Doc Brown's Advanced Level Chemistry Notes

Inorganic Chemistry Periodic Table Revision Notes

 Part 2 Electronic Structure, Spectroscopy & Ionisation Energies

Sections 2.6 Hydrogen Spectrum and 2.7 Ionisation energies

Part 2.6 covers the basic quantum theory to explain the hydrogen spectrum and introduce the concept of the 1st ionisation energy and how it can be determined. Calculations using Planck's Equation are also covered in 2.6. Part 2.7 looks at the spectroscopic-ionisation energy evidence for the electron configurations previously introduced and explained in sections 2.2 to 2.5. This involves considering 1st ionisation energies of the elements and successive ionisation energies for a particular element.

Note: ionisation = ionization !

GCSE/IGCSE/AS Atomic Structure Notes  *  GCSE/IGCSE Periodic Table notes

INORGANIC CHEMISTRY Part 2 sub-index: 2.1 The electronic basis of the modern Periodic Table * 2.2 The electronic structure of atoms (including s p d f subshells/orbitals/notation) * 2.3 Electron configurations of elements (Z = 1 to 56) * 2.4 Electron configuration and the Periodic Table * 2.5 Electron configuration of ions and oxidation states * 2.6 Spectroscopy and the hydrogen spectrum * 2.7 Evidence of quantum levels from ionisation energies

Advanced Level Inorganic Chemistry Periodic Table Index * Part 1 Periodic Table history * Part 2 Electron configurations, spectroscopy, hydrogen spectrum, ionisation energies * Part 3 Period 1 survey H to He * Part 4 Period 2 survey Li to Ne * Part 5 Period 3 survey Na to Ar * Part 6 Period 4 survey K to Kr and important trends down a group * Part 7 s-block Groups 1/2 Alkali Metals/Alkaline Earth Metals * Part 8  p-block Groups 3/13 to 0/18 * Part 9 Group 7/17 The Halogens * Part 10 3d block elements & Transition Metal Series * Part 11 Group & Series data & periodicity plots * All 11 Parts have their own sub-indexes near the top of the pages

 2.6 Spectroscopy and the hydrogen spectrum

• Spectroscopy is the study of how electromagnetic radiation (e.g. light) interacts with matter.
• Studying the spectrum of hydrogen is good example to start with in studying spectroscopy, which in most cases, is the interaction of electromagnetic radiation with atoms or molecules at the quantum level.
• Electromagnetic radiation forms a wide ranging spectrum from radio - microwave - infrared - visible light - uv - x-rays - gamma rays.
• Light can be considered as energy packets called photons which have both the properties of a 'particle' or a transverse  'wave'.
• The relationship between the speed of light, wavelength of the radiation and the frequency of the photon is given by ...
  • c =  , = wavelength (m), = frequency (Hz = s^-1), c = speed of light 3 x 10⁸ ms^-1
• The relationship between the energy of the photon and its wave frequency is given by Planck's Equation 
  • E = h , E = energy of a single photon (J), = h =  Planck's Constant (6.63 x 10-34 JHz^-1), = frequency (Hz)
  • The energy E, is for one photon interacting with one electron in one atom, so E represents the difference in energy between the two electronic quantum levels involved.
  • Therefore you need to multiply E by the Avogadro Constant (N_A = 6.02 x 10²³ mol^-1) to get J mol^-1, and then divide by 1000 to get kJ mol^-1
• When atoms absorb energy e.g. in hot flames, high voltage discharge etc., they can become excited from their normal stable ground state (n=1 in the case of hydrogen), up to a higher 'energy level' state.
• When the excited atoms lose energy and return to the ground state, they emit electromagnetic radiation, usually in the infrared, visible or ultraviolet regions.
• The emitted light can be split and analysed into its constituent frequencies, using a prism or grating in a spectrometer, to produce an atomic emission spectrum of 'lines' of different colour.
• Its also possible for the reverse process to happen, so if light is passed through the atoms in their ground state, absorption of energy occurs at exactly the same frequencies as observed in the emission spectrum. This shows up as black lines against the coloured spectrum background and is known as the absorption spectrum.
• Both emission and absorption spectra can be used to identify elements from their 'finger print' pattern, and from the intensity of the 'signal' quantitative measurements can be made See bottom of page).
• Neils Bohr was the first scientist to successfully explain the spectrum of hydrogen using the theory of 'quantisation of energy' i.e. quantum theory.
  • Atomic spectra are caused by electrons moving between energy levels (shells or sub-shells) and the accompanying quanta of energy being emitted or absorbed.
  • When atom is 'excited', the electron 'jumps' to a higher electronic quantum level e.g. on absorption of a photon.
    • This gives rise to absorption spectra.
  • The atom 'relaxes' back to lower/ground electronic state and loses energy - emission of photons.
    • This gives rise to emission spectra. (see Fig.1)
  • The electron can only exist in certain definite energy (quantum) levels.
  • For each atom a photon of light is absorbed or emitted, the electron changes from one level to another.
  • The energy of the photon is the difference between the energies of the two quantised levels involved in the electronic change.
    • e.g. E of photon = E_n=2 - E_n=1 for the 1st line in the 1st series of the hydrogen spectrum, (see Fig.2)
    • where E_n=2 and E_n=1 are the specific energy values of the electron in the 1st and 2nd principal quantum levels.
  • The frequency of the emitted or absorbed light is given by Planck's Equation: E = hv (details above)

