Ch. 7 Atomic Structure and Periodicity. AP Chemistry

Ch. 7 Atomic Structure and Periodicity AP Chemistry

Ch. 7 Atomic Structure and Periodicity In this chapter we will see that the modern theory of atomic structure accounts for periodicity in terms of the e- arrangements in atoms Quantum mechanics was developed to account for the behavior of light and atoms

7.1 Electromagnetic Radiation Electromagnetic radiation - exhibit wavelike behavior - travels at the speed of light Ex s sunlight, microwaves, x-rays, radiant heat Wavelength (l) distance between two consecutive peaks or troughs in a wave (m or nm) Frequency (n) the number waves or cycles per second 1/s or s -1 or Hz Eqn: ln = c

Note units Sample exercise 7.1 Frequency of Electromagnetic Radiation (complete below) n = c/l = 2.9979 x 10 8 m/s = 4.61 x 10 14 Hz 650. x 10-9 m

7.2 Nature of Matter At the end of the 19 th century the idea prevailed that matter and energy are distinct MATTER ENERGY 1) Consists of particles 1) described as a wave 2) Have mass 2) massless 3) Position can be specified 3) delocalized

7.2 Nature of Matter Max Plank Studied radiation profiles emitted by solid bodies heated to incandescence Found results couldn t be explained in terms of physics of his day (which held that matter could absorb or emit any quantity of energy) Postulated the energy could only be gained or lost in whole-number multiples of the quantity hn

7.2 Nature of Matter ΔE = nhn Where n =# photons h = 6.626 x 10-34 Js Had assumed energy of matter was continuous. Energy is in fact quantized. which means it can occur only in discrete units of size hn. KEY: This means energy has particulate properties.

Sample Exercise 7.2 The energy of a photon (complete below) DE = hn (Δ not always used) n = c/l = 2.9979 x 10 8 m/s = 6.66 x 10 14 s -1 4.50 x 10-7 m What is this in kj/mol?

7.2 Nature of Matter Albert Einstein Proposed electromagnetic radiation itself is quantized. Suggested that electromagnetic radiation can be viewed as a stream of particles. E photon = hn = hc l

Photoelectric effect - when electrons are emitted from the surface of a metal when light strikes it. Observations: 1. Studies in which the frequency of the light is varied show that no electrons are emitted by a given metal below a specific threshold frequency, n o 2. For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light. 3. For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light. 4. For light with frequency greater than the threshold frequency, the kinetic energy, of the emitted electrons increases linearly with the frequency of the light.

Photoelectric Effect KEY: These observations can be explained by assuming that electromagnetic radiation is quantized (consists of photons) (and that the threshold frequency represents the minimum energy required to remove the electrons from the metal s surface.) Light intensity is a measure of number of photons.

Related development, famous eqn: E = mc 2 Main significance: Energy has mass! Thus we can calculate the mass of a photon. Note: This is only in a relativistic sense; there is no rest mass.

7.2 Nature of Matter Summary of Plank and Einstein 1. Energy is quantized it can occur only in discrete amounts 2. Electromagnetic radiation has wave and particle properties Dual nature of light

De Broglie Eqn: l = h mv Key: it allows us to calculate the wavelength for a particle. Sample Exercise 7.3 Calculations of Wavelength (complete below) (Take note of the relative l s you just calculated. How do they compare in size?) the smaller the object, the longer the wavelength.

7.2 Nature of Matter Diffraction when light is scattered from a regular array of points or lines. Ex s CD

7.2 Nature of Matter x-rays directed at a NaCl crystal produce diffraction pattern.

7.2 Nature of Matter X-ray diffraction of a beryl crystal KEY: diffraction patters can only be explained in terms of waves. Thus diffraction provides a test for debroglie s postulate that electrons have wavelengths.

7.2 Nature of Matter Diffraction patterns occur most efficiently when the spacing between the scattering points is about the same length as the wavelength being diffracted. When a beam of electrons were directed at a Ni crystal, Davisson and Germer observed a diffraction pattern which verified debroglie s relationship. KEY: This means electrons have wavelike properties. Pg. 282 Electron diffraction of a titanium/nickel alloy

7.2 Nature of Matter SUMMARY: Electromagnetic Radiation has dual properties (wave & particles). Electrons have dual properties (waves & particles). All matter exhibits particulate and wave properties.

7.3 The Atomic Spectrum of Hydrogen Impt. Expt. study of the emission of light by excited hydrogen atoms. Hydrogen atoms release excess energy by emitting light (of various wavelengths) to produce emission spectrum.

