Chemistry 11 Unit 8 Atoms and the Periodic Table Part II Electronic Structure of Atoms
2 1. Atomic number and atomic mass In the previous section, we have seen that from 50 to 100 years after Dalton proposed his atomic theory, scientists had collected many evidence for the more subtle structure of atoms. By 1920, people had already identified electrons and protons as two major constituents of atoms. (Plus neutron which was not yet identified until 1932.)
3 It has been discovered that chemical elements differ from one another by the number of protons in their nuclei. For example, hydrogen has 1 proton, nitrogen has 7 protons and oxygen has 8 protons. Conversely, an atom that has 1 proton must be hydrogen, while an atom that has 8 protons must be oxygen. The number of protons in a nucleus is called the atomic number (Z).
4 Atomic number also implies the followings: (1) Each proton bears one unit of positive charge. Hence, the atomic number equals the total positive charges on the nucleus. (2) Since a neutral atom has zero net charge, the number of protons must be equal to the number of electrons (each of which has a negative charge). So, atomic number is also equal to the number of electrons for neutral atoms.
5 There are three pieces of information about each element that are always present in the periodic table. Atomic symbol (X) Unique label to identify the element Atomic number (Z) Position in PT; also equals the number of protons Atomic mass (A) Mass of the element
6 How do we calculate atomic mass? Proton, neutron and electron have their own masses. They are not measured in terms of grams but in atomic mass unit (amu). Particle Mass (in amu) Proton 1.00728 Neutron 1.00894 Electron 0.0005414 Usually in quick calculations, we assume both proton and neutron have the mass of 1 amu while neglecting the mass of electron.
7 So, the atomic mass of an atom is determined by the combined total masses of protons and neutrons. Example: To the nearest integer, calculate the mass in amu of a nucleus that contains (a) 17 protons and 18 neutrons, and (b) 17 protons and 20 neutrons. (a) Mass = 17 amu + 18 amu = 35 amu (b) Mass = 17 amu + 20 amu = 37 amu Note that these atoms are equal in type but different in mass.
8 Atoms that have the same atomic number but different in masses are called isotopes. That means, isotopes have the same number of protons (type) but different number of neutrons (mass). The total number of protons and neutrons is called the mass number (A) of an isotope. For instance, 6 has the mass number of 12, while 14 6 C has the mass number of 14. 12 C
9 In general, isotopes are written in either form: A ZX X A where X is the atomic symbol of the element. For example, 23 11 Na is equivalent to Na-23. This isotope of sodium (Na) has 11 protons(of course, as it is sodium), 12 neutrons (because 23 11 = 12), and 11 electrons. Its mass number is 23. Sometimes, the atomic number can be dropped for redundancy.
10 Most elements in nature exist as a mixture of different isotopes. Therefore, the atomic mass reported in the periodic table is the weighed average of the isotopes of an element. For example: Naturally occurring copper consists of 69.17% of Cu-63 and 30.83% Cu-65. The mass of Cu- 63 is 62.939598 amu, and the mass of Cu-65 is 64.927793 amu. What is the atomic mass of Cu? The weighed average is 62.939598 0.6917 + 64.927793 0.3083 = 63.55 amu
11 Practice: Experiments show that chlorine is a mixture which is 75.77% Cl-35, and 24.23% Cl-37. If the precise mass of Cl-35 is 34.968853 amu and of Cl-37 is 36.965903 amu, what is the weighed average mass of chlorine? [35.45 amu]
12 Through certain processes, electrons could be added or removed from an atom to produce ions. (1) If electrons are removed, the resulting species is called cation. The ion is positively charged because there are fewer electrons than protons. (2) If electrons are added, the resulting species is called anion. The ion is negatively charged because there are more electrons than protons.
13 Example: Fill up the following table. Particle # Protons # Neutrons # Electrons 13 27 Al 13 27-13=14 13 33 75 As 33 75-33=42 33 122 51Sb 3+ 51 122-51=71 51-(+3)=48 19 9F 9 19-9=10 9-(-1)=10
14 2. Electronic structure of atoms When hydrogen is irradiated by electricity, some energy is absorbed and re-emitted. With an aid of a prism, the emitted light can be transformed into a line spectrum.
15 How do we explain the line feature of the hydrogen spectrum? Niels Bohr in 1913 proposed that electrons in an atom could not exist in a stable way anywhere outside the nucleus unless they are in a fixed, quantized energy levels.
16 The observed spectrum represents energy level differences occurring when an electron in a higher level gives off energy and drops down to a lower level.
17 The quantized nature of energy levels was explained when the concept of matter wave and the modern quantum theory were developed, respectively, by Louis de Broglie in 1924, and independently by Erwin Schrödinger and Werner Heisenberg in 1925. Louis de Broglie (1892-1987) Erwin Schrödinger (1887-1961) Werner Heisenberg (1901-1976)
18 According to the quantum mechanical model of atoms, electrons possess both wave and particle behaviors. (wave-particle duality) Each energy level of an atom is associated with one unique waveform of the electron wave. This waveform is called an orbital. More precisely, an orbital is a region of space occupied by an electron in an energy level.
