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outermost valence electron moving into d block elements the elements sc with a 3d 1 electronic configuration has a higher ip 21 sc 6 56 ev than the preceding element 20 ca 6 11 ev contrary to the decreases on moving into s block and p block elements the 4s and 3d electrons have similar shielding ability the 3d orbital forms part of the n 3 shell whose average position is closer to the nucleus than the 4s orbital and the n 4 shell but electrons in s orbitals experience greater penetration into the nucleus than electrons in d orbitals so the mutual shielding of 3d and 4s electrons is weak and the effective nuclear charge acting on the ionized electron is relatively large yttrium 39 y similarly has a higher ip 6 22 ev than 38 sr 5 69 ev moving into f block elements the elements 57 la 5 18 ev and 89 ac 5 17 ev have only very slightly lower ip s than their preceding elements 56 ba 5 21 ev and 88 ra 5 18 ev though their atoms are anomalies in that they add a d electron rather than an f electron as can be seen in the above graph for ionization energies the sharp rise in ie values from 55 cs 3 89 ev to 56 ba 5 21 ev is followed by a small increase with some fluctuations as the f block proceeds from 56 ba to 70 yb this is due to the lanthanide contraction for lanthanides 23 24 25 this decrease in ionic radius is associated with an increase in ionization energy in turn increases since the two properties correlate to each other 9 as for d block elements the electrons are added in an inner shell so that no new shells are formed the shape of the added orbitals prevents them from penetrating to the nucleus so that the electrons occupying them have less shielding capacity ionization energy anomalies in groups edit ionization energy values tend to decrease on going to heavier elements within a group 12 as shielding is provided by more electrons and overall the valence shells experience a weaker attraction from the nucleus attributed to the larger covalent radius which increase on going down a group 26 nonetheless this is not always the case as one exception in group 10 palladium 46 pd 8 34 ev has a higher ionization energy than nickel 28 ni 7 64 ev contrary to the general decrease for the elements from technetium 43 tc to xenon 54 xe such anomalies are summarized below group 1 hydrogen s ionization energy is very high at 13 59844 ev compared to the alkali metals this is due to its single electron and hence very small electron cloud which is close to the nucleus likewise since there are not any other electrons that may cause shielding that single electron experiences the full net positive charge of the nucleus 27 francium s ionization energy is higher than the precedent alkali metal cesium this is due to its and radium s small ionic radii owing to relativistic effects because of their large mass and size this means that its electrons are traveling at extremely high speeds which results in the electrons coming closer to the nucleus than expected and they are consequently harder to remove higher ie 28 group 2 radium s ionization energy is higher than its antecedent alkaline earth metal barium like francium which is also due to relativistic effects the electrons especially the 1s electrons experience very high effective nuclear charges to avoid falling into the nucleus the 1s electrons must move at very high speeds which causes the special relativistic corrections to be substantially higher than the approximate classical momenta by the uncertainty principle this causes a relativistic contraction of the 1s orbital and other orbitals with electron density close to the nucleus especially ns and np orbitals hence this causes a cascade of electron changes which finally results in the outermost electron shells contracting and getting closer to the nucleus group 4 hafnium s near similarity in ie with zirconium the effects of the lanthanide contraction can still be felt after the lanthanides 24 it can be seen through the former s smaller atomic radius which contradicts the observed periodic trend archived 2018 10 11 at the wayback machine at 159 pm 29 empirical value which differs from the latter s 155 pm 30 31 this in turn makes its ionization energies increase by 18 kj mol 1 titanium s ie is smaller than that of both hafnium and zirconium hafnium s ionization energy is similar to zirconium s due to lanthanide contraction however why zirconium s ionization energy is higher than the preceding elements remains unclear we cannot attribute it to atomic radius as it is higher for zirconium and hafnium by 15 pm 32 we also cannot invoke the condensed ionization energy as it is more or less the same ar 3d 2 4s 2 for titanium whereas kr 4d 2 5s 2 for zirconium additionally there are no half filled nor fully filled orbitals we might compare hence we can only invoke zirconium s full electron configuration which is 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 2 5s 2 33 the presence of a full 3d block sublevel