Ionisation

If the excitation is to the continuum, then a number of multidifferential cross sections are possible. Consider, for instance, the single ionisation of an atom A  

If only one free electron, say the scattered electron i, is detected and its energy and angular dependence are measured, then the double differential cross section is obtained. This is given by 

Accurate absolute measurements of double-differential cross sections are quite difficult to make. Measurements carefully taken by competent investigators often differ significantly. Kim (1983) gave a recommended 

The single-differential cross section is obtained by integrating the doubledifferential cross section over all angles of emission of the electron 

Single-differential cross sections are difficult to obtain in a direct measurement and they are usually obtained by numerical integration of the double-differential cross sections over all angles (2.28). The singledifferential cross section describes the energy distribution of secondary electrons and is therefore important in modelling radiation damage, in studies of stellar and upper atmospheric phenomena, plasma fusion work. 

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Real Time Radiography (RTR) is an advanced method of radiography in which the image is formed while the job is exposed to ionising radiation. RTR is often applied to objects on assembly lines for rapid inspection. Accept-or-reject decisions may be made immediately without the delay or expense of film development. The main advantages of RTR are thus, reduction in inspection cost and processing time. 

One of these is the first ionisation energy. This is the energy needed to remove one electron from a free atom of the element, i.e. for the process ... 

Clearly the general tendency is for metals to have low ionisation energies and non-metals to have rather high ionisation energies. We should also note that the first ionisation energies rise as we cross a... 

In any group of the periodic table we have already noted that the number of electrons in the outermost shell is the same for each element and the ionisation energy falls as the group is descended. This immediately predicts two likely properties of the elements in a group (a) their general similarity and (b) the trend towards metallic behaviour as the group is descended. We shall see that these predicted properties are borne out when we study the individual groups. 

Consider first the formation of cations by electron loss. Here the important energy quantity is the ionisation energy. As we have seen (p. 15). the first ionisation energy is the energy required to remove an electron from an atom, i.e. the energy for the process... 

Table 2.1 gives data for Group I elements. The ionisation energies are all positive, i.e. energy is absorbed on ionisation. Several conclusions can be drawn from this table ... 

Loss of one electron gives the noble gas configuration the very large difference between the first and second ionisation energies implies that an outer electronic configuration of a noble gas is indeed very stable. 

Ionisation energy falls as the group is descended, i.e. as the size of the atom increases and hence the distance between the nucleus and the outer electron increases. 

Atomic number Element Atomic radius (s) Radius oj M ion (nm) Ionisation energies (kJ mol I 1st 2nd 3rd ... 

The number of electrons in the outermost quantum level of an atom increases as we cross a period of typical elements. Figure 2.2 shows plots of the first ionisation energy for Periods 2 and 3,... 

The first ionisation energies of the first transition elements are shown in Figure 2.3. The changes across these 10 elements contrast... 

Figure 2.3. First ionisation energies oj the first series o] transition elements...

Ionisation energy decreases down a group of elements as the atomic size increases. The elements in consequence become more metallic down the group. 

With certain irregularities only, the ionisation energy increases across a period. The elements therefore become less metallic across a period. 

Tables 2.1, 2.2, 2.3 and 2.4 give data for atomic radii, ionisation energies and electron affinities which allow these rough rules to be justified.

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

Ah second ionisation energy for sodium (additional) +4561 A/13 enthalpy of atomisation of chlorine, x 2 (since two... 

This is an exothermic process, due largely to the large hydration enthalpy of the proton. However, unlike the metallic elements, non-metallic elements do not usually form hydrated cations when their compounds dissolve in water the process of hydrolysis occurs instead. The reason is probably to be found in the difference in ionisation energies. Compare boron and aluminium in Group III ... 

Ionisations 2, 3 and 5 are complete ionisations so that in water HCI and HNO3 are completely ionised and H2SO4 is completely ionised as a monobasic acid. Since this is so, all these acids in water really exist as the solvated proton known as the hydrogen ion, and as far as their acid properties are concerned they are the same conjugate acid species (with different conjugate bases). Such acids are termed strong acids or more correctly strong acids in water. (In ethanol as solvent, equilibria such as 1 would be the result for all the acids quoted above.) Ionisations 4 and 6 do not proceed to completion... 

The enthalpy changes AH involved in this equilibrium are (a) the heat of atomisation of the metal, (b) the ionisation energy of the metal and (c) the hydration enthalpy of the metal ion (Chapter 3). 

Heat of atomisation Sum of 1st and 2nd ionisation energies Hydration enthalpy AH... 

Liquid ammonia, which boils at 240 K, is an ionising solvent. Salts are less ionised in liquid ammonia than they are in water but, owing to the lower viscosity, the movement of ions through liquid ammonia is much more rapid for a given potential gradient. The ionisation of liquid ammonia... 

Element Ionisation energy (kj mof ) Metallic radius (nm) Ionic radius (nm) Heal oj laporibation at 298 K (kJ mol ) Hydration energy oj gaseous ion (kJ moI ) (V)... 

I i-(. s. lirM lonisaiion enerjjv. Be Bii Mini ol first and second ionisation enercies... 

A full discussion of the changes in ionisation energy with group and period position has been given in Chapter 2. These data are given again in Table 6.2. 

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