Atomic masses and Isotopic Abundances

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Most of the elements occur in nature as a mixture of two or more isotopes. To determine atomic mass of such an element, it is necessary to know not only the masses of the individual isotpes but also their atom percents (isotopic abudance) in nature.

The mass spectrum gives us all the information needed to calculate the atomic weight; the masses of isotope and their relative  numbers or isotopic abudances also called fractional abundances.

The isotopic or fractional abundance of an isotope is the fraction of the total number of atoms that is composed of a perticular isotope.

For chlorine which has two stable isotopes, Cl-35 and Cl-37. The atomic masses and relative abundances of these isotopes as determined by mass spectroscopy is as follows

                  atomic mass                  abudance

Cl-35            34.97 amu                     75.53%

Cl-37           36.97 amu                     24.47%

We interpret this to mean that in elemental chlorine, 75% of the atoms have a mass of 34.97 amu and the remaining atoms 24.47% of the total, have a mass of 36.97 amu. With this information we can readily calculate the atomic mass of chlorine using general equation.

Atomic mass Y = ( atomic mass Y1) x %Y1             (atomic mass Y2) x %Y2                 

                                                  -----------  +                                 -----------    +   ..........

                                                  100%                                           100%

where Y, Y2.... are the isotopes of element Y.

atomic mass of Cl= 34.97 amu x 75.53         36.97 amu x 24.47

                                           -----------  +                     .........                                                          

                                              100                               100

                            =   35.46 amu

Example; What is the atomic mass of chromium?

mass number                isotopic mass(amu)               isotopic abundance(amu)

50                                    49.94                                 0.0435

52                                   51.94                                  0.837

53                                     52.94                                0.0950

54                                     53.93                                0.023

 

atomic mass  of Cl = 49.94 x 0.0435 + 51.94 x 0.837+52.94 x 0.0950+ 53.93 x 0.023

                          =  51.99 amu