is tantamount to a higher shielding efficiency compared to the 4d block elements which are only two electrons a group 5 akin to group 4 niobium and tantalum are analogous to each other due to their electron configuration and to the lanthanide contraction affecting the latter element 34 ipso facto their significant rise in ie compared to the foremost element in the group vanadium can be attributed due to their full d block electrons in addition to their electron configuration another intriguing notion is niobium s half filled 5s orbital due to repulsion and exchange energy in other words the costs of putting an electron in a low energy sublevel to completely fill it instead of putting the electron in a high energy one overcoming the energy gap between s and d or f block electrons the ec does not follow the madelung rule group 6 like its forerunners groups 4 and 5 group 6 also record high values when moving downward tungsten is once again similar to molybdenum due to their electron configurations 35 likewise it is also attributed to the full 3d orbital in its electron configuration another reason is molybdenum s half filled 4d orbital due to electron pair energies violating the aufbau principle groups 7 12 6th period elements rhenium osmium iridium platinum gold and mercury all of these elements have extremely high ionization energies compared to the elements preceding them in their respective groups the essence of this is due to the lanthanide contraction s influence on post lanthanides in addition to the relativistic stabilization of the 6s orbital group 13 gallium s ie is higher than aluminum s this is once again due to d orbitals in addition to scandide contraction providing weak shielding and hence the effective nuclear charges are augmented thallium s ie due to poor shielding of 4f electrons 5 in addition to lanthanide contraction causes its ie to be increased in contrast to its precursor indium group 14 lead s unusually high ionization energy 82 pb 7 42 ev is akin to that of group 13 s thallium a result of the full 5d and 4f subshells the lanthanide contraction and the inefficient screening of the nucleus by the 4f electrons results in slightly higher ionization energy for lead than for tin 50 sn 7 34 ev 36 5 bohr model for hydrogen atom edit the ionization energy of the hydrogen atom z 1 displaystyle z 1 can be evaluated in the bohr model 37 which predicts that the atomic energy level n displaystyle n has energy e 1 n 2 z 2 e 2 2 a 0 z 2 r h n 2 z 2 13 6 e v n 2 displaystyle e frac 1 n 2 frac z 2 e 2 2a_ 0 frac z 2 r_ text h n 2 frac z 2 times mathrm 13 6 ev n 2 r h displaystyle r_ text h is the rydberg constant for the hydrogen atom for hydrogen in the ground state z 1 displaystyle z 1 and n 1 displaystyle n 1 so that the energy of the atom before ionization is simply e 13 6 e v displaystyle e mathrm 13 6 ev after ionization the energy is zero for a motionless electron infinitely far from the proton so that the ionization energy is i e h e h 13 6 e v displaystyle i e mathrm h e mathrm h mathrm 13 6 ev this agrees with the experimental value for the hydrogen atom quantum mechanical explanation edit this section needs expansion with more calculation formulas for ionization energies you can help by adding missing information september 2020 according to the more complete theory of quantum mechanics the location of an electron is best described as a probability distribution within an electron cloud i e atomic orbital 38 39 the energy can be calculated by integrating over this cloud the cloud s underlying mathematical representation is the wavefunction which is built from slater determinants consisting of molecular spin orbitals 40 these are related by pauli s exclusion principle to the antisymmetrized products of the atomic or molecular orbitals there are two main ways in which ionization energy is calculated in general the computation for the n th ionization energy requires calculating the energies of z n 1 displaystyle z n 1 and z n displaystyle z n electron systems calculating these energies exactly is not possible except for the simplest systems i e hydrogen and hydrogen like elements primarily because of difficulties in integrating the electron correlation terms 41 therefore approximation methods are routinely employed with different methods varying in complexity computational time and accuracy compared to empirical data this has become a well studied problem and is routinely done in computational chemistry the second way of calculating ionization energies is mainly used at the lowest level of approximation where the ionization energy is provided by koopmans theorem which involves the highest occupied molecular orbital or homo and the lowest unoccupied molecular orbital or lumo and states that the ionization energy of an atom or molecule is equal to the negative value of energy of the orbital from which the electron is ejected 42 this means that the ionization energy is equal to the negative of homo energy which in a