Binding Energy of an Atom

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Binding Energy of an Atom The binding energy of an atom nucleus is the energy required to split the nucleus into its constituent parts of protons and neutrons 1. The following table shows the binding energy of a number of element element isotopes. Note that the units units are in MeV or million electron volts. The electron volt is a unit of energy (1 electron volt = 1.60217646 × 10-19 joules).

Element

Mass of  nucleons (u)

Nuclear Mass (u)

Binding Energy (MeV)

Binding Energy per Nucleon (MeV)

Deuterium

2.01594

2.01355

2.23

1.12

Helium 4

4.03188

4.00151

28.29

7.07

Lithium 7

7.05649

7.01336

40.15

5.74

Beryllium 9

9.07243

9.00999

58.13

6.46

Iron 56

56.4491

55.9207

492.24

8.79

Silver 107

107.862

106.879

915.23

8.55

Iodine 127

128.027

126.875

1072.53

8.45

Lead 206

207.671

205.93

1622.27

7.88

Polonium 210

211.703

209.937

1645.16

7.83

Uranium 235

236.908

234.994

1783.8

7.59

Uranium 238

239.934

238

1801.63

7.57

The following graph links together the binding energy per nucleon of elements through the periodic table and their isotopes.

Binding Energy Per Nucleon    n    o    e     l    c    u    n    r    e    p    y    g    r    e    n    e    g    n    i     d    n    i    B

10 9 8 7 6 5 4 3 2 1 0 0

50

100

150

Mass Number

1

Atomic Structure and the Periodic Table

200

250

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Note the overall binding energy graph. The binding energy per nucleon rises up until the element iron (Fe) and then steadily falls. This indicates that elements up to iron tend to have more and more stable nulei and then nuclei become more and more unstable as the number of  nucleons in the nucleus increases beyond iron. This suggests two basic methods of harnessing energy from nuclear reactions; fusion reactions;  fusion and fission and fission.. Fusion If we combine two elements with a low atomic mass number to produce a new element with an atomic mass number of less than iron then energy must be released. This is particularly marked in the conversion of hydrogen to helium. It is the conversion of hydrogen to helium that  produces the energy from the sun, is utilised in hydrogen bombs and could become a practical source of energy in thermo-nuclear fusion reactor. Fission If we can split the atoms of an element with a high atomic mass number into elements with an atomic mass numbers that are higher than iron then energy must be released. This process ias called nuclear fission. Nuclear reactors produce energy by the fission of uranium and this is the source of power in atomic weapons.

Mass Defect and Binding Energy of a Nucleus The mass of a nucleus is always observed to be less than the mass of its constituent nucleons. The difference between is called the mass defect. If we first think of the separate nucleons then to get them to be combined in a nucleus nucleus then energy must must be released. This is explained by Einstein’s famous equation E = m c2, which relates energy E and mass m, with c being the speed of light (c ≈ 3 × 108 m/s). Mass of proton Mass of neutron Mass of electron Speed of light (c) 1amu =

1.0073 amu 1.0087 amu 0.00055 amu 3 × 108 m/s 931.4 MeV

A helium ( ) atom has a mass of 4.0026 amu A helium atom has two protons, two neutrons and t wo electrons, so the mass of the individual components is 2×1.0073 + 2×1.0087 + 2×0.00055 = 4.0331 amu. Hence the mass defect is 0.0305amu. Binding energy = 0.0305 × 931.4 = 28.4 MeV The binding energy per per nucleon for helium is 28.4/4 28.4/4 = 7.1 MeV. See the assosciated spreadsheet 2 for computing computing binding energy. energy. Exercises Find the binding binding energy of oxygen– oxygen–16 (mass 15.992439amu) and uranium-234 (mass 234.040947amu). 2

Binding Energy Spreadsheet