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How Is The Atomic Mass of An Element Calculated?

May 4, 2013

Introduction to atomic mass of an element

The atomic mass of an element depends on the abundance of its isotopes. If we know the mass of the isotopes and the fractional abundance of the isotopes, we can calculate the element’s atomic weight. It will be represent in atomic mass units(amu).

Formula for calculating Atomic mass of an element

The atomic weight or atomic mass is calculated by finding the sum of each isotope mass multiplied by its fractional abundance.

For example, for an element with 2 isotopes formula for atomic weight is below.

Atomic weight = mass a x fractional a + mass b x fractional b

If there were three isotopes, atomic weight = mass a x fractional a + mass b x fractional b+mass c x fractional c etc.

Example 

If chlorine has two naturally-occurring isotopes where:

Cl-35 mass is 34.968852 and fractional is 0.7577

Cl-37 mass is 36.965303 and fractional is 0.2423

Atomic weight = mass a x fractional a + mass b x fractional b

Atomic weight = 34.968852 x 0.7577 + 36.965303 x 0.2423

Atomic weight = 26.496 amu + 8.9566 amu

Atomic weight = 35.45 amu

The Abundance of Some Naturally Occurring Isotopes

Element          Isotopes          Mass Number       Relative Abundance (%)

hydrogen         1H                       1                                99.99

2H                       2                                  0.01

lithium               6Li                       6                                  7.59

7Li                       7                                 92.41

boron                10B                    10                                19.6

11B                    11                                 80.4

carbon              12C                    12                                 98.89

13C                    13                                   1.11

nitrogen            14N                    14                                 99.63

15N                    15                                   0.37

oxygen              16O                    16                                 99.76

17O                    17                                   0.04

18O                    18                                   0.20

magnesium      24Mg                   24                                 78.99

25Mg                   25                                 10.00

26Mg                   26                                 11.01

silicon                28Si                    28                                 92.23

29Si                    29                                  4.68

30Si                    30                                  3.09

chlorine             35Cl                    35                                 75.78

37Cl                    37                                 24.22

argon                 36Ar                    36                                   0.34

38Ar                    38                                   0.06

40Ar                    40                                 99.60

copper              63Cu                   63                                 69.17

65Cu                   65                                30.83

silver                 107Ag                 107                                 51.84

109Ag                 109                                 48.16

barium              130Ba                 130                                   0.11

132Ba                 132                                  0.10

134Ba                 134                                   2.42

135Ba                 135                                   6.59

136Ba                 136                                  7.85

137Ba                 137                                 11.23

138Ba                 138                                 71.70

lead                   204Pb                 204                                    1.5

206Pb                 206                                  23.6

207Pb                 207                                  22.6

208Pb                 208                                  52.3

uranium           234U                   234                                   0.01

235U                   235                                   0.72

238U                   238                                  99.27

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