7.3 The Atomic Spectrum of Hydrogen

7.3 The Atomic Spectrum of Hydrogen Significance: only certain energies are allowed for the electron in a hydrogen atom. in other words: the energy of the electron in hydrogen is quantized. ΔE = hn = hc l

7.3 The Atomic Spectrum of Hydrogen

7.4 The Bohr Model Bohr developed the first quantum model for the hydrogen atom. He proposed electrons in Hydrogen move around the nucleus in certain allowed circular orbits. He calculated orbit radii. With the assumption that angular momentum of the electron could occur only in certain increments. Bohr s model gave the hydrogen atom energy levels consistent with the hydrogen emission spectrum.

7.4 The Bohr Model Fig. 7.8

7.4 The Bohr Model Important equation is the expression for the energy levels available to the electron in the hydrogen atom: energy level E = - 2.178 x 10-18 J Z 2 n = integer n 2 Z = nuclear charge Negative sign means energy of the e- bound to the nucleus is lower than it would be if the e- were at an infinite distance (n = ) from nucleus. Bohr calculated hydrogen atom energy levels that exactly matched by experiment.

Calculate the energy of a hydrogen atom when its electron is at n = 6 at n = 1 Calculate ΔE when the electron falls from n = 6 to n = 1. Calculate the wavelength of this emitted photon..

7.4 The Bohr Model Sample Exercise 7.4 Energy Quantization in Hydrogen

7.4 The Bohr Model Two Points of emphasis for Bohr s model: 1. Correctly fits quantized hydrogen; certain circular orbits 2. As the electron gets closer to nucleus, energy is lower/more negative; energy is released

7.4 The Bohr Model In the space below, derive the general equation for determining the energy change when an electron moves from one level to another. (pg. 287) Sample Exercise 7.5 Electron Energies

7.4 The Bohr Model NOTE: Bohr s model applied to other atoms did NOT work. KEY: Bohr s model paved the way for later theories. Electrons do NOT move around the nucleus in circular orbits.

Lyman, Balmer, Paschen Series (Emission) n = 5 n = 4 n = 3 n = 2 n = 1

Balmer, Lyman, and Paschen Series:

Balmer, Lyman, and Paschen Series:

7.5 The Quantum Mechanical Model Werner Heisenberg of the Atom Louis debroglie originated the idea that the electron shows wave properties. Erwin Schrodinger gave emphasis to the wave properties of the electron.

Electron bound to the nucleus is similar to a standing wave. KEY: there are limitations on the allowed wavelengths of a standing wave. Considering the wavelike properties of the electron is a possible explanation for the observed quantization of the hydrogen atom.

^Hy = Ey Schrodinger s eqn: y(psi) = wave function ^H Contains mathematical terms that produce the total energy of an atom when they are applied to the wave function When the equation is analyzed many solutions are found. Each solution consists of a wave function (y) that is characterized by a particular value of E (for an electron). A specific wave function is often called an orbital. An orbital is NOT a Bohr orbit. The wave function gives us NO information about the detailed pathway of the electron.

7.5 The Quantum Mechanical Model of the Atom 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. Eqn: Δx Δ (mv) h 4p What this equation really says is the more accurately we know the particle s position, the less accurately we know its momentum.

7.5 The Quantum Mechanical Model of the Atom The physical meaning of a wave function Psi itself has NO easily visualized meaning. psi 2 indicates the probability of finding an electron near a particular point in space. Eqn:

7.5 The Quantum Mechanical Model of the Atom psi 2 is conveniently represented as a probability distribution. Fig. 7.11 This is of a hydrogen 1s wavefunction

7.5 The Quantum Mechanical Model of the Atom The total probability of finding the electron at a particular distance is called radial probability distribution. Fig. 7.12

The total probability of finding the electron at a particular distance is called radial probability distribution. Fig. 7.12 The maximum in the curve occurs because of the two opposing effects. 1. Probability finding the electron is greatest near the nucleus 2. The volume of the spherical shell increases w/distance from the nucleus. Orbitals usually described as the radius of the sphere that encloses 90%of the total electron probability.

