Chem 110 General Principles of Chemistry Chapter 5 lectronic Structure of Atoms Chapter 5 deals with the electronic structure of atoms. It is because of the different numbers of electrons in atoms and their different arrangements around the nucleus that atoms react with each other. A reaction will occur, depending on whether or not electrons can either be shared between or transferred from one molecule to another. You will find that the outermost electrons in an atom are the ones that are involved in the breaking of bonds and the formation of new bonds and that we can describe the position of any electron in atom using four basic numbers known as quantum numbers. It is therefore important that we gain a basic understanding of how electrons are arranged around the nucleus of an atom. Chapter 5 1. Read the section on electromagnetic radiation in your textbook and make notes on the following: a) amplitude, wavelength and frequency (the diagram on page 194 is good to gain a better understanding. You should also be visiting these concepts in your Physics lectures.) b) the speed of light and how to relate the frequency and wavelength of electromagnetic radiation. Go through Sample xercise 5.1 and 5.2 as well as the Practice xercises. 2. Read the section on atomic spectra and know how atomic spectra are produced. Also know how to calculate the wavelength of each of the lines in the hydrogen spectrum using Balmer s equation (Note the different values of n for each of the lines). 3. Know what Planck s equation is and what Planck s constant is (You will not be required to memorise constants in an examination). Know how to use Planck s equation to calculate the energy of photons of light. Go through Sample xercise 5.3.and the Practice xercise. 1
4. Read up on the Bohr atom in your textbook and take note of the following points. a) How the energies of the allowed energy levels are calculated. 5. Go through Sample xercises 5.4 and 5.5 as well as the Practice xercises in your textbook to reinforce your understanding of quantum theory. Chapter 5. Nos. 5.6, 5.7, 5.11(a), 5.11(b), 5.15, 5.26. Additional Notes Quantisation If a property is said to be quantised it means that it can adopt only certain values. For instance the number of peas in a pod are quantised as you can only have a whole number of peas. The values such as 2.2 or 5.7 peas are said to be FORBIDDN as you cannot have a fraction of a pea growing in a pod. Is the energy that an electron can have in an atom quantised? The answer to the question is YS, the energies of an electron in an atom are quantised. lectrons can only have certain energies. These energies are the ALLOWD energies. In a certain energy level, all the electrons have the same energy, much like all the cars driving on a highway at 100 km hr -1. Any car that drives faster or slower than this speed is not allowed on that highway. The energy that electrons can adopt is therefore said to be quantised. The diagram overleaf illustrates the difference between non-quantised energy (continuous energy) and quantised energy. 2
nergy continuum Quantised nergy The energy continuum on the left is that which arises from any of Newton s Laws of Motion, which are covered in physics. A car travelling on a straight road can adopt any energy depending upon its mass and its velocity. At the atomic level of matter, however, the energy that electrons can adopt is limited to certain values (in the case above the electron could adopt only six discrete values). The Interaction of lectrons and lectromagnetic Radiation There is a fundamental rule of science that we must remind ourselves of at this point. nergy can neither be created nor destroyed. nergy is conserved. Therefore, when any interaction between atoms and electromagnetic radiation occurs, the energy that goes into this interaction must be the same as the resulting energy after the interaction occurs. This is best explained by the equation below: Atom + photon Atom * 3