• Spectra are very complex, even for the simplest single electron system of the hydrogen atom discussed below.

  • Fig.1

  • 

• The hydrogen spectrum consists of several series of sharp spectral lines and the 1st series is illustrated in Fig.1

  • Within each series, the lines get closer and closer together and eventually converge.

  • To understand the origin of the series and their 'convergent' character you need study Fig.2 below.

  •  

• The horizontal lines on the diagram Fig.2 represent the increasingly higher electronic energy levels, as you go from the ground state (closest to the nucleus, shell 1, level 1, principal quantum number n = 1), to the point where the electron is lost in ionisation (n = infinity)
  • Each series arises from the possible electronic transitions between a particular level and all the levels above it e.g.
    • The 1st or Lyman Series is between n = 1 (ground state of H) and n = 2, 3, 4 etc. (ultra-violet region).
    • The 2nd or Balmer Series arise from electronic transitions from n = 2 and n = 3, 4, 5, etc. (visible region).
  • Fig.3
  • 
• Particular changes are represented on electronic energy level diagram Fig.3. For hydrogen, arrow ..
  1. represents the 4th line in the 3rd series of the emission spectrum (n=7 to n=3),
  2. represents the 4th line in the 2nd series of the absorption spectrum (n=2 to n=6),
  3. represents the 6th line in the 1st series of the absorption spectrum (n=1 to n=7), and
  4. represents the 4th line of the 1st series of the emission spectrum (n=5 to n=1)

• If the absorbed photon has enough energy, it can remove the most loosely bound electron in a process called ionisation ...
  • The 1st ionisation energy (or enthalpy) is defined as the energy required to completely remove the most weakly held electron from 1 mole of the gaseous atoms.
  • e.g. for the process:  Na_(g) ==> Na⁺_(g) + e^- 
    • this is the equation for the first ionisation energy of sodium atoms
    • ionisation is always endothermic, heat absorbed ΔH = +493 kJ mol^-1
  • For hydrogen, this energy can be calculated from the frequency of the light emitted or absorbed at the conversion point in the first series because it corresponds to the quantum level change from n =1 to n = infinity or vice versa. (see Fig.1)
  • Note that the lines in any series, for any atom, tend to converge in the increasing frequency direction because the energy levels converge in quantum level value the further they are from the influence of the positive nucleus.
• The spectra of multi-electron systems, from He onwards, are much more complex, but from spectroscopy a great deal can be learned about their electronic structure, which aids our understanding of an elements chemical behaviour.
• The emission or absorption spectra of elements can be used to identify and quantify elements from distant stars to the analysis of steel samples.
  • Every element has its 'fingerprint' pattern, though usually, a few selected and unique frequencies are used in practice.
  • The astronomer Hubble provided some of the first evidence of the 'Big Bang' or 'expanding universe' theory by recognising the spectral pattern of the hydrogen series of lines in stars of very distant galaxies. However all the frequencies were displaced to lower values because the immense receding of these distance galaxies causes a Doppler shift, known as the 'red shift'.  In the visible spectrum, VIBGYOR (left to right decreasing frequency, longer wavelength), you can imagine the 'intergalactic' electromagnetic waves being 'stretched' producing a longer wavelength i.e. lower frequency, that is a shift in the 'blue' to 'red' frequency direction. The 'red shift' is observed in every direction from Earth.
    • If the 'Big Bang' reverses, then the 'Big Crunch' would be preceded by observing a 'blue shift' as the waves get 'crunched up' by the Doppler effect.
    • Incidentally a good sound Doppler analogy is the increasing pitch of a car engine as it approaches you (a 'blue shift') at high speed and the decrease in pitch as it moves away from you (a 'red shift').
  • The element helium was identified by its absorption spectrum in our Sun and also by its emission spectrum, when the products of alpha particle decay were collected in a tiny glass container and subjected to spectroscopic study i.e. high voltage discharge to create an emission spectrum.
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2.7 Evidence of quantum levels from ionisation energies

