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 (NA = 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 = En=2 - En=1 for the 1st line in the 1st series of the hydrogen spectrum, (see Fig.2)
      • where En=2 and En=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.

  • 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.
    • -


TOP OF PAGE


 

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.


TOP OF PAGE


Spectra of elements - the result of electronic energy level changes

Spectra are not just used to elucidate details of electronic quantum levels, but they are used in chemical analysis to identify and quantitatively elements in a sample and by astronomers to identify elements in distant objects like stars.

Examples of emission and absorption spectra are given at the end of the page.

Emission spectra - electrons are excited to higher quantum level by e.g. high temperature or a high voltage discharge. An electron in an excited atom, drops back down to a lower level and in doing so emits a photon. So all the lines represent all the possible electronic transitions giving a complex emission line spectrum - characteristic fingerprint for every element. Parts 2 and 3 of the above diagram represents what happens on excitation. You can observe emission spectra from the chromosphere of our Sun (~6000-20000oC).

Absorption spectra -  If the visible spectrum of white light is shone through gaseous atoms, particular wavelengths (of photons of specific energy) are absorbed leaving 'black' lines in the spectrum. The photon's energy must match that required to move an electron from one energy level to another higher level. Parts 1 and 2 of the above diagram represents what happens when electrons absorb photons to give the atom an excited state. You can observe absorption spectra from the surface of our Sun (~5500oC).

A non–chemical test method for identifying elements – atomic emission line spectroscopy
 
FLAME EMISSION SPECTROSCOPY - an instrumental method for elements from high resolution line spectra

If the atoms of an element are heated to a very high temperature in a flame they emit light of a specific set of frequencies (or wavelengths) called the line spectrum. These are all due to electronic changes in the atoms, the electrons are excited and then lose energy by emitting energy as photons of light. Each line represents one specific electron energy level change.

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.

These emitted frequencies can be recorded on a photographic plate, or these days a digital camera. Every element atom/ion has its own unique and particular set of electron energies so each emission line spectra is unique for each element (atom/ion) because of a unique set of electron level changes. This produces a different pattern of lines i.e. a 'spectral fingerprint' by which to identify any element in the periodic table .e.g. the diagram on the left shows some of the visible emission line spectra for the elements hydrogen, helium, neon, sodium and mercury.

Note the double yellow line for sodium, hence the dominance of yellow in its flame test colour. In fact the simple flame test colour observations for certain metal ions relies entirely on the observed amalgamation of these spectral lines.

This is an example of an instrumental chemical analysis called spectroscopy and is performed using an instrument called an optical spectrometer (simple ones are called spectroscopes). This method, called flame emission spectroscopy, is a fast and reliable method of chemical analysis. This type of optical spectroscopy has enabled scientists to discover new elements in the past and today identify elements in distant stars and galaxies. The alkali metals caesium (cesium) and rubidium were discovered by observation of their line spectrum and helium identified from spectral observation of our Sun.

Examples of real emission spectra (from student days in 1965!)

Emission spectra hydrogen, helium, neon and sodium

450 to 750 nm in the visible region

Note the brightest lines for sodium are in the yellow region - strongest emission above and strongest absorption below.

Therefore its not surprising in simple flame tests for cations that sodium gives a bright yellow.

 

Emission spectra for potassium, calcium, strontium and barium

450 to 750 nm in the visible region.

The lines for potassium don't seem to indicate a lilac-purple flame test colour but look on the left and there a lot of lines close together in the purple-violet region.

Calcium has many lines in the orange-red region and the flame test colour is often quoted as 'brick red'.

Strontium gives lots of strong emission lines in the red region and the flame colour is red.

Barium shows lots of strong emission lines right across the visible spectrum and the flame colour seems to 'average' them all out with a pale green - which is one of the strongest emission lines.

 


keywords: Na(g) ==> Na+(g) + e- * Na+(g) ==> Na2+(g) + e- * He(g) ==> He+(g) + e- *  chemistry revision notes ionisation energy patterns & hydrogen spectrum AS AQA GCE A level chemistry ionisation energy patterns & hydrogen spectrum AS Edexcel GCE A level chemistry ionisation energy patterns & hydrogen spectrum AS OCR GCE A level chemistry ionisation energy patterns & hydrogen spectrum AS Salters GCE A level chemistry ionisation energy patterns & hydrogen spectrum US grades 11 & 12 chemistry ionisation energy patterns & hydrogen spectrum notes for revising ionisation energy patterns & hydrogen spectrum

KS3 SCIENCE QUIZZES ALPHABETICAL INDEX
GCSE grade 9-1 & IGCSE CHEMISTRY Doc Brown's Travel Pictures & Notes
ADVANCED LEVEL CHEMISTRY [SEARCH BOX] - see below
GCSE 9-1 Physics Revision Notes GCSE 9-1 Biology Revision Notes
All website content © Dr Phil Brown 2000 onwards. All copyrights reserved on revision notes, images, quizzes, worksheets etc. Copying of website material is NOT permitted. Exam revision summaries and references to science course specifications are unofficial. Email doc b: chem55555@hotmail.com

 Doc Brown's Chemistry 

*

 For latest updates see https://twitter.com/docbrownchem

 Have your say about doc b's website

TOP OF PAGE