If an atom and a photon interact, the atom is said to have absorbed the photon. When the atom does this, its energy must be increased by the same amount of energy as that carried by the photon. The atom is now in a higher energy state as is indicated by the asterisk (*) next to it. We say the atom is excited. Let s take the simplest case. We have an atom which has one electron. That electron has only two allowed energies, a lower energy, 1, and a higher energy, 2. 2 1 Chemists use the symbol for an electron. Now given a free choice an electron will always adopt the lowest energy it can. That state of lowest energy is called the ground state. Q: From the diagram above, which energy will the electron adopt? A: The electron in our atom will choose to adopt energy 1. 2 1 This state of the atom is the ground state. If we now interact our atom with a photon, the atom can absorb the energy of the photon by promoting the electron in 1 up to 2. 2 photon 2 Ground state 1 xcited state 1 4
When an electron goes from one allowed energy to another this is called a TRANSITION. This is symbolized as shown below 2 The electron undergoes a transition from 1 to 2. 1 When the electron is in 2 the atom is now no longer in its lowest possible energy state. It is said to be in an excited state. The energy of the excited state of the atom must be equal to the energy of the ground state of the atom plus the energy of the photon. nergy of the excited atom = nergy of the atom in the ground state + energy of the photon atom* = atom + energy of the photon We know that the energy of the photon is hν and thus atom* atom hν or when we re-arrange this equation atom * - atom hν We can use the symbol 2 to represent the atom in its excited state and 1 to represent the atom in its ground state 1 2 hν We can write the difference between 2 and 1 as Δ 12. 5
Δ 12 hν Therefore to promote an electron from 1 to 2 we must add an amount of energy equal to hν. In this case, as there is a definite value of Δ 12, the atom can only absorb one definite frequency, ( ν ), of photons. Now comes the clever part. The energy of the photon must equal exactly Δ 12 to be absorbed by our atom. If the energy of the photon is anything but Δ 12 it will not be absorbed because the resultant excited atom would not have an allowed energy. Remember a photon is the smallest amount of light one can get. It cannot be divided into smaller parts. Thus if we interact a photon of higher energy than Δ12with the atom then the following would have to occur: The dashed line represents an energy state that is not allowed 2 hν 2 1 1 The energy of the photon is greater than Δ 12. This means that if the atom were to absorb the energy hν the electron would be promoted to. But is not an allowed energy. Therefore the atom will not absorb this photon. Similarly if we interact our atom with a photon of lower energy than Δ 12 then 2 hv 2 1 1 The dashed line represents an energy state that is not allowed 6
Will the atom absorb a photon with energy hv? The electron is not allowed to have energy. Thus again this photon will not be absorbed. In fact our atom can only absorb one particular type of photon; those photons with the exact energy corresponding to Δ 12. This is known as selective absorption and this phenomenon is the basis for atomic spectroscopy. Think of it this way. If the allowed energy states are all stepping stones in a pond and to get one from one stepping stone to the other, you need to gain a certain amount of energy to make the jump, absorbing less energy would mean you would not make it to the next stone and if you tried, you would fall in the water. If you absorbed too much energy, you would jump pass the stone and you would still fall in the water. Therefore to land on the stone, you need to absorb the right amount of energy. Absorption Spectroscopy Atomic absorption spectroscopy uses an instrument known as a spectrometer to direct photons of light through a sample of atoms. The atoms selectively absorb some of the photons; that is, those that correspond to the differences in the allowed energies of the atom. A detector measures indirectly those energies that have been absorbed. The detector produces an absorption spectrum, which is a plot of absorbance, A, vs. the energy of the photons that have been directed at the sample. The absorbance is a measure of the amount of light of a particular energy absorbed by the atom. A nergy For our imaginary atom that contained one electron and two allowed energies what would the absorption spectrum look like? We know that our atom can only absorb 7
