The mass spectrum of bromine \(\left(\mathrm{Br}_{2}\right)\) consists of three peaks with the following characteristics: $$\begin{array}{|lc|}\hline \text { Mass }(\mathrm{u}) & \text { Relative Size } \\\\\hline 157.84 & 0.2534 \\\159.84 & 0.5000 \\\161.84 & 0.2466 \\\\\hline\end{array}$$ How do you interpret these data?

A mass spectrum is a distribution of the ions produced in a mass spectrometer (such as a mass spectroscopy) as a function of their mass-to-charge ratio. In this case, the mass spectrum provides the distribution of Bromine (\(\mathrm{Br_{2}}\)) ions. Isotopes are elements with the same number of protons but a different number of neutrons. In the case of Bromine, it consists of isotopes, primarily \(\mathrm{^{79}Br}\) and \(\mathrm{^{81}Br}\). The presence of these isotopes contributes to the different peaks in the mass spectrum.

There are three peaks in the mass spectrum of \(\mathrm{Br_{2}}\), and their masses are \(157.84\,\mathrm{u}\), \(159.84\,\mathrm{u}\), and \(161.84\,\mathrm{u}\). The corresponding relative sizes are \(0.2534\), \(0.5000\), and \(0.2466\). By looking at the mass values, we can assume that these peaks are formed due to the combination of the isotopes of \(\mathrm{^{79}Br}\) and \(\mathrm{^{81}Br}\) in the Bromine molecule (\(\mathrm{Br_{2}}\)). We will now explain the source of each peak: 1. The first peak, with a mass of \(157.84\,\mathrm{u}\), can be attributed to the \(\mathrm{^{79}Br - ^{79}Br}\) combination. 2. The second peak, with a mass of \(159.84\,\mathrm{u}\), can be caused by the presence of both \(\mathrm{^{79}Br - ^{81}Br}\) and \(\mathrm{^{81}Br - ^{79}Br}\) combinations. 3. The third peak, with a mass of \(161.84\,\mathrm{u}\), can be attributed to the \(\mathrm{^{81}Br - ^{81}Br}\) combination. The relative sizes of the peaks indicate the abundance of the corresponding isotopic combinations.

Using the information from the mass spectrum, we can calculate the average atomic mass of the Bromine molecule by multiplying the mass values with their corresponding relative sizes and adding them together: Average atomic mass of \(\mathrm{Br_{2}} = (157.84\,\mathrm{u} \times 0.2534) + (159.84\,\mathrm{u} \times 0.5000) + (161.84\,\mathrm{u} \times 0.2466)\) \(= 39.97\,\mathrm{u} + 79.92\,\mathrm{u} + 39.88\,\mathrm{u}\) \(= 159.77\,\mathrm{u}\) The average atomic mass of \(\mathrm{Br_{2}}\) is approximately \(159.77\,\mathrm{u}\). In conclusion, the given data in the mass spectrum of Bromine helps us understand the presence of isotopes in the molecule and their combinations, and we have interpreted the data by explaining the source of each peak. Additionally, we have calculated the average atomic mass of \(\mathrm{Br_{2}}\), which is approximately \(159.77\,\mathrm{u}\).