26.08.2015   Modern Power Station Practice

Mass defect and binding energy

Knowing the mass of the neutron and proton one would expect to be able to calculate the mass of a nucleus, knowing its constituent^ For example, the nuclide Au-197 (gold) has 118 neutrons and 79 protons. The nucleus would be expected to have a mass of:

(118 x 1.008665 u) + (79 x 1.007277 u)

= 198.597353 u

Direct measurement however gives a value of 196.9232 u: there is a ‘mass defect1 of 1.6741 u. The energy equivalent to the mass defect, 1559 MeV, was released at the time of formation of the gold nucleus.

All nuclei (with the exception of hydrogen, H-I) have some measure of mass defect — an individual nucleon has less mass when it is part of a nucleus than when it is in isolation. The following expression allows comparison between the mass defect of a nucleon in different nuclides:

Z/rip + N/«n — Л/

Mass defect per nucleon = ——————————-

A

where /tip and tnn are the proton and neutron masses and Л/ the observed mass of the nucleus. As an example, for gold:

, 1.6741

Mass defect per nucleon = ————— u

197

= 0.0085 u s 7.9 MeV

Figure 1.3 (a) shows how the mass per nucleon varies with the atomic number Z. It may be seen that the nuclides with the largest mass defect per nucleon are those with medium atomic numbers, rather less deficit for the heavier nuclei and substantially less for the lighter elements.

The energy equivalent to the mass defect per nucleon is the energy required to overcome the nuclear forces and ‘force’ a nucleon out of the nucleus — the nucleon having a slightly larger mass after its successful removal. The energy equivalent to the mass defect of a nucleus is known as the binding energy: the energy required to dismantle the nucleus into its individual constituent nucleons or, alternatively, the energy re­leased when the nucleons come together to form the nucleus. Figure 1.3 (b) gives the binding energy per nucleon for the different atomic numbers and is the mirror image of the mass defect in Fig 1.3 (a) but in the energy units MeV.

Figure 1.3 (b) shows that if the nucleus of a heavy element is split into two nuclei of medium atomic numbers each nucleon will have less mass than pre­viously and the equivalent amount of energy will be spontaneously released. To illustrate this assume for simplicity that uranium 236 divides into exactly two halves (an unlikely event in practice), giving two palladium 118. From Fig 1.3 (b) we have:

Binding energy of 236 n = 236 x 8.5 MeV 92 U

Binding energy of 2 x 118n = 118 x 7.5 x 2 MeV
46 p

Energy released = 236 MeV

Most of the energy released appears as kinetic energy of the two palladium nuclei. The above process is of course fission and is the source of energy for all

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ATOMIC NUMBER

(a) Variation of mass per nucleon with atomic number

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ATOMIC NUM8ER

[bj Variation of binding energy per nucleon with atomic number

Fig. 1.3 Variation of mass and binding energy with
atomic number

present day nuclear reactors. Fission is discussed in detail in Section 3 of this chapter.

Fusion is the process by which the nuclei of two light elements combine to form a single nucleus, again resulting in the total mass being reduced and the equivalent energy released. Fusion reactions are the source of the energy of the sun where hydrogen

An event which results in the same transformation to the nucleus as positron emission is the capture of an electron in the nearest orbit (known as the К shell) by a proton in the nucleus — the proton is transformed into a neutron. This is called *К electron capture X-rays are emitted as the elec­trons rearrange themselves in their orbits. Positron emission and К electron capture tend to occur in light or medium elements lying above the stability region shown in Fig 1.4.

• Alpha decay The nucleus ejects an alpha (a) parti­cle. This is a very stable ‘package’ of two protons and two neutrons. See also Section 1.5.2 of this chapter. The mass number of the unstable nucleus reduces by four and the atomic number by two, resulting in a different element:

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1.4.2 Radioactive nuclei

In the radioactive decay of an unstable nucleus the proton/neutron combination may undergo one of the

following changes:

 

+ °/3

+ 1

Positron

 
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Argon

 

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Fig. 1.4 Graph showing region of nuclei stability

 

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