Electronic Structure of Atom and Periodicity

1. Electromagnetic Radiation 2. The Nature of Photon 3 1. Electromagnetic Radiation 2. The Nature of Photon 3. The Atomic Spectrum of Hydrogen 4. The Bohr Model 5. The Quantum Mechanical Model of the Atom 6. Quantum Numbers 7. Orbital Shapes and Energies 8. Electron Spin and the Pauli Principle 9. Polyelectronic Atoms 10. The History of the Periodic Table 11. The Aufbau Principle and the Periodic Table 12. Periodic Trends in Atomic Properties

Why do different chemicals give us different colors? Colors in Fireworks: Red: Sr, Li Orange: Fe/Charcoal Yellow: Na Blue: Cu Green: Ba Purple: Cu+Sr Why do different chemicals give us different colors? 

Characteristics of EM Waves Electromagnetic (EM) Radiation: One of the ways that energy travels through space. Characteristics of EM Waves Speed (c) – speed of trough or crest passing through the space. speed of light (2.9979×108 m/s) Wavelength ( l ) – distance between two peaks or troughs in a wave. 

Frequency (v) vs. Wavelength (l) Frequency ( v ) – number of waves (cycles) per second that pass a given point in space. Unit: sec-1, or Hertz For EM wave, frequency is inversely proportional to Wavelength: c = v x l Or v = c/l

Classification of Electromagnetic Radiation

Practice: What is the frequency of red light from common laser pointer (wavelength at 650 nm)? c = 2.9979×108 m/s 4.62 x 1014 Hz

Practice: What is energy for ultraviolet light (wavelength at 350 nm) in kJ/mol? c = 2.9979×108 m/s

c = 2.9979×108 m/s Practice: Household microwave use 2.45 GHz electromagnetic wave. Calculate the energy of this microwave radiation in kJ/mol.

Types of Electromagnetic Radiation By Wavelength Radiowaves Microwaves Infrared (IR) Visible: 400 nm < l < 800nm ROYGBIV Ultraviolet (UV) X-rays Gamma rays high frequency and energy

Pickle Light: https://www.youtube.com/watch?v=2vNeMeniYWY (Dangerous! don’t try at home without Dr. Wen :O ) Household 120V through the pair of gater clip Yellow glow from sodium in the pickled cucumber

Marx Planck’s theory Energy is quantized. Electromagnetic radiation is a stream of “particles” called photons. Energy of one photon: h (Planck’s constant) = 6.625×10-34 J • s Dual nature of light: Electromagnetic radiation (and all matter) exhibits wave properties and particulate properties.

Mystery in the Line Spectrum Continuous spectrum vs. Line spectrum:

Bohr’s Theory on Hydrogen Atom Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. Energy of the electron in the hydrogen atom is quantized. Ground state – lowest possible energy state (n = 1) Only certain energies are allowed for the electron in the hydrogen atom.

Electronic Transitions in the Bohr Model vs Electronic Transitions in the Bohr Model vs. Line Spectrum for Hydrogen Atom

The Bohr explanation of three series of spectral lines emitted by the H atom.

Energy for Electronic Transitions in the Hydrogen Atom For a single electron transition from one energy level to another: ΔE = change in energy of the atom (energy of the emitted photon) nfinal = integer; final energy level (orbital) ninitial = integer; initial energy level (orbital) For emission spectrum, the frequency of light can be calculated through DE = hv

Exercise What color of light is emitted when an excited electron in the hydrogen atom falls from: n = 5 to n = 2 n = 4 to n = 1 DE = hv h = 6.625×10-34 J • s For each transition, use ΔE = hc / λ = (–2.178×10–18)[(1/nf) – (1/ni)]. Solve for λ in each case. a) blue (λ = 434 nm) b) green (λ = 486 nm) c) orange/red (λ = 657 nm) The longest wavelength of light is from transition n = 3 to n = 2 (letter c). blue, λ = 434 nm uv, λ = 97.3 nm

Bohr’s Theory Explains the Line Spectrum in Hydrogen Atom The model suggests only certain allowed circular orbits for the electron. As the electron becomes more tightly bound (smaller n), its energy becomes more negative relative to the zero-energy reference state (free electron). As the electron is brought closer to the nucleus, aka, nf < ni, energy is released from the system. When electron receives photon, it transits into higher energy levels, ni < nf

