Chapter 61 Electronic Structure of Atoms Chapter 6

2 The Wave Nature of Light -Visible light is a small portion of the electromagnetic spectrum

Chapter 63 The Wave Nature of Light Frequency (v, nu  – The number of times per second that one complete wavelength passes a given point. Wavelength (  lambda) – The distance between identical points on successive waves. v = c c = speed of light, x 10 8 m/s

Chapter 64 The Wave Nature of Light -We can also say that light energy is quantized -This is used to explain the light given-off by hot objects. -Max Plank theorized that energy released or absorbed by an atom is in the form of “chunks” of light (quanta). E = h v h = plank’s constant, 6.63 x J/s - Energy must be in packets of (hv), 2(hv), 3(hv), etc.

Chapter 65 Quantized Energy and Photons The Photoelectric Effect

Chapter 66 Quantized Energy and Photons -The photoelectric effect provides evidence for the particle nature of light. -It also provides evidence for quantization. -If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. -The electrons will only be ejected once the threshold frequency is reached. -Below the threshold frequency, no electrons are ejected. -Above the threshold frequency, the number of electrons ejected depend on the intensity of the light. The Photoelectric Effect

Chapter 67 Quantized Energy and Photons -Einstein assumed that light traveled in energy packets called photons. -The energy of one photon, E = h. -This equation means that the energy of the photon is proportional to its frequency. The Photoelectric Effect

Chapter 68 Bohr’s Model of the Hydrogen Atom Line Spectra

Chapter 69 Bohr’s Model of the Hydrogen Atom Line Spectra

Chapter 610 Bohr’s Model of the Hydrogen Atom Line Spectra Line spectra can be “explained” by the following equation:

Chapter 611 Bohr’s Model of the Hydrogen Atom Line Spectra Line spectra can be “explained” by the following equation: - this is called the Rydberg equation for hydrogen.

Chapter 612 Bohr’s Model of the Hydrogen Atom -Assumed that a single electron moves around the nucleus in a circular orbit. -The energy of a given electron is assumed to be restricted to a certain value which corresponds to a given orbit. Bohr’s Model

Chapter 613 Bohr’s Model of the Hydrogen Atom -Assumed that a single electron moves around the nucleus in a circular orbit. -The energy of a given electron is assumed to be restricted to a certain value which corresponds to a given orbit. k = x Jz = atomic number n = integer for the orbit Bohr’s Model

Chapter 614 Bohr’s Model of the Hydrogen Atom -Assumed that a single electron moves around the nucleus in a circular orbit. -The energy of a given electron is assumed to be restricted to a certain value which corresponds to a given orbit. n = integer for the orbita o = angstroms z = atomic number Bohr’s Model

Chapter 615 Bohr’s Model of the Hydrogen Atom -Quantitized energy and angular momentum -The first orbit in the Bohr model has n = 1 and is closest to the nucleus. -The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy. -Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (h ). Bohr’s Model – Important Features

Chapter 616 Bohr’s Model of the Hydrogen Atom Ground State – When an electron is in its lowest energy orbit. Excited State – When an electron gains energy from an outside source and moves to a higher energy orbit. Bohr’s Model – Line Spectra

Chapter 617 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

Chapter 618 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

Chapter 619 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

Chapter 620 Bohr’s Model of the Hydrogen Atom Bohr’s Model – Line Spectra

Chapter 621 Bohr’s Model of the Hydrogen Atom -Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. Bohr’s Model

Chapter 622 The Wave Behavior of Matter -DeBroglie proposed that there is a wave/particle duality. -Knowing that light has a particle nature, it seems reasonable to assume that matter has a wave nature. -DeBroglie proposed the following equation to describe the relationship:

Chapter 623 The Wave Behavior of Matter -DeBroglie proposed that there is a wave/particle duality. -Knowing that light has a particle nature, it seems reasonable to assume that matter has a wave nature. -DeBroglie proposed the following equation to describe the relationship:

Chapter 624 The Wave Behavior of Matter -DeBroglie proposed that there is a wave/particle duality. -Knowing that light has a particle nature, it seems reasonable to assume that matter has a wave nature. -DeBroglie proposed the following equation to describe the relationship: -The momentum, mv, is a particle property, where as is a wave property.

Chapter 625 The Wave Behavior of Matter Heisenberg’s Uncertainty Principle - on the mass scale of atomic particles, we cannot determine exactly the position, speed, and direction of motion simultaneously. -For electrons, we cannot determine their momentum and position simultaneously. The Uncertainty Principle

Chapter 626 Quantum Mechanics -These theories (wave/particle duality and the uncertainty principle) mean that the Bohr model needs to be refined.  Quantum Mechanics 

Chapter 627 Quantum Mechanics -The path of an electron can no longer be described exactly, now we use the wavefunction(  ). Wavefunction (  ) – A mathematical expression to describe the shape and energy of an electron in an orbit. -The probability of finding an electron at a point in space is determined by taking the square of the wavefunction: Probability density =  

