We would like to invite you to participate in the Analytical Challenge, a series of puzzles to entertain and challenge our readers. This special feature of “Analytical and Bioanalytical Chemistry” has established itself as a truly unique quiz series, with a new scientific puzzle published every three months. Readers can access the complete collection of published problems with their solutions on the ABC homepage at http://www.springer.com/abc. Test your knowledge and tease your wits in diverse areas of analytical and bioanalytical chemistry by viewing this collection.

In the present challenge, measurement is the topic. And please note that there is a prize to be won (a Springer book of your choice up to a value of €100,- given to one winner selected randomly). Please read on...

Meet the challenge

Metrology, which is the science of measurement, focuses on evaluating the uncertainties associated with measurement results. It can also identify experimental designs that lead to better measurements.

Consider the example of weighing three bananas with a single-pan balance [1]. A trivial approach would be to weigh each banana separately. However, if the uncertainty associated with each weighing is unaffected by the mass of the objects being weighed, it is more efficient to weigh the three bananas in pairs. First, we weigh bananas #1 and #2 together, then bananas #1 and #3, followed by #2 and #3. In this way, the uncertainty associated with the estimates of the three individual masses is 13% smaller compared to what one would obtain by weighing the three bananas separately [2]. This simple example illustrates the benefits of a clever experimental design that takes into account the characteristics of the measurement device.

The challenge

This Analytical Challenge invites us to think about the best way to measure the isotopic abundance of bromine-81. For this purpose, we use tribromobenzene and obtain its mass spectrum using gas chromatography coupled with electron impact mass spectrometer. The molecular ion of this compound (Fig. 1) shows the familiar 1:3:3:1 pattern which is a signature of three bromine atoms [3].

Fig. 1
figure 1

Electron impact ionization mass spectrum of tribromobenzene showing the molecular ion, C6H3Br3+

Full size image

From this mass spectrum we obtain two peak area ratios: A314/A312 and A316/A312. Both of these ratios have the same numerical value, approximately 2.9, and both of them involve signals of the same intensity. Therefore, we expect the measurement uncertainty for both peak area ratios to be identical. Although these two ratios are of equal quality, it turns out that they give very different quality results for the isotopic abundance of bromine-81.

Which of these two peak area ratios gives the best estimate of the isotopic abundance of bromine-81? Why?