Beyond Bohr’s Model Bohr’s model only works for hydrogen, also electrons do not move around the nucleus in circular orbits. Heisenberg uncertainty principle: There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time. Δx = uncertainty in a particle’s position Δ(mν) = uncertainty in a particle’s momentum h = Planck’s constant

Wave Behavior of Electrons Louis de Broglie (1892–1987) de Broglie proposed that particles could have wave-like character de Broglie predicted that the wavelength of a particle was inversely proportional to its momentum Because it is so small, the wave character of electrons is significant Tro: Chemistry: A Molecular Approach, 2/e

Electron Diffraction Proof that the electron had wave nature came a few years later with the demonstration that a beam of electrons would produce an interference pattern as waves do If electrons behave only like particles, there should only be two bright spots on the target However, electrons actually present an interference pattern, demonstrating they behave like waves Tro: Chemistry: A Molecular Approach, 2/e

Diffraction patterns of aluminum with x-rays (“true wave”) and electrons. x-ray diffraction of aluminum foil electron diffraction of aluminum foil

Electron microscope: High speed electrons behaves like light, used for imaging

The Quantum-Mechanical Model of the Atom The matter-wave of the electron occupies the space near the nucleus and is continuously influenced by it. The Schrödinger wave equation () allows us to solve for the energy states associated with a particular atomic orbital.

Sample Wave Functions of Hydrogen Atom 1s orbital: n = 1, l = 0 2s orbital: n = 2, l = 0 2p orbital: n = 2, l = -1, 0, +1

Physical Meaning of a Wave Function The square of the function (2) indicates the probability of finding an electron near a particular point in space. Probability distribution – intensity of color is used to indicate the probability value near a given point in space.

Relative Orbital Size Difficult to define precisely. Orbital is a wave function. Picture an orbital as a three-dimensional electron density map. Hydrogen 1s orbital: Radius of the sphere that encloses 90% of the total electron probability.

Principal quantum number (n) – size and energy of the orbital. Angular momentum quantum number (l) – shape of atomic orbitals (sometimes called a subshell). For each n, l = 0, 1, … n-1. Subshells we learned: l = 0 (s), 1 (p), 2 (d), 3 (f) Magnetic quantum number (ml) – orientation of the orbital in space relative to the other orbitals in the atom. For each l, ml = -l, -l+1, …, 0, 1,.., l

Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atom

Electron probability density in the ground-state H atom.

Quantum Numbers (n, l, ml) An atomic orbital is specified by three quantum numbers. Principal quantum number (n): a positive integer: relative size of the orbital and therefore its relative distance from the nucleus. “Shell number” Angular momentum quantum number (l): integer from 0 to (n –1)m, the shape of the orbital. “Subshell number”. Magnetic quantum number (ml): an integer with values from –l to +l, the spatial orientation of the orbital.

Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Quantum Numbers Principal, n (size, energy) Positive integer (1, 2, 3, ...) 1 2 3 1 2 Angular momentum, l (shape) 0 to n – 1 1 +1 +2 -1 -2 -1 +1 -1 +1 Magnetic, ml (orientation) -l,…,0,…,+l

Practice: Determining Sublevel Names and Orbital Quantum Numbers Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers: n = 3, l = 2 n = 2, l = 0 n = 5, l = 1 n = 4, l = 3

Exercise For principal quantum level n = 3, determine the number of allowed subshells (different values of l), and give the designation (such as 3s, etc.) of each. The allowed values of l run from 0 to 2, so the number of allowed subshells is 3. Thus the subshells and their designations are: l = 0, 3s l = 1, 3p l = 2, 3d

Exercise Which of the following sets of quantum numbers is for an electron in 5f subshell? n = 5, l = 3, ml = 3 n = 5, l = 3, ml = -4 n = 5, l = 3, ml = -2 n = 5, l = 2, ml = -3 The magnetic quantum numbers are -2, -1, 0, 1, 2. The number of orbitals is 5.

The 1s, 2s, and 3s orbitals

Energy levels of the H atom.