• Evidence for electronic 'shell structure' is obtained from spectroscopy and ionisation energy measurements

• Interpretations of graphs of the first and successive ionization energies of the elements provides evidence for the existence of the main quantum levels and the energy sub-levels too e.g.

• (1) Ionisation energies steadily decrease down a group

  • e.g. for the process:  Na_(g) ==> Na⁺_(g) + e^-  etc.

  • Generally speaking the 1st energy decreases down a group of the periodic table (see graph on the right of the 1st ionisation energies of the group 1 and metals).

  • As you go down the group, each element has an extra shell of occupied electronic energy levels which shield the outermost and most loosely bound electron.

  • Therefore the most outer electron is becoming further and further from the nucleus as the atom gets bigger.

  • The further the electron (in the s sub-shell) is from the nucleus, the less strongly it is held, so less energy is required to remove it in the ionisation process.

  • This appears to outweigh the effect of the increasing nuclear charge (Z) because the volume of the atom is also expanding, allowing for the space required by the orbitals of the extra shell of electrons.

  • Although this simple pattern shows some feature of the group 1/2 atoms is steadily changing, I wouldn't say it was the greatest evidence for the existence of principal quantum levels ('shells').

• (2) The patterns of the 1st ionisation energies when plotted against atomic number (Z)

  • This graph does provide substantial evidence the principal quantum levels and directly relates to the structure of the periodic table which is based on the chemical properties of the elements.

  • The 1st ionisation energy, and is the energy required to remove the most loosely bound electron from one mole of the neutral gaseous atom (it is always endothermic) e.g.

  • 1st IE of helium, He_(g) ==> He⁺_(g) + e^-  (ΔH = +2370 kJ mol^-1 )

    • this is the equation for the first ionization energy of helium atoms.
    • You write a similar equation for ANY element of the periodic table.

  • The energy required to remove the 2nd most loosely bound electron is called the 2nd ionisation energy (first possible with helium), which is therefore defined as the energy required to remove an electron from one mole of the monopositive ions e.g. Na⁺, but here we are just concerned with the first ionization energy.

  • 

  • Graph of periodic ionization data for elements 1 to 38 above.

  • Generally speaking the 1st ionisation energy increase from left to right across a period of the periodic table. As you go across the period from one element to the next, the positive nuclear charge is increasing by one unit as the atomic number increases by one unit and the positive charge is acting on electrons in the same principal quantum level. The effective nuclear charge can be considered to be equal to the number of outer electrons (this is very approximate and NOT a rule) and this is increasing from left to right as no new quantum shell is added i.e. no extra shielding. Therefore the outer electron is increasingly more strongly held by the increasing positive charge of the nucleus and so, increasingly, more energy is needed remove it.