19 Different orbitals that electrons can reside are determined by solving the Schrödinger s equation, which is the central formula of quantum mechanics. On solving this, it is found that orbitals (or electron waves) are characterized by three quantum numbers: n, l, and m. n l m Principal quantum number Orbital angular momentum quantum number (or Azimuthal quantum number) Magnetic quantum number
20 (1) Principal quantum number n This quantum number determines the size of the orbital (or electron wave) and how far it is extended from the nucleus. Orbitals having the same n are said to be in the same shell. n ranges from 1 to (in theory)
21 (2) Orbital angular momentum quantum number l It divides a shell into smaller groups of orbitals called subshells. The subshells are identified by the letter s, p, d, f, The values of l range from 0 to n 1 for a shell with the principal quantum number n. Value of l 0 1 2 3 4 Letter designation s p d f g The higher the level, the more subshells it has.
22 (3) Magnetic quantum number m It splits the subshells into individual orbitals. This number describes the orientation of the orbital in space. m has the values ranging from l 1 to l + 1 for a subshell with the Azimuthal quantum number l. Type of subshell s p d f g Azimuthal quantum number l Number of possible values of m 0 1 2 3 4 1 3 5 7 9
23 Orbitals with different sets of n, l, m values can be visualized in the following diagrams. (1) s-type orbitals Spherical in shape Two spheres are separated by a node.
24 (2) p-type orbitals Look like dumbbells Each p-subshell has three p-orbitals which are perpendicular to each other. The two lobes are separated by a nodal plane.
25 (3) d-type orbitals The shapes are cross-like, except for one. Each d-subshell has 5 orbitals.
26 (4) f-type orbitals There are 7 orbitals in the f-subshell.
27 In summary (so far):
28 Solving the Schrödinger equation for hydrogen atom yields the energies for different orbitals. It is found that the orbital energy depends only on the principal quantum number n. That means, all subshells with the same value of n, such as 3s, 3p and 3d subshells will have the same energy (they are said to be degenerate). In addition, the higher the value of n, the higher the energy of the orbital. Mathematically: E n = 13.6 ev n 2
29 Schematically: n = 4 n = 3 n = 2 n = 1
30 The diagram shown on the previous slide is true for hydrogen atom and hydrogen-like ions (which have only one electron). For polyelectronic atoms and ions (that means, many electrons), however, the subshells with the same value of n no longer have the same energy (i.e., they are non-degenerate). The repulsion between electrons in the same or different orbitals cause the orbitals to have different energies.
31 The resulting energy level diagram looks like the following: Orbital energy depends on both n and l. The larger the value of l, the higher the orbital energy.
32 (FYI) The effect of disturbance is directly proportional to the charges on the nucleus and the number of electrons.
33 3. Electron configurations of atoms With each successive increase in atomic number, a given atom has one more electron than the previous atom. Therefore, starting from hydrogen, we can build up the electron configuration of each of the other elements by adding electron one at a time. However, what is the sequence of orbitals in which electrons are added?
34 There are 3 rules that govern the order of orbitals which are filled. (1) Aufbau principle It is also called building-up principle. (Aufbau means building-up in German) This principle states that the electrons of an atom fill the lowest-energy available subshell before filling higher ones. It ensures that the resulting electron configuration corresponds to the most stable form of the element. (Some exceptions, however!)
35 The sequence of the orbitals in ascending order of energy is depicted by the diagram on p.31. 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < There is a trick that helps memorize this pattern.
36 (2) Pauli exclusion principle In addition to the three quantum numbers as proposed in the Schrödinger s quantum mechanics, Wolfgang Pauli (1900-1958) proposed in 1924 that there is the fourth quantum number called spin quantum number. Only 2 possible values: + 1 2 or 1 2 The identity of spin was verified by George Uhlenbeck (1900-1988) and Samuel Goudsmit (1902-1978) in 1925.
37 The actual statement of the Pauli exclusion principle is beyond the scope of chemistry 11. (Something related to the symmetry of wave functions of particles) But in simple words, this principle states that it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers. Its implication is important: Each orbital could have two electrons in maximum!
38 (3) Hund s rule This rule was proposed by Friedrich Hund (1896-1997) in 1927. There are indeed three Hund s rules, but they are usually abbreviated to just Hund s rule. The first rule states that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pair. The other two rules are related to the analysis of atomic and molecular spectra.
39 Using these three rules, we can determine the occupancy of electron shells in an atom. Energy level Types of subshells Number of subshells Number of orbitals Maximum number of electrons 1 S 1 1 2 2 s, p 2 4 8 3 s, p, d 3 9 18 4 s, p, d, f 4 16 32 5 s, p, d, f, g 5 25 50
40 A common way of representing the electron configurations of atoms is as follows: For example: Hydrogen Rule: consecutively write the number of the energy level, the type of subshell, and the number of electrons in that subshell, as superscript.
