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

In nature, bromine exists as two stable isotopes: \(\mathrm{^{79}Br}\) (mass number 79) and \(\mathrm{^{81}Br}\) (mass number 81). Since bromine naturally pairs up to form Br₂, the peaks in the mass spectrum are representing the combinations of these isotopes.

For a Br₂ molecule, there can be the following combinations of the two stable isotopes: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): Two \(\mathrm{^{79}Br}\) isotopes combined. 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): One \(\mathrm{^{79}Br}\) and one \(\mathrm{^{81}Br}\) isotope combined. 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): Two \(\mathrm{^{81}Br}\) isotopes combined.

Next, determine the molecular mass of each combination: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): \( 2 \times 79 = 158 \) 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): \( 79 + 81 = 160 \) 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): \( 2 \times 81 = 162 \)

Compare the calculated masses of each combination to the masses given in the mass spectrum: 1. Peak at 157.84 amu: Molecular combination of \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\) which is around 158 amu. 2. Peak at 159.84 amu: Molecular combination of \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\) which is around 160 amu. 3. Peak at 161.84 amu: Molecular combination of \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\) which is around 162 amu.

The relative sizes of each peak represent the relative abundances of the isotopes in the Br₂ molecule: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): Relative size 0.2534 indicates that 25.34% of Br₂ molecules are composed of two \(\mathrm{^{79}Br}\) isotopes. 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): Relative size 0.5000 indicates that 50.00% of Br₂ molecules are composed of one \(\mathrm{^{79}Br}\) and one \(\mathrm{^{81}Br}\) isotope. 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): Relative size 0.2466 indicates that 24.66% of Br₂ molecules are composed of two \(\mathrm{^{81}Br}\) isotopes. In conclusion, the mass spectrum data of bromine Br₂ shows that Br₂ molecules are made up of a mixture of stable isotopes \(\mathrm{^{79}Br}\) and \(\mathrm{^{81}Br}\) with relative abundances of 25.34%, 50.00%, and 24.66% for the molecular combinations \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\), \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\), and \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\), respectively.