  • BUT if the next 1st electron to be removed from the next element is from a principal 'shell' of electrons, it is much less strongly held, hence the minimum value (as argued above). This occurs at atomic numbers 3, 11, 19, 37, 55 and 87 (alkali metals). The highest values indicate the most stable electron arrangements and these occur at atomic numbers 2, 10, 18, 36, 54 and 86 (noble gases). These numbers themselves indicate a numerical pattern.

  • The 1st ionisation energy (1st IE) pattern shows evidence ...

    • From the broad periodic patterns of 1st IE, electrons are distributed in fixed patterns of principal quantum levels,

      • The minimum ionisation energies correspond to the first element in a period (group 1 alkali metal) and the peaks correspond to the last element in a period (group 0/18 noble gas).

      • These two sets on minimums and maximums correspond to 'new' sets of ionisation energies in a 'new' principal quantum level.

      • BUT, that's not all the graphs show ...

    • From the 'kinks' evidence of sub-shells of electronic energy levels even within principal quantum levels (see section (3) below on the two 'unexpected' decreases in ionisation energy in period 3.

    • You can also see evidence of the d block of elements (3d shell) if you look at the pattern of first ionisation energies of elements 1-38.

      • There is a slow' rise in ionization energy from Z = 21 to Z = 30 (Sc to Zn), it then dips before the expected rise from a group 3/13 element to a group 0/18 element along the same period.

• (3) Evidence from sub-levels - the 'kinks' in the 1st ionization energy graph

  • In the 1st ionisation energy graph you 'kinks' or abrupt decreases  (e.g. Be to B, N to O, Mg to Al and P to S) which provides evidence of sub-shells of principal quantum levels. On the right, period 3 ionisation energies are shown in more detail and you can clearly see this effect and its similar for period 4. To fully these two 'drops' in ionization energy, counter to the period trend, you need to bring in your hopefully gained electron configuration knowledge!

  • (i) A decrease from Mg [1s²2s²2p⁶3s²] to Al [1s²2s²2p⁶3s²3p¹]

    Box spin diagram of 3s3p orbitals ==>

    The anomalously low value for aluminium is considered to be due to the first time a 3p electron is shielded by the full 3s sub–shell and, more importantly, the 3p electron is a bit further away (higher in energy) on average from the nucleus than the 3s electrons (so less strongly bound), so less energy needed to remove it. The effect to some extent overrides the effect of increasing proton number i.e. increase in positive nuclear charge from Mg to Al. However, after the kink, the continued increase in nuclear charge ensures the Period 3 trend for the 1st ionisation energy continues as expected until sulfur, the 2nd anomaly.

  • (ii) A decrease from P [1s²2s²2p⁶3s²3p³]  to S [1s²2s²2p⁶3s²3p⁴]

    Box spin diagram of 3s3p orbitals ==>

    Prior to the 4th 3p electron, the other three p electrons occupy separate p sub–orbitals (Hund's Rule of maximum multiplicity) to minimise repulsion between adjacent orbitals. The anomalously low values for sulphur is considered to be due to the effect of the first pairing of electrons in the 3p orbitals producing a repulsion effect that to some extent overrides the effect of increasing proton number (increase in positive nuclear charge), so less energy needed to remove the 4th p electron. From the 'kink', the Period 3 trend for the 1st ionisation energy continues as expected from sulfur to argon with increase in nuclear charge.

• (4) The consecutive ionisation enthalpies for the same element:

  • e.g. for the process:  Na_(g) ==> Na⁺_(g) + e^- 
    • this is the equation for the first ionisation energy of sodium
    • ionisation is always endothermic, heat absorbed ΔH = +493 kJ mol^-1

  • 2nd IE of sodium, Na⁺_(g) ==> Na²⁺_(g) + e^-  (ΔH = +4562 kJ mol^-1)

    • this is the equation for the 2nd ionisation energy of sodium and dramatically more endothermic.
    • 3rd: Na²⁺_(g) ==> Na³⁺_(g) + e^-  (ΔH = +6940 kJ mol^-1)
    • 4th: Na³⁺_(g) ==> Na⁴⁺_(g) + e^-  (ΔH = +9540 kJ mol^-1)
    • etc. etc. and you can do the same for ANY element of the periodic table until you run out of electrons to be removed!

