
  4. 4Double the magnetic field and test whether both radii halve while the mean atomic mass stays fixed.

The model

The mean uses neutral isotopic masses and prescribed number fractions.
All ions are accelerated through the same potential difference.
The detector intercepts the end of a semicircular trajectory.

Assumptions

  • Masses and representative abundance values are from NIST. Natural isotopic abundances can vary between samples.
  • Ions have the same selected positive integer charge. Electron rest masses are subtracted; ionisation binding-energy mass corrections are neglected.
  • Acceleration is instantaneous at injection; the magnetic field is uniform. Collisions, beam width and detector response are omitted. The fitted drawing scale does not change the millimetre readouts.

Try this in class

  1. Q1Why does changing abundance alter peak height but not peak position?
  2. Q2Why is an isotope mass different from its integer mass number?

Frequently asked questions

Is the weighted average the mass of one atom?

Usually no. It is the number-weighted average for a population of isotopes; an individual atom has one isotopic mass.

Does a higher charge bend the beam more strongly?

At fixed voltage and mass, radius is inversely proportional to the square root of charge. The ion also leaves the accelerator faster.