one particular energy of photons that corresponds to 12. Thus the absorption spectrum would look like this: A Δ12 nergy The spectrum shows us that one line would be seen at the energy corresponding to Δ 12. Atomic absorption spectra are termed Line Spectra as only specific energies are absorbed due to selective absorption. Note that absorption spectra are often plotted as absorbance vs. wavenumber or absorbance vs. wavelength. Note that the wavenumber ν = 1/λ and taking into account that = hv = hc/λ, = hc ν. xample Q: The absorption spectrum of our imaginary atom was measured to give this spectrum. A 32 500 Wavenumber/cm -1 What is the difference in energy between 1 and 2 in joules? A: Remember: when converting from wavenumber to joules, the unit of the speed of light must be changed to cm s -1. 8
Therefore, c = 2.998 10 1s 8 m 100 cm 1m We know that Δ = hc ν Therefore, = 2.998 10 10 cm s -1 Δ 12 = 6.626 10-34 J s 2.998 10 10 cm s -1 32 500 cm -1 = 6.456 10-19 J Real atoms have many more allowed energy levels than the two we have been dealing with up to now. However the same rules apply. lectrons will always occupy the lowest energy and the atom will normally exist in its ground state. Photons are generally only absorbed by the ground state of the atom, as most atoms in a sample will be in the ground state (at normal room temperatures more than 99.99% of the atoms are in the ground state). Let s say we now have an atom with one electron and four allowed energy states 4 3 2 1 Q: How many lines will we see in the absorption spectrum? A: Three; at the following energies Δ 12, Δ 13 and Δ 14. mission Spectroscopy If we supply a lot of energy to atoms, say through heating them up from normal room temperatures, then the electrons will be promoted from the ground state energy to allowed energy states. Once at those higher excited energies the electron s only wish 9
is to return from whence it came, i.e. back to the ground state. We now have the following situation Atom * Atom How does an atom lose energy? Simple; it emits a photon. Not any photon but a photon that leaves the atom in an allowed energy state. Therefore Atom * Atom + hv High nergy Lower nergy It is important to note here that the electron does not have to return directly to the ground state. Instead it can return stepwise down the energy ladder. In the situation - 4 3 2 - how many transitions can the electron undergo? Remember the only rule is that it must end up at an allowed energy. 1 The answer to the above problem is that the electron can undergo six different transitions thus 10
4 1 2 4 3 2 3 5 6 1 ventually all the electrons will return to the ground state of the atom. To measure an emission spectrum, the detector of our spectrometer measures the energies of the photons emitted when the atoms are excited (usually by heating them up). An emission spectrum is a series of lines, which corresponds to the lowering of the energies of the electrons as they move from one energy level to a lower energy level. In the above case the emission spectrum would have six lines, as six different transitions can occur at six different energies. For instance, it might look like this Intensity of mission 34 23 24 12 13 14 nergy If you look at the figure on the previous page, you will notice that the line labelled 34 corresponds to the transition from 4 to 3. Therefore the line labelled 14 will correspond to the transition from 4 to 1. 11
As in the absorption spectrum we will see a line spectrum. The lines will occur at exactly the same energies as the differences between the allowed energies involved in the transition. Both absorption and emission spectroscopy give us a means to measure the differences between the allowed energies of the electron. THY DON T TLL US ANYTHING ABOUT TH ABSOLUT LCTRONIC NRGIS THAT AR ALLOWD IN TH ATOM. The Allowed lectronic nergies We have already noted that the energies of electrons in atoms are quantised only certain energies are allowed. Spectroscopic measurements such as atomic absorption and emission prove that this is the case. We would not obtain line spectra unless selective absorption (or emission) was occurring. We would not get selective absorption (or emission) if we did not have discrete energies allowed for the electrons. Firstly, however, we must recognise a very important concept. The allowed energies that electrons can adopt are all NGATIV NRGIS. lectrons are negatively charged and the nucleus is positively charged. If the electron is at an infinite distance from the nucleus then, by convention, its potential energy is defined as zero. As we bring the electron closer to the nucleus then a force of attraction between the