7.6 Quantum Numbers 1 st number: principal quantum number (n) n = 1,2,3 As n increases, orbital size and energy increases 2 nd number: angular momentum quantum numbers (l) s p d f l = (0 n-1) 3 rd number: magnetic quantum number (m l )

7.6 Quantum Numbers Sample Exercise 7.6 Electron subshells (complete below)

7.7 Orbital Shapes and Energies Methods of representing an orbital 1. Probability distribution 2. The surface that surrounds 90% of the total electron probability nodes/nodal surfaces Orbital # nodes s p d f

7.7 Orbital Shapes and Energies p-orbitals (fig. 7.14) Surfaces of orbitals increases as the value of n increases.

7.7 Orbital Shapes and Energies

7.7 Orbital Shapes and Energies

7.7 Orbital Shapes and Energies Degenerate have the same all H s of same n degenerate energypolyelectronic atoms have orbitals in the same sublevel that are degenerate Ex. All 3d orbitals are degenerate in a polyelectronic atom Fig. 7.18

7.7 Orbital Shapes and Energies 4 th Quantum Number: electron spin quantum number (m s ) Quantum # Summary n = 1, 2, 3, 4 l = 0, 1, 2, 3 (n-1) m l = -l 0 +l m s = +1/2 or -1/2 + ½ or - ½

7.7 Orbital Shapes and Energies 1. Give the set of quantum numbers for the highest energy electron in each of the following: Mg Cu Fe P I U 2. Which of the following sets of quantum # s are NOT possible? 3, 1, -1, +1/2 4, 4, 0, +1/2 2, 1, 0, -1/2 2, 0, -1, +1/2 2, 2, 1, +1/2 3, 2, -3, -1/2

7.7 Orbital Shapes and Energies Pauli Exclusion Principle in a given atom no two electrons can have the same set of 4 quantum numbers. Which means an orbital can only. Hold two electrons Which must have opposite spins

7.9 Polyelectronic Atoms Three energy contributions are important: 1. KE of e- 2. PE (+) nucleus (-) e - 3. PE (-) e -..(-) e - Electron correlation problem since electron paths are unknown, their repulsions cannot be calculated exactly

7.9 Polyelectronic Atoms We treat electrons as if it were moving in a field of charge that is the net results of the nuclear attraction and the average repulsions of all the other electrons. Each electron is screened/shielded from nuclear charge by the repulsions of the other electrons. i.e. It s not held as tightly due to their presence.

7.9 Polyelectronic Atoms Hydrogen-like orbitals Have the same general shapes Have different sizes and energies due to the interplay between nuclear attractions and the electron repulsions.

7.9 Polyelectronic Atoms Hydrogen: E ns E np E nd E nf Polyelectronic atoms: E ns E np E nd E nf

7.9 Polyelectronic Atoms The hump of electron density that occurs in the 2s profile very near the nucleus means that although an electron in the 2s orbital spends most of its time a little farther from the nucleus than does an electron in the 2p orbital, it spends a small but very significant amount of time very near the nucleus. We say the 2s electron penetrates the nucleus more than the electron in the 2p orbitals.

7.9 Polyelectronic Atoms This penetration effect causes and electron in the 2s orbital to be attracted to the nucleus more strongly than an electron in the 2p orbital. The 2s orbital is lower in energy than the 2p orbitals for a polyelectronic atom.

7.9 Polyelectronic Atoms In general, the more effectively an orbital allows its electron to penetrate the shielding electrons to be close to nuclear charge, the lower is the energy of that orbital.

(See fig. 7.21) Orbtial Shapes/Energies An s-orbital with nodes, thus from quantum level. 3s = nodes 3p = nodes 3d = nodes

7.9 Polyelectronic Atoms

7.10 The History of the Periodic Table Johann Dobereiner 1 st to recognize patterns triads John Newlands Law of octaves Julius Lothar Meyer Dmitri Ivanovich Mendeleev used atomic masses Given most credit because could be used to make predictions of exitence and properties Predicted the existence of Ga, Sc, Ger Corrected several values for atomic masses The only fundamental difference between our current periodic table and Mendeleev s is uses atomic # now

7.10 The History of the Periodic Table

7.10 The History of the Periodic Table

7.10 The History of the Periodic Table

7.11 The Aufbau Principle and the Periodic Table Valence electrons in outermost energy level Core electrons inner electrons Key: the elements in the same group (vertical columns) have the same valence electron configuration.

7.11 The Aufbau Principle and the Periodic Table

7.11 The Aufbau Principle and the Periodic Table Electron filling rules: 1. (n+1)s orbitals always fill before nd orbitals (e.g. 4s before 3d) Which can be explained by the penetration effect 2. Note that sometimes and electron occupies a 5d orbital instead of a 4f orbital because 4f and 5d energies are similar 3. Note that sometimes and electron occupies a 6d orbital instead of a 5f orbital because 6d and 5f are similar 4. The group labels for Groups 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A indicate # valence e- 5. The groups 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A are called main group elements

2n 2 n 2 Energy Level # electrons # orbitals # of each orbital type 1 2 3 4 5 6

7.12 Periodic Trends in Atomic Properties Ionization Energy the energy required to remove an electron from a gaseous atom or ion. (usually expressed in kj/mol) I 1 I 2 I 3 I 4 (use <, >, or =) Because. Increase in (+) charge binds the electrons more firmly.

