Honors chemistry
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Honors Chemistry. Chapter 7: Quantum Mechanics. 7.1 Wave Properties. Wavelength ( l ) = distance between two in-phase points Measured in meters Frequency ( n ) = number of waves per second Measured in Hertz (Hz) Amplitude ( y ) = distance of maximum displacement from rest position

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Honors Chemistry

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Honors chemistry

Honors Chemistry

Chapter 7: Quantum Mechanics


7 1 wave properties

7.1 Wave Properties

  • Wavelength (l) = distance between two in-phase points

  • Measured in meters

  • Frequency (n) = number of waves per second

  • Measured in Hertz (Hz)

  • Amplitude (y) = distance of maximum displacement from rest position

  • Amplitude corresponds to wave energy


7 1 the wave equation

7.1 The Wave Equation

  • v = ln

  • Find the wavelength of a 256 HZ (middle C) sound wave traveling at 343 m/s.

  • v = ln

  • 343 m/s = l (256 Hz)

  • l = 1.34 m

  • Try this….

    • Find the frequency of a 25.0 cm wave traveling at 0.75 m/s.


7 1 electromagnetic radiation

7.1 Electromagnetic Radiation

  • James Clerk Maxwell (1873)

  • Mathematical description of light waves

  • Light is an electromagnetic wave

  • Speed of light (c) is constant

  • c = 2.99792458 x 108 m/s

  • To 3 sig dig, 3.00 x 108 m/s is fine

  • Try this….

    • Find the frequency of a 250 nm light wave. (Don’t forget about the “nano” prefix!)


7 1 electromagnetic spectrum

7.1 Electromagnetic Spectrum

  • Radio, micro, IR, ROYGBIV, UV, X, g

  • long l ------------------------------- short l

  • low n -------------------------------- high n

  • Radio wave end of the spectrum is low energy radiation

  • Gamma ray end is high energy radiation

  • Black body radiation

  • Wave theory fails to account for this!


7 1 quantum theory

7.1 Quantum Theory

  • Max Planck (1900)

  • Energy is emitted and absorbed only in small, discrete packets called quanta

  • Energy of a quantum of energy given byE = hn

  • h = 6.626 x 10-34 Js (Planck’s constant)

  • Correctly accounts for blackbody curves

  • Planck has no idea why it works!


7 1 quantum theory1

7.1 Quantum Theory

  • Find the energy of a 2.50 x 1014 Hz light wave.

  • E = hn

  • E = (6.626 x 10-34 Js)(2.50 x 1014 Hz)

  • E = 1.66 x 10-19 J

  • A quantum holds a tiny amount of energy!

  • Try this….

    • Find the energy of a 475 nm light wave.

    • Hint: Use the wave equation first!


7 2 the photoelectric effect

7.2 The Photoelectric Effect

  • Albert Einstein (1905)

  • Electrons ejected from surface of metal exposed to light

  • Depends on frequency of light

    • Electrons ejected at a certain cutoff frequency

    • Above cutoff n, electrons leave with more energy

  • Bright light ejects more electrons

  • Quantum theory explains results

  • Light is made of quanta called photons


  • 7 3 spectroscopy

    7.3 Spectroscopy

    • Emission spectra – light given off by glowing objects

    • Can be continuous or discontinuous

    • Line spectra – series of bright lines emitted by gas phase atoms

    • Pattern of bright lines is characteristic of the element that is glowing

    • Absorption spectra – dark lines in spectrum as light passes through a gas


    7 3 bohr s model

    7.3 Bohr’s Model

    • Niels Bohr (1913)

    • Electron energies are quantized

    • Only certain orbits are allowed

    • - RHEn = ------ n2

    • RH = 2.18 x 10-18 J (Rydberg constant)

    • n = 1, 2, 3, 4, ….


    7 3 bohr s model1

    7.3 Bohr’s Model

    • DE = Ef – E0

    • -RH -RHDE = ----- - ----- nf2 n02

    • Factor out RH

    • 1 1 DE = RH (----- - ----- ) n02 nf2

    Link to Hydrogen energy states


    7 3 bohr s model2

    7.3 Bohr’s Model

    • Find the energy of a photon of light emitted by an electron jumping from level 5 down to level 2.

    • DE = RH (1/n52 – 1/n22)

    • DE = (2.18 x 10-18 J)(1/25 – 1/4)

    • DE = -4.58 x 10-19 J

    • Try this….

      • Find the energy of the jump from level 1 to level 4.

      • Find the frequency of the light produced.


    7 4 duality

    7.4 Duality

    • Louis de Broglie (1924)

    • Electrons can be treated as waves

    • Each orbit must contain a whole number of waves…explains orbit quantization!

    • hl = ---- mv

    • mv is momentum (p), so we can write l = h/p

    • Verified by Davisson, Germer, and Thomson

    Link to quantum atom model


    7 4 duality1

    7.4 Duality

    • Find the wavelength of a 3.00 kg duck flying at 5.00 m/s.

    • l = h/mv

    • l = (6.626 x 10-34 Js) / (3.00 kg)(5.00 m/s)

    • l = 4.42 x 10-35 m

    • Try this….