two will develop. If we now want to remove the electron back to an infinite distance away from the nucleus we must supply energy to overcome the force of attraction between the nucleus and the electron. If we supply energy to a system, this, again by convention, is given a positive sign. As the electron has zero potential energy once it regains an infinite distance from the nucleus it must have had a negative energy when attracted to the nucleus (to satisfy the conservation of energy rule). The closer the electron comes to the nucleus the greater will be the force of attraction and the more negative the electron s energy will be. The ground state of the electron will therefore be the most negative energy available. 12
xample Q: A one electron atom has three allowed energies. (a) - 100 000 cm -1 (b) - 50 000 cm -1 (c) - 20 000 cm -1 Which is the ground state of the atom? A: The ground state will be (a) because 100 000 cm -1 is the most negative energy and therefore the lowest energy. Question From the above example, predict the number of lines and the energies (cm -1 ) they occur at in a) the absorption spectrum and b) the emission spectrum of this atom. xample Q: A one-electron atom is irradiated with visible light. The complete atomic emission spectrum shows peaks at 323 nm, 600 nm and 700 nm. Show that this data is fully consistent with the atom having only three allowed energy states. A: If the atom has only three allowed energy states then we can draw the following energy level diagram. 2nd excited state 1st excited state ground state We can now insert the transitions we would expect in the emission spectrum. 13
A B C 3 transitions are observed and 3 transitions are predicted. Our diagram however imposes a limitation on the energy of the transitions. nergy of Transition B = nergy of Transition A + nergy of Transition C Which is transition B? Well, B must be the highest energy transition, or put another way the lowest wavelength transition. Thus: B (323 nm) = A + C (We cannot say which of the remaining two transitions is transition A and which is transition C, but we don t need this information to answer the question). RMMBR is not proportional to energy and therefore we need to convert the wavelengths to something that is. The easiest option is to convert the wavelengths to wavenumbers. Since A = hc ν A, B = hc ν B and C = hc ν C, B = A + C can be written hc ν B, = hc ν A + hc ν C and therefore ν B = ν A + ν C ν B = 1-9 323 x 10 m = 30960 cm -1 ν ( = 700 nm) = 1m 100 cm 1-9 700 x 10 m = 14290 cm -1 1m 100 cm 14
ν ( = 600 nm) = 1-9 600 x 10 m = 16670 cm -1 1m 100 cm 30960 cm -1 = 16670 cm -1 + 14290 cm -1 30960 cm -1 = 30960 cm -1 Therefore the data is fully consistent with the atom having three allowed energy states. Additional Questions 1. What is the difference between a continuous spectrum and a line spectrum? 2. The emission spectrum of a one-electron atom showed 6 lines: 90000 cm -1 ; 75000 cm -1 ; 50000 cm -1 ; 40000 cm -1 ; 25000 cm -1 ; and 15000 cm -1. How many lines would you expect to see in the absorption spectrum and at what energies? xpress your answer in cm -1. 3. An atom has three allowed energy states; - 100 000 cm -1, - 50 000 cm -1 ; and -30 000 cm -1 a) Draw an energy level diagram for the atom b) Indicate on your diagram, which transitions can occur i) during absorption ii) during emission c) Sketch the absorption spectrum and the emission spectrum one would measure for such an atom showing clearly the energies (cm -1 ) the lines occur at. 15
Past exam questions 1. A light photon of wavelength 500 nm, when compared to light of wavelength 600 nm, has: A) a higher frequency. B) lower energy. C) a greater velocity. D) a shorter wavelength. (1) 2. The frequency of a spectral line of lithium is 4.47 x 10 14 s -1. Calculate the energy of one photon of this light. (1) 3. What is the wavelength of light emitted, in nm, when the electron in a hydrogen atom undergoes a transition from energy level n = 2 to level n = 1? (3) 4. Indicate whether energy is emitted or absorbed when the following electronic transitions occur: (2) i) From n = 3 to n = 5 ii) An electron adds to a H + ion and ends up in the n = 1 energy level. 16
