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Chapter 6 Electronic Structure of Atoms. David P. White. The Wave Nature of Light. All waves have a characteristic wavelength, l , and amplitude, A . The frequency, f , of a wave is the number of cycles which pass a point in one second.

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Chapter 6 electronic structure of atoms
Chapter 6Electronic Structure of Atoms

David P. White

Chapter 6

The Wave Nature of Light

  • All waves have a characteristic wavelength, l, and amplitude, A.

  • The frequency, f, of a wave is the number of cycles which pass a point in one second.

  • The speed of a wave, v, is given by its frequency multiplied by its wavelength:

  • c = fλ

  • c is the speed of light

Chapter 6

Chapter 6

Example 1: A laser produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation.

Example 2: The YFM radio station broadcasts EM radiation at 99.2 MHz. Calculate the wavelength of this radiation (1 MHz = 106 s-1).

Chapter 6

Quantized Energy and Photons 640.0 nm. Calculate the frequency of this radiation.

  • Planck: energy can only be absorbed or released from atoms in fixed amounts called quanta.

  • For 1 photon (energy packet):

  • E = hf = hc/λ

  • where h is Planck’s constant (6.63  10-34 J.s).

Chapter 6

The Photoelectric Effect and Photons 640.0 nm. Calculate the frequency of this radiation.

  • If light shines on the surface of a metal, there is a point (threshold frequency) at which electrons are ejected from the metal.

Chapter 6

Example 3: (a) A laser emits light with a frequency of 4.69 x 1014s-1. What is the energy of one photon of the radiation from this laser? If the laser emits a pulse of energy containing 5.0 x 1017 photons of this radiation, what is the total energy of that pulse?

Chapter 6

Line Spectra and the Bohr Model x 10

  • Line Spectra

  • Monochromatic light – one λ.

  • Continuous light – different λs.

  • White light can be separated into a continuous spectrum of colors.

Chapter 6

  • Balmer: x 10 discovered that the lines in the visible line spectrum of hydrogen fit a simple equation.

  • Later Rydberg generalized Balmer’s equation to:

  • where RHis the Rydberg constant (1.096776  107 m-1), h is Planck’s constant, n1 and n2 are integers (n2 > n1).

Chapter 6

Bohr Model explains this equation x 10

  • Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun.

  • However, a charged particle moving in a circular path should lose energy, ie, the atom is unstable

  • Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states called orbits.

Chapter 6

Colors from excited gases arise because

electrons move between energy states in the


Black regions show λs absent in the light

Chapter 6

  • Bohr Model because

  • Energy states are quantized, light emitted from excited atoms is quantized and appear as line spectra.

  • Bohr showed that

  • where n is the principal quantum number (i.e., n = 1, 2, 3).

Chapter 6

  • The first orbit has becausen = 1, is closest to the nucleus, and has negative energy by convention.

  • The furthest orbit 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

  • ∆E = Efinal – Einitial = hf

Chapter 6

  • We can show that because

  • When ni > nf, energy is emitted.

  • When nf > ni, energy is absorbed


Chapter 6

  • Limitations of the Bohr Model because

  • Can only explain the line spectrum of hydrogen adequately.

  • Electrons are not completely described as small particles.

Chapter 6

The Wave Behavior of Matter because

  • Explores the wave-like and particle-like nature of matter.

  • Using Einstein’s and Planck’s equations, de Broglie showed:

  • The momentum, mv, is a particle property, whereas  is a wave property.

Chapter 6

The Uncertainty Principle because

  • Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.

  • For electrons: we cannot determine their momentum and position simultaneously.

  • If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then

Chapter 6

Quantum Mechanics and Atomic Orbitals because

  • Schrödinger proposed an equation that contains both wave and particle terms.

  • Solving the equation leads to wave functions, ψ (orbitals).

  • ψ2 gives the probability of finding the electron

  • Orbital in the quantum model is different from Bohr’s orbit

Chapter 6

Chapter 6 because

  • Schrödinger’s 3 QNs: because

    • Principal Quantum Number, n. - same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

Chapter 6

  • Azimuthal Quantum Number, l. - becausedepends on the value of n. The values of l begin at 0 and increase to (n - 1). The letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.

  • Magnetic Quantum Number, ml. - depends on l. Has integral values between -l and +l. Gives the 3D orientation of each orbital. There are (2l +1) allowed values of ml and this gives the no. of orbitals.

  • Total no. of orbitals in a shell = n2

Chapter 6

Chapter 6 because

Representations of Orbitals have the same energy

  • The s-Orbitals

  • All s-orbitals are spherical.

  • As n increases, the s-orbitals get larger & no. of nodes increase.

  • A node is a region in space where the probability of finding an electron is zero, 2 = 0.

  • For an s-orbital, the number of nodes is (n - 1).

Chapter 6

  • The p-Orbitals have the same energy

  • There are three p-orbitals px, py, and pz.

  • The letters correspond to allowed values of ml of -1, 0, and +1.

  • The orbitals are dumbbell shaped and have a node at the nucleus.

  • As n increases, the p-orbitals get larger.

Chapter 6

Chapter 6 have the same energy

  • The d and f-Orbitals have the same energy

  • There are five d and seven f-orbitals.

  • They differ in their orientation in the x, y,z plane

Chapter 6

Many-Electron Atoms have the same energy

  • Orbitals and Their Energies

  • Orbitals of the same energy are said to be degenerate.

  • For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other.

  • Therefore, the Aufbau diagram looks different for many-electron systems.

Chapter 6

Chapter 6

2 opposite directions of spin produce oppositely directed magnetic fields leading to the splitting of spectral lines into closely spaced spectra

  • Since electron spin is quantized, we define magnetic fields leading to the splitting of spectral lines into closely spaced spectrams = spin quantum number = + ½ and - ½ .

  • Pauli’s Exclusion Principle: no two electrons can have the same set of 4 quantum numbers.

    • Therefore, two electrons in the same orbital must have opposite spins.

Chapter 6

Chapter 6

Electron Configurations degeneracy of the electrons.

  • Hund’s Rule

  • Electron configurations - in which orbitals the electrons for an element are located.

  • For degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron.

Chapter 6

  • Condensed Electron Configurations degeneracy of the electrons.

  • Neon completes the 2p subshell.

  • Sodium marks the beginning of a new row.

  • Na: [Ne] 3s1

  • Core electrons: electrons in [Noble Gas].

  • Valence electrons: electrons outside of [Noble Gas].

Chapter 6

  • Transition Metals degeneracy of the electrons.

  • After Ar the d orbitals begin to fill.

  • After the 3d orbitals are full, the 4p orbitals begin to fill.

  • Transition metals: elements in which the d electrons are the valence electrons.

Chapter 6

  • Lanthanides and Actinides degeneracy of the electrons.

  • From Ce onwards the 4f orbitals begin to fill.

  • Note: La: [Xe]6s25d14f0

  • Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

  • Elements Th - Lr have the 5f orbitals filled and are called actinides.

  • Most actinides are not found in nature.

Chapter 6

Electron Configurations and the Periodic Table degeneracy of the electrons.

  • The periodic table can be used as a guide for electron configurations.

  • The period number is the value of n.

  • Groups 1A and 2A have the s-orbital filled.

  • Groups 3A - 8A have the p-orbital filled.

  • Groups 3B - 2B have the d-orbital filled.

  • The lanthanides and actinides have the f-orbital filled.

Chapter 6