The Boundary Surface Representations of All Three 2p Orbitals (n = 2, l = 1)

The Boundary Surfaces of All of the 3d Orbitals (n = , l = )

Representation of the 4f Orbitals in Terms of Their Boundary Surfaces (n = , l = )

Electron Spin Electron spin quantum number (ms) – can be +½ or -½. Pauli exclusion principle - in a given atom no two electrons can have the same set of four quantum numbers. An orbital can hold only two electrons, and they must have opposite spins.

Atoms with more than one electron. Electron correlation problem: Since the electron pathways are unknown, the electron repulsions cannot be calculated exactly. When electrons are placed in a particular quantum level, they “prefer” the orbitals in the order s, p, d, and then f.

Penetration Effect A 2s electron penetrates to the nucleus more than one in the 2p orbital. This causes an electron in a 2s orbital to be attracted to the nucleus more strongly than an electron in a 2p orbital. Thus, the 2s orbital is lower in energy than the 2p orbitals in a polyelectronic atom.

A Comparison of the Radial Probability Distributions of the 2s and 2p Orbitals

Penetration Effect for Electron in a 3s Orbital: Opportunity of electron getting “access” to nucleus (low energy state)

A Comparison of the Radial Probability Distributions of the 3s, 3p, and 3d Orbitals: Penetration Effect leads to the order of energy among the subshells, s < p < d < f

Aufbau Principle As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to hydrogen–like orbitals. An oxygen atom as an electron arrangement of two electrons in the 1s subshell, two electrons in the 2s subshell, and four electrons in the 2p subshell. Oxygen: 1s22s22p4

Hund’s Rule The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate (same energy) orbitals.

Orbital Diagram A notation that shows how many electrons an atom has in each of its occupied electron orbitals. Oxygen: 1s22s22p4 Oxygen: 1s 2s 2p

Valence Electrons The electrons in the outermost principal quantum level of an atom. 1s22s22p6 (valence electrons = 8) 1s22s22p63s23p64s23d104p2 (valence electrons= 4) The elements in the same group on the periodic table have the same valence electron configuration.

The Orbitals Being Filled for Elements in Various Parts of the Periodic Table

Order of Subshell Filling in Ground State Electron Configurations 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 1. Diagram putting each energy shell on a row and listing the subshells, (s, p, d, f), for that shell in order of energy, (left-to-right) 2. draw arrows through the diagonals, looping back to the next diagonal each time

Effective Nuclear Charge Zeff Electron configuration determines chemical properties: the Periodicity. Why? Core electrons form cloud of negative charge, “shielding” the attraction between nuclear charge Z and outer electrons. Different atoms have different electron configuration, valence electrons “feel” differently from nuclear attraction Effective Nuclear Charge Zeff: The actual positive charge from nucleus attracting the outer electrons (valence electrons).

Estimate of Effective Nuclear Charge Zeff Zeff = full nuclear charge Z - #core electrons Example: Mg atom: 1s22s22p63s2 Zeff  12 – 10 = 2 Mg2+ ion: 1s22s22p6 Zeff  12 – 2 = 10 O atom: 1s22s22p4 Zeff  8 – 2 = 6

Application of Effective Nuclear Charge Higher Zeff leads to stronger attraction towards the valence electrons, causing Higher Ionization Energy Higher Electron Affinity Smaller Atomic Radius

Ionization Energy Mg → Mg+ + e– I1 = 735 kJ/mol (1st IE) Energy required to remove an electron from a gaseous atom or ion. X(g) → X+(g) + e– Mg → Mg+ + e– I1 = 735 kJ/mol (1st IE) Mg+ → Mg2+ + e– I2 = 1445 kJ/mol (2nd IE) Mg2+ → Mg3+ + e– I3 = 7730 kJ/mol *(3rd IE) *Core electrons are bound much more tightly than valence electrons.

The Values of First Ionization Energy for the Elements in the First Six Periods

Ionization Energy within Period Why In general, as we go across a period from left to right, the first ionization energy increases? Electrons added in the same principal quantum level do not completely shield the increasing nuclear charge caused by the added protons. Zeff consistently increases from left to right across the period. Electrons in the same principal quantum level are generally more strongly bound from left to right on the periodic table.