formal equation can be written as 43 i i e i displaystyle i_ i e_ i molecules vertical and adiabatic ionization energy edit figure 1 franck condon principle energy diagram for ionization of a diatomic molecule the only nuclear coordinate is the bond length the lower curve is the potential energy curve of the neutral molecule and the upper curve is for the positive ion with a longer bond length the blue arrow is vertical ionization here from the ground state of the molecule to the v 2 level of the ion ionization of molecules often leads to changes in molecular geometry and two types of first ionization energy are defined adiabatic and vertical 44 adiabatic ionization energy edit the adiabatic ionization energy of a molecule is the minimum amount of energy required to remove an electron from a neutral molecule i e the difference between the energy of the vibrational ground state of the neutral species v 0 level and that of the positive ion v 0 the specific equilibrium geometry of each species does not affect this value vertical ionization energy edit due to the possible changes in molecular geometry that may result from ionization additional transitions may exist between the vibrational ground state of the neutral species and vibrational excited states of the positive ion in other words ionization is accompanied by vibrational excitation the intensity of such transitions is explained by the franck condon principle which predicts that the most probable and intense transition corresponds to the vibrationally excited state of the positive ion that has the same geometry as the neutral molecule this transition is referred to as the vertical ionization energy since it is represented by a completely vertical line on a potential energy diagram see figure for a diatomic molecule the geometry is defined by the length of a single bond the removal of an electron from a bonding molecular orbital weakens the bond and increases the bond length in figure 1 the lower potential energy curve is for the neutral molecule and the upper surface is for the positive ion both curves plot the potential energy as a function of bond length the horizontal lines correspond to vibrational levels with their associated vibrational wave functions since the ion has a weaker bond it will have a longer bond length this effect is represented by shifting the minimum of the potential energy curve to the right of the neutral species the adiabatic ionization is the diagonal transition to the vibrational ground state of the ion vertical ionization may involve vibrational excitation of the ionic state and therefore requires greater energy in many circumstances the adiabatic ionization energy is often a more interesting physical quantity since it describes the difference in energy between the two potential energy surfaces however due to experimental limitations the adiabatic ionization energy is often difficult to determine whereas the vertical detachment energy is easily identifiable and measurable analogs of ionization energy to other systems edit while the term ionization energy is largely used only for gas phase atomic cationic or molecular species there are a number of analogous quantities that consider the amount of energy required to remove an electron from other physical systems electron binding energy edit binding energies of specific atomic orbitals as a function of the atomic number because of the increasing number of protons electrons occupying the same orbital are more tightly bound in heavier elements electron binding energy is a generic term for the minimum energy needed to remove an electron from a particular electron shell for an atom or ion due to these negatively charged electrons being held in place by the electrostatic pull of the positively charged nucleus 45 for example the electron binding energy for removing a 3p 3 2 electron from the chloride ion is the minimum amount of energy required to remove an electron from the chlorine atom when it has a charge of 1 in this particular example the electron binding energy has the same magnitude as the electron affinity for the neutral chlorine atom in another example the electron binding energy refers to the minimum amount of energy required to remove an electron from the dicarboxylate dianion o 2 c ch 2 8 co 2 the graph to the right shows the binding energy for electrons in different shells in neutral atoms the ionization energy is the lowest binding energy for a particular atom although these are not all shown in the graph solid surfaces work function edit work function is the minimum amount of energy required to remove an electron from a solid surface where the work function w for a given surface is defined by the difference 46 w e ϕ e f displaystyle w e phi e_ rm f where e is the charge of an electron ϕ is the electrostatic potential in the vacuum nearby the surface and e f is the fermi level electrochemical potential of electrons inside the material note edit nonetheless further research is still needed ...