There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br? molec2?es, and the mass of a Br? molecule is th2?sum of the masses of the two atoms in the molecule. The mass spectrum of Br? consists of thre2?peaks: (a) What is the origin of each peak (of what isotopes does each consist)? (b) What is the mass of each isotope? (c) Determine the average molecular mass of a Br? molecule, 2? (d) Determine the average atomic mass of a bromine atom, (e) Calculate the abundances of the two isotopes.
Solution : Bromine (Br) has two stable isotopes, Br and Br, and 30 radioisotopes. Bromine and chlorine are the only halo gens with more than one stable isotope Step 1 : Here, the problem is based on the m ass spectrometer and the massspectrum. First let’s see what is a mass spe ctrometer and mass spectrum and then proceed with answering questions. The mass spectrometer is an instrument which can measure the masses and relative concentrations of atoms and molecules. Mass spectrometry is very powerful technique for identifying isotopes and its abundance and mass because of its ability to distinguish the isotopes of an element. Mass spectrum of a sample is a pattern representing the distribution of ions by mass-to-charge ratio in a sample. (a) What is the origin of each peak (of what isotopes does each consist) The intensity of the peak depends o n the bundance of the i sotope. The larger the intensity of the peak, the greater the abundance of the isotope. Here for Br, the relative size of the peak for Br 2 molecule consisting of two different isotopes will be larger than the Br molecule co2isting of same isotopes, i.e relative size of the peak for Br molecu2 consisting of different isotopes is twice as that of Br m2ecule consisting of same isotopes. Hence, from the data in the table we could say that the peak of mass 157.836 represents 79Br - Br peak, 159.834 represents Br - Br peak and peak of mass 161.832 represents Br - 81 81 Br peak. Step 2: (b) What is the mass of each isotope Mass of each isotope is calculated as : 157.836 (i) 2 [it is divided by 2 br atom, as 1 br molecule consists of 2 br atom] = 78.918 amu/atom. (ii) 159.834 2 = 79.917 amu/atom. 161.832 (iii) 2 = 80.916 amu/atom. Step 3: (c) Determine the average molecular mass of a Br molecule: 2 Formula to calculate average molecular mass is : Mass(in amu) × Relative size. Therefore, Average molecular mass of a Br molecule is calculated as : 2 =(157.836 amu)(0.2569) + (159.834amu)(0.4999) + (161.832amu)(0.2431) = 40.5480 amu + 79.9010amu + 39.3413amu = 159.79amu.