Chem 110 General Principles of Chemistry Quantum numbers, Hund s rule, Pauli s exclusion principle, electronic configurations and the periodic table. Chapter 5 (Sections 5.5 to 5.9) You will find that electrons occupy orbitals within a principle shell and there is a method with which they fill up these orbitals. In this section you will learn the sequential way that electrons fill these orbitals and some methods to use to work these out; the most common being using the periodic table. You will find that many atoms belonging to the same group have similar chemistry. This is because their valence shells are the same. After completing this section you will see how we arrive at this. 1. Know what the four quantum numbers are. Write down the possible values of these quantum numbers in your workbook. 2. Relate these four quantum numbers to principle electronic shells, subshells, orbitals and spin. 3. Read up on penetration and shielding in multi electron atoms and try and understand why there is a difference in energy between s, p and d orbitals within a single principle shell. You also need to understand why a 4s orbital is at a lower energy than the 3d orbital and the 6s orbital is at lower energy than the 4f orbital. 4. Read Sections 5.8 in your textbooks on electron configurations. Important here is the rules for assigning electrons to orbitals. These rules contain Pauli s exclusion principle and Hund s rule. 5. You must know the condensed and expanded spdf notation as well as orbital diagrams for writing electron configurations. 6. Know how to use the Aufbau process in writing electron configurations. 7. Section 5.6 has some descriptions and nice pictures of the s, p and d orbitals. Take note of the shapes of these orbitals. In order to understand the different orientations of these orbitals, you need to understand the planes in which they are represented. Imagine the xy plane being the floor you are standing on; the xz plane being a wall in front of you and the yz plane being a wall to the side of you. This will help you put things into perspective while reading your text. 17
Go through Sample xercises 5.6 to 5.9 in your textbooks and their practice exercises to reinforce these concepts and practice for tests and examinations. Chapter 5. Nos. 5.36, 5.38, 5.40, 5.48, 5.52, 5.54. Additional Questions 1. If there was a g-block in the periodic table how many elements would it consist of? 2. Write down the electron configuration and the orbital diagram for: i) Sulfur ii) Cobalt (Co) iii) Hafnium (Hf) 3. In which groups in the Periodic Table would you find elements with the following valence shell electronic configuration: i) ns 2 np o ii) ns 2 np 4 iii) ns 2 (n-1)d 10 np 4 4. a) Give the symbol and name all the elements which have the valence shell electronic configuration ns 2 (n-1)d 5. b) Write down the electronic configuration and the orbital diagram for the lightest element with the above valence shell configuration. c) Write down a set of four quantum numbers (n, l, m l and m s ) for each of the valence electrons in the above atom. (You will need seven sets of quantum numbers). 18
5. Which of the following sets of quantum numbers for an electron in an atom would be possible, and which would be impossible? xplain your reasoning. i) n = 0, l = 1, m l = -1, m s = + ½ ii) iii) n = 2, l = 0, m l = 0, m s = ½ n = 1, l = 1, m l = 1, m s = + ½ iv) n = 3, l = 2, m l = 0, m s = +1 v) n = 3, l = 2, m l = -3, m s = + ½ vi) n = 4, l = 2, m l = -2, m s = + ½ 6. Identify the sets of four quantum numbers for the bold electrons in the diagrams below: a) 2p b) 4d c) 5f 7. Which of the following sub-shells cannot exist in an atom? i) 2d ii) 3f iii) 4f iv) 1p v) 6p vi) 4g vii) 5g 8. In which block of the periodic table do the following elements belong? i) Xenon ii) uropium iii) Tungsten iv) Strontium v) Scandium vi) Antimony Past exam questions Multiple Choice Questions 1. Which electron configuration is impossible? 2 2 6 2 A) 1s 2s 2p 3s B) 1s 2 2s 2 2p 6 3s 2 3p 6 C) 1s 2 2s 2 2p 6 2d 2 D) 1s 2 2s 2 2p 5 3s 1 (1) 19
2. A bismuth atom has one more electron than a lead atom. Into which energy sub level does this added electron go? A) 5p B) 6p C) 6s D) 7s (1) 3. The electron configuration of the two outer sublevels of vanadium, element number 23, is: A) 3d 2 4s 3 B) 4s 2 4p 3 C) 3d 3 4s 2 4 1 D) 3d 4s (1) 4. If the orbital angular quantum number is l = 3, what are the possible m l values? (1) 5. How many orbitals are there in each of the following sub-levels? i) 3d ii) 4f (1) 6. For each of the following write the condensed/core electronic configuration (2) i) Rb ii) Bi 20