Ionization Energy for GIIIA and GVIA atoms within Period Group IIIA atoms and Group VIA atoms showed lower ionization energy than preceding atoms S orbital has significantly lower energy than p orbital due to penetration effect. Groups IIIA atom (configuration ns2np1) loses 1 electron from p orbital. Groups IIA atom loses from s orbital Group VA atoms has half-filled p orbital (np3) , extra stability. Thus GVIA atoms (np4) loses e- from filled p orbital to achieve half-filled p orbitals.

Ionization Energy within Group In general, as we go down a group from top to bottom, the first ionization energy decreases. Why? Zeff maintains at similar level. However, the outer electrons are at higher energy level. The electrons being removed are, on average, farther from the nucleus, thus easier to be removed.

Successive Ionization Energies (KJ per Mole) for the Elements in Period 3

Determination of valence electrons from successive Ionization Energy Example: The successive ionization energies of an element in kJ/mol are as follows: I1 = 1,780 I2 = 8,975 I3 = 10,220 I4 = 11,950 I5 = 13,100 Which group does this element most likely belong to?

Electron Affinity Energy change associated with the addition of an electron to a gaseous atom. X(g) + e– → X–(g) In general as we go across a period from left to right, the electron affinities become more negative. In general electron affinity becomes more positive in going down a group.

Figure 8.18 Electron affinities of the main-group elements (in kJ/mol).

Atomic Radius In general as we go across a period from left to right, the atomic radius decreases. Effective nuclear charge increases, therefore the valence electrons are drawn closer to the nucleus, decreasing the size of the atom. In general atomic radius increases in going down a group. Orbital sizes increase in successive principal quantum levels.

Atomic Radii for Selected Atoms

The Alkali Metals Li, Na, K, Rb, Cs, and Fr Most chemically reactive of the metals React with nonmetals to form ionic solids Going down group: Ionization energy decreases Atomic radius increases Density increases Melting and boiling points smoothly decrease

Behavior Patterns for IE and EA Reactive nonmetals have high IEs and highly negative EAs. - These elements attract electrons strongly and tend to form negative ions in ionic compounds. Reactive metals have low IEs and slightly negative EAs. - These elements lose electrons easily and tend to form positive ions in ionic compounds. Noble gases have very high IEs and slightly positive EAs. - These elements tend to neither lose nor gain electrons.

Trends in three atomic properties. Figure 8.19 Trends in three atomic properties. ` Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Metallic Behavior Metals are typically shiny solids with moderate to high melting points. Metals are good conductors of heat and electricity, and can easily be shaped. Metals tend to lose electrons and form cations, i.e., they are easily oxidized. Metals are generally strong reducing agents. Most metals form ionic oxides, which are basic in aqueous solution.

Figure 8.20 Trends in metallic behavior.

Figure 8.22 Highest and lowest O.N.s of reactive main-group elements.

Figure 8.23 Oxide acidity. CaO, the oxide of a main-group metal, is strongly basic. P4O10, the oxide of a main-group nonmetal, is acidic.

Figure 8.24 Acid-base behavior of some element oxides. Oxides become more basic down a group and more acidic across a period.

Figure 8.25 Main-group elements whose ions have noble gas electron configurations.

Ionic Size vs. Atomic Size Cations are smaller than their parent atoms while anions are larger. Ionic radius increases down a group as n increases. Cation size decreases as charge increases. An isoelectronic series is a series of ions that have the same electron configuration. Within the series, ion size decreases with increasing nuclear charge. 3– > 2– > 1– > 1+ > 2+ > 3+

Ionic vs. atomic radii.

Ranking Ions by Size Rank each set of ions in order of decreasing size a) Ca2+, Sr2+ , Mg2+ b) K+, S2- , Cl- c) Au3+, Au+

Practice: Estimate Zeff for outmost e- K, Na+, Al, S, Cl, F Step 1. Write the electron configuration Step 2. identify core electrons vs. outmost electrons Step 3. Zeff = Z – #core electrons F, Cl would require more energy to remove an electron because the electron is more tightly bound due to the increase in effective nuclear charge. K = 1, Na = 1, Na+ = 9, Al = 3, S = 6, Cl = 7, F = 7