7.11 The Aufbau Principle and the Periodic Table

7.11 The Aufbau Principle and the Periodic Table First Ionization energies Increase as we go across a period because electrons in the same level do not shield the increasing nuclear charge thsu the electrons are held more tightly. Decrease as we go down a group because electrons are on average farther from nucleus and are thus less tightly held. Discontinuities: Be B N O

7.11 The Aufbau Principle and the Periodic Table Sample Exercise 7.8 The first IE for phosphorus is 1060 kj/mol, and that for sulfur is 1005 kj/mol. Why? Sample Exercise 7.9 Which atom has the largest 1 st IE, and which one has the smallest second IE? Explain your choices.

7.11 The Aufbau Principle and the Periodic Table Electron Affinity the energy change associated with the addition of an electron to a gaseous atom. X (g) + e - X - (g) Note: Many books define it as the energy released. The more negative the energy, the greater the quantity of energy released..

7.11 The Aufbau Principle and the Periodic Table Generally become more negative across periods because there is a stronger nuclear pull without more electron repulsions. Does NOT form Does form N - vs. C - vs. O - O 2- Does NOT form Does form Electron affinity becomes more positive down columns because the electron is added farther from the nucleus.

7.11 The Aufbau Principle and the Periodic Table Table 7.7 Electron Affinities Of the Halogens Electron Atom Affinity (kj/mol) F -327.8 Cl -348.7 Br -324.5 I -295.2 Fluorine has a smaller electron affinity because Attributed to smaller size of 2p orbitals; e - is closer thus there are more e - /e - repulsions.

7.11 The Aufbau Principle and the Periodic Table Atomic Radius Covalent radii ½ distance between two covalently bonded diatomic molecules Metallic radii ½ distance between metal atoms in solid metal crystals. Decreases across periods because effective nuclear charge is increasing. Increases down columns because there is an increase in orbital sizes in successive principal quantum # s.

7.11 The Aufbau Principle and the Periodic Table Sample Exercise 7.10 Trends in Radii Predict the trends in radius for the following ions: Be 2+, Mg 2+, Ca 2+, Sr 2+.

7.13 The Properties of a Group: The Alkali Metals Information Contained in the Periodic Table: 1. # and type of valence e - determine an atom s chemistry 2. e - configurations are important: Cr, Cu exceptions 3. know group names 4. Metals tendency to give up e - making (+) ions low IE s reactivity increases toward Fr (smallest IE) Nonmetals gain e - making (-) ions large IE s more reactive toward F Metalloids metallic/nonmetallic properties

7.13 The Properties of a Group: The Alkali Metals Alkali Metals Down columns Densities increase mp/bp decrease First IE s decrease Atomic radii increases Ionic radii increases Ionic radii are smaller than covalent radii

7.13 The Properties of a Group: The Alkali Metals Most characteristic chemical property of metals is.ability to lose valence e - Metal + nonmetal Nonmetal acts as oxidizing agent (gets reduced) Metal acts as reducing agent (gets oxidized) 2 Na (s) + S (s) Na 2 S (s) 6 Li (s) + N 2 (g) 2 Li 3 N (s) 2 Na (s) + O 2(g) Na 2 O 2 (s)

7.13 The Properties of a Group: The Alkali Metals Expected trend in reducing ability: Cs> Rb > K > Na > Li With water.. 2 M (s) + 2 H 2 O (l) H 2 (g) + 2 M + (aq) + 2 OH - (aq) + energy The order of reducing ability is: Li > Na > K

7.13 The Properties of a Group: The Alkali Metals Hydration Energies for Li +, Na +, and K + Ions. Ion Hydration Energy kj/mol Li + -510 Na + -402 K + -314 Hydration energy change in energy that occurs when water molecules attach to the M + ion.

7.13 The Properties of a Group: The Alkali Metals Li atoms become Li + ions more easily in water than in gas phase. Polar water molecules are more strongly attracted to Li + ddue to its small size than K + Potassium appears to react more violently with water because K melts thus more surface area leads to a more vigorous reaction.

7.13 The Properties of a Group: The Alkali Metals Peroxide Rxns: metal peroxide + H 2 O base + hydrogen peroxide Na 2 O 2 + BaO 2 + H 2 O H 2 O Metal Oxide + H 2 O base Nonmetal oxide + H 2 O acid