  • The graphs of ionisation versus ionisation number (1st, 2nd, 3rd etc.) also provide evidence 'shells' of electrons, by looking for sudden extra large leaps in the progressively increasing ionisation energy as each electron is removed.

  • Successive ionisation energies for a given element will always increase because less electrons are being increasingly more strongly held nearer the nucleus by the constant positive nuclear charge Z.

IONISATION ENERGY PATTERNS

• For an a particular element, if successive ionization energies are plotted versus ionisation numbers you get significant increases when the next 'inner shell' has its first electron removed.

  • e.g. successive ionisation energies of oxygen, magnesium, silicon and potassium (graphs above)

  • The resulting patterns show clear evidence of quantum shells and you need to connect the diagrams from the link above with the notes below.

  • For a particular element, each successive ionization energy is larger than the previous one because the positive nuclear charge remains the same but the remaining surrounding electrons are increasingly more strongly held nearer the nucleus by the residual, and increasingly positive, ion. Consequently, more energy is required to remove the next remaining most loosely bound electron.

    • BUT, every so often, coincident with breaking into a new shell of electrons, the ionisation energy takes a much larger increase beyond a 'steady' increase.

  • Oxygen, Z = 8, is 1s²2s²2p⁴ (2.6).

    • The first six ionisation energies (IE) rise steadily (removal of 2s²2p⁴ electrons), then a big jump at the 7th IE to the last two IE's which correspond to the removal of the inner helium shell of electrons (1s²).

    • This suggests the existence of two principal energy levels.

    • You would see a similar initial pattern for the other Group 6 elements, S and Se etc. and each pattern indicative of the number of principal quantum levels from upwards.

  • Magnesium, Z = 12, is 1s²2s²2p⁶3s² (2.8.2).

    • The first two ionization energies are quite low for the removal of the outer 3s electron.

    • A significant rise at the 3rd IE which starts the steadily increasing removal of eight 2s and 2p electrons.

    • Eventually at the 11th IE final jump up to remove the 1s electrons closest to the nucleus, and therefore the most strongly held.

    • This suggests the existence of three principal energy levels.

    • You would see a similar initial pattern for the other Group 2 elements, Be and Ca etc. and each pattern indicative of the number of principal quantum levels from 2 upwards.

  • Silicon, Z = 14, is 1s²2s²2p⁶3s²3p² (2.8.4).

    • The first four ionisation energies rise steadily for removal of the outer most loosely held 3s²3p² electrons until the more stable neon core is left.

    • Then a big jump to the 5th IE to the removal of eight electrons from an inner neon shell (removal of  2s²2p⁶ electrons).

    • Finally, an even bigger jump at the 13th IE for last two ionisation energies which correspond to the removal an inner helium shell of electrons (1s²).

    • This suggests the existence of three principal energy levels.

    • You would see a similar pattern for the other Group 4 elements, C, Ge, Sn and Pb and each pattern indicative of the number of principal quantum levels from 2 upwards.

  • Potassium, Z = 19, is 1s²2s²2p⁶3s²3p⁶4s¹ (2,8,8,1)

    • Because of the wide range of IE values, the 'shell pattern' in ionization energies is better seen by doing a logarithmic plot of the IE values.

    • The first ionization energy is very low (removal of outer 4s electron) leaving an argon core of 18e.

    • Then, on the 2nd IE, eight ionisation energies rise steadily (removal of 3s²3p⁶ electrons).

    • At the 10th IE there is the 2nd big jump when eight ionisation energies rise steadily (removal of 2s²2p⁶ electrons).

    • Then a big jump to the last two IE's which correspond to the removal of the inner helium shell of electrons (1s²).

    • This suggests the existence of four principal energy levels.

    • You would see a similar initial pattern for the other Group 1 elements, Li (first jump only), same initial pattern for Na and Rb etc. and each pattern indicative of the number of principal quantum levels from 2 upwards.

450 to 750 nm in the visible region

450 to 750 nm in the visible region.

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Doc Brown's Advanced Level Chemistry Revision Notes

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