Chapter 628 Quantum Mechanics -The use of wavefunctions generates four quantum numbers. Principal Quantum Number (n) - This is the same as Bohr’s n - Allowed values: 1, 2, 3, 4, … (integers) - The energy of an orbital increases as n increases - A shell contains orbitals with the same value of n Quantum Numbers

Chapter 629 Quantum Mechanics Secondary (Azimuthal) Quantum Number (l) -Allowed values: 0, 1, 2, 3, 4,., (n – 1) (integers) -Each l represents an orbital type Quantum Numbers

Chapter 630 Quantum Mechanics Secondary (Azimuthal) Quantum Number (l) -Allowed values: 0, 1, 2, 3, 4,., (n – 1) (integers) -Each l represents an orbital type lorbital 0s 1p 2d 3f Quantum Numbers

Chapter 631 Quantum Mechanics Secondary (Azimuthal) Quantum Number (l) -Allowed values: 0, 1, 2, 3, 4,., (n – 1) (integers) -Each l represents an orbital type -Within a given value of n, types of orbitals have slightly different energy s < p < d < f Quantum Numbers

Chapter 632 Quantum Mechanics Magnetic Quantum Number (m l ). -This quantum number depends on l. -Allowed values: -l  +l by integers. -Magnetic quantum number describes the orientation of the orbital in space. Quantum Numbers

Chapter 633 Quantum Mechanics Magnetic Quantum Number (m l ). -This quantum number depends on l. -Allowed values: -l  +l by integers. -Magnetic quantum number describes the orientation of the orbital in space. lOrbitalmlml 0s0 1p - 1, 0, + 1 2d - 2, - 1, 0, + 1, + 2 Quantum Numbers

Chapter 634 Quantum Mechanics Magnetic Quantum Number (m l ). -This quantum number depends on l. -Allowed values: -l  +l by integers. -Magnetic quantum number describes the orientation of the orbital in space. -A subshell is a group of orbitals with the same value of n and l. Quantum Numbers

Chapter 635 Quantum Mechanics Spin Quantum Number (s) -Allowed values: - ½  + ½. -Electrons behave as if they are spinning about their own axis. -This spin can be either clockwise or counter clockwise. Quantum Numbers

Chapter 636 Quantum Mechanics Orbitals and Quantum Numbers

Chapter 637 Representation of Orbitals -All s-orbitals are spherical. -As n increases, the s-orbitals get larger. -As n increases, the number of nodes increase. -A node is a region in space where the probability of finding an electron is zero. The s Orbitals

Chapter 638 Representation of Orbitals The s Orbitals

Chapter 639 Representation of Orbitals -There are three p-orbitals p x, p y, and p z. (The letters correspond to allowed values of m l of -1, 0, and +1.) -The orbitals are dumbbell shaped. The p Orbitals

Chapter 640 Representation of Orbitals The p Orbitals

Chapter 641 Representation of Orbitals -There are 5 d- and 7 f-orbitals. -Four of the d-orbitals have four lobes each. -One d-orbital has two lobes and a collar. The d and f Orbitals

Chapter 642 Representation of Orbitals The d and f Orbitals

Chapter 643 Orbitals in Many Electron Atoms Effective nuclear charge - The charge experienced by an electron in a many-electron atom. Effective Nuclear Charge

Chapter 644 Orbitals in Many Electron Atoms -Electrons are attracted to the nucleus, but repelled by the electrons that screen it from the nuclear charge. -The nuclear charge experienced by an electron depends on its distance from the nucleus and the number of core electrons. -As the average number of screening electrons (S) increases, the effective nuclear charge (z eff ) decreases. -As the distance from the nucleus increases, S increases and z eff decreases. z eff = z - S Effective Nuclear Charge

Chapter 645 Orbitals in Many Electron Atoms -Orbitals can be ranked in terms of energy to yield an Aufbau diagram. -As n increases, note that the spacing between energy levels becomes smaller. Orbitals and Quantum Numbers

Chapter 646 Orbitals in Many Electron Atoms

Chapter 647 Orbitals in Many Electron Atoms - Pauli’s Exclusions Principle - no two electrons can have the same set of 4 quantum numbers. -Therefore, two electrons in the same orbital must have opposite spins. Pauli Exclusion Principle

Chapter 648 Electron Configurations Electron configurations tells us in which orbitals the electrons for an element are located. Three rules: -Electrons fill orbitals starting with lowest n and moving upwards. -no two electrons can fill one orbital with the same spin (Pauli Exclusion Principle). -for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule).

Chapter 649 Electron Configurations

Chapter 650 Electron Configurations and the Periodic Table

Chapter 651 Electron Configurations and the Periodic Table -There is a shorthand way of writing electron configurations -Write the core electrons corresponding to the filled Noble gas in square brackets. -Write the valence electrons explicitly. Example, P: 1s 2 2s 2 2p 6 3s 2 3p 3 but Ne is 1s 2 2s 2 2p 6 Therefore, P: [Ne]3s 2 3p 3

Chapter 652 Homework problems: 6.24, 6.26, 6.34, 6.40, 6.42, 6.44, 6.52, 6.60, 6.64