41 Example: Determine the electron configurations of the first ten elements Element Electron configuration Hydrogen 1s 1 Helium 1s 2 Lithium 1s 2 2s 1 Beryllium 1s 2 2s 2 Boron 1s 2 2s 2 2p 1 Carbon 1s 2 2s 2 2p 2 Nitrogen 1s 2 2s 2 2p 3 Oxygen 1s 2 2s 2 2p 4 Fluorine 1s 2 2s 2 2p 5 Neon 1s 2 2s 2 2p 6
42 Practice: Predict the electron configuration of the following elements. (1) Silicon (2) Technetium (3) Calcium (4) Zirconium (5) Gallium
43 The electron configurations of atoms can also be depicted by energy level diagrams. Each electron that is located in an orbital is represented by an arrow, whose direction (up or down) shows its spin.
44 Example: Draw the energy diagrams for the following elements: (1) Potassium (2) Gallium
45 There are two scenarios we have to pay attention on when constructing the energy level diagrams of atoms. (1) Due to the Hund s rule, electrons will occupy degenerate orbitals singly whenever possible.
46 (2) It has been observed that fully filled or half-filled subshells have a greater stability than subshells having some other numbers of electrons. It results from a quantum mechanical effect between electrons. It happens for atoms with d 4 and d 9 configurations.
47 The electron configurations of most atoms can be deduced easily using the orbital version of the periodic table.
48 The expressions of electron configurations of atoms we have talked about so far are called full configurations because they include all the electrons of the atoms. In fact, the electrons in an atom can be divided into two types: (1) Core electrons: the set of electrons with the configuration of the preceding noble gas. They are not involved in chemical reactions usually. (2) Outer electrons: electrons outside the core. They are the electrons that are involved in chemical reactions.
49 Since the core electrons are usually not significant chemically, they can be represented by a core notation, [X], in which X is the chemical symbol of the preceding noble gas. For example: Aluminum Full configuration: 1s 2 2s 2 2p 6 3s 2 3p 1 Core notation: [Ne] 3s 2 3p 1 For example: Cobalt Full configuration: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 7 Core notation: [Ar] 4s 2 3d 7
50 3. Electron configurations of ions The determination of the electron configurations of ions is similar to that for atoms. (1) For negative ions (anions): Starting from the electron configuration of the neutral atom, add the extra electrons one by one to the orbitals according to the Aufbau principle. For example: O 2- Configuration for O: 1s 2 2s 2 2p 4 Configuration for O 2- : 1s 2 2s 2 2p 4 + 2e - = 1s 2 2s 2 2p 6
51 (2) For positive ions (cations): When electrons are removed, the order does not follow exactly as predicted by the Aufbau principle. Instead, electrons in the outermost shell (i.e., the shell with the largest value of n) are removed first. If electrons fill more than one subshell in the outermost shell, then the electrons in the p subshells are removed first. The order of removing electrons is p electrons > s electrons > d electrons
52 For example: Sn 2+ and Sn 4+ Configuration of Sn: [Kr] 5s 2 4d 10 5p 2 Configuration of Sn 2+ : [Kr] 5s 2 4d 10 Configuration of Sn 4+ : [Kr] 4d 10 (not [Kr] 5s 2 4d 8 ) For example: V 2+ and V 3+ Configuration of V: [Ar] 4s 2 3d 3 Configuration of V 2+ : [Ar] 3d 3 (not [Ar] 4s 2 3d 1 ) Configuration of V 3+ : [Ar] 3d 2
53 Practice: Write down the full electron configurations of the following ions. (1) S 2- (2) K + (3) Co 2+ (4) Fe 3+ (5) Tl 3+
54 4. Valence electrons Depending on the chemical behavior, electrons in an atom can be classified as either core electrons or outer electrons. (p.48 of the notes) The electrons that actively participate in chemical reactions are called valence electrons. But valence electrons are not necessarily outer electrons. The outer electrons in filled d or f subshells do not react and therefore are not valence electrons.
55 For example, for aluminum whose electron configuration is [Ne] 3s 2 3p 1. Only the electrons in the 3s and 3p orbitals are counted toward valence electrons. Hence, it has 2 + 1 = 3 valence electrons. On the other hand, gallium has the configuration of [Ar] 4s 2 3d 10 4p 1. Although it has 13 outer electrons, the 3d subshell is filled; therefore these 10 electrons are excluded. The total number of valence electrons is thus 2 + 1 = 3. Similarly, lead, whose configuration is [Xe] 6s 2 4f 14 5d 10 6p 2, has only 4 valence electrons rather than 28 because its 5d and 4f subshells are filled.
56 If the d subshell is not filled such as Mn: [Ar]4s 2 3d 5, all the 3d electrons should be included, and therefore it will have 2 + 5 = 7 valence electrons. Special cases are those for noble gases. For instance, xenon has the electron configuration of [Kr] 5s 2 4d 10 5p 6. All the outer subshells are filled. These electrons are dormant and will not participate in any chemical reactions. Hence, it has zero valence electron. This explains why noble gases are noble and unreactive. (FYI: Noble gases do react! We will see more in Part III of Chapter 8)
57 There is a trick to help memorize the numbers of valence electrons for main group atoms. # valence electrons = group number
58 Practice: Determine the number of valence electrons for the following species. (1) Silicon (2) Krypton (3) Antimony (4) Iron