      • Find the wavelength of an electron traveling at 500,000 m/s. (me = 9.11 x 10-31 kg)


    7 5 uncertainty principle

    7.5 Uncertainty Principle

    • Werner Heisenberg (1926)

    • Complementary variables cannot be known to arbitrary precision

    • dp dq ≥ħ/2

    • Minimum limits to uncertainties in values are inversely proportional

    • Position and momentum are an important complementary pair

    • dx dpx≥ħ/2


    7 5 uncertainty principle1

    7.5 Uncertainty Principle

    • Find the uncertainty in velocity of an electron confined to a hydrogen atom (dx = 0.037 nm).

    • dx dpx≥ħ/2

    • (3.7 x 10-11 m) dp ≥ 5.27 x 10-35 Js

    • dp ≥ 1.4 x 10-24 kg m/s

    • p = mv

    • 1.4 x 10-24 kg m/s = (9.11 x 10-31 kg) dv

    • dv = 1.5 x 106 m/s


    7 5 uncertainty principle2

    7.5 Uncertainty Principle

    • Try this…

      • Find the uncertainty in position of a 20.0 mg fly whose position is known to within ±0.5 mm.

  • Uncertainty limits are not significant for macroscopic objects, but they are significant to subatomic particles

  • Cannot know the position and momentum of an electron at the same time!

  • Concept of orbits will not work


  • 7 5 quantum mechanics

    7.5 Quantum Mechanics

    • Erwin Schrödinger (1926)

    • Schrödinger equation – treat electron as a standing wave surrounding the nucleus

    • Schrödinger equation is ugly!

    • Solve for amplitude function (y)

    • Remember – amplitude is energy

    • Produces an energy diagram like Bohr’s, but this one actually works

    • Wave function has no physical meaning


    7 5 copenhagen interpretation

    7.5 Copenhagen Interpretation

    • Max Born (1926)

    • y2 denotes probability

    • Electron is delocalized

    • Wave function collapses on observation

    • electron density refers to magnitude of the probability wave for the electron

    • Orbital = spatial probability distribution

    • Electron clouds

    • Objections: Schrödinger’s Cat

    • Other interpretations


    7 6 quantum numbers

    7.6 Quantum Numbers

    • Set of numbers that describe the distribution of electrons in the atom

    • Principal Quantum Number (n)

      • n = 1, 2, 3, 4, …

      • Corresponds to the n value used by Bohr

  • Describes energy level of the shell

  • Defines the size of the electron cloud


  • 7 6 quantum numbers1

    7.6 Quantum Numbers

    • Angular Momentum Quantum Number (l)

      • l = 0, 1, 2, … , n – 1

      • There are a total of n values

  • Sublevels of the energy level

  • Angular distribution of electron cloud

  • For hydrogen, sublevels are degenerate

  • Correspond to fine structure spectral lines

    • l = 0 is s orbital l = 2 is d orbital

    • l = 1 is p orbital l = 3 is f orbital


  • 7 6 quantum numbers2

    7.6 Quantum Numbers

    • Magnetic Quantum Number (ml)

      • ml = -l, … , 0, …, +l

      • There are a total of 2l + 1 values

  • Number of degenerate orbitals in sublevel

  • Spatial orientation of the orbital

  • Zeeman Effect

  • Electron Spin Quantum Number (ms)

    • ms = +½, -½

    • Two possible electron spin states

    • Spin up, spin down


  • 7 7 atomic orbitals

    7.7 Atomic Orbitals

    • s, p, d, f orbitals

    • Radial probability distributions

    • distance from nucleus of high e- probability


    7 7 atomic orbitals1

    7.7 Atomic Orbitals

    • Angular probability distributions

    • Show regions of high e- probability

    • Cool 3d pictures


    7 7 orbital energies

    7.7 Orbital Energies

    • n determines energy

    • For H, all subshells are degenerate

    • Multielectron atomseach subshell liesat a different energy

    • Shielding effect

    • Fill lowest energyorbitals first


    7 7 the diagonal rule

    7.7 The Diagonal Rule

    • Rule of thumb

    • Shows the orderin which orbitalsare filled

    • Paramagnetic

      • Unpaired e-

      • Attracted to mag

  • Diamagnetic

    • Paired e-

    • Not attracted


  • 7 8 electron configurations

    7.8 Electron Configurations

    • H has 1 electron

    • Put it in 1s

    • Write it 1s1

    • Read “one-s-one”

    • What about He?

    • You got it…1s2

    • Keep filling 1s until it is full

    • But when is it full?


    7 8 pauli exclusion principle

    7.8 Pauli Exclusion Principle

    • No two electrons may share the exact set of quantum numbers

    • Consider Helium’s 1s2 configuration

    • First electron: n = 1, l = 0, ml = 0, ms = +½

    • Second electron: same n, l, ml

    • ms must be -½

    • No room for more electrons in 1s orbital

    • Each orbital can hold only two electrons!


    7 8 electron configurations1

    7.8 Electron Configurations

    • What is the electron configuration of Li?

    • 1s2 2s1

    • What about N?

    • 1s2 2s2 2p3

    • But how are p electrons organized?

    • Hund’s Rule – arrange electrons in such a way as to maximize total spin state

    • Put e-’s in separate orbitals, same spin


    7 9 aufbau principle

    7.9 Aufbau Principle

    • Build up on previous e- configurations

    • Each atom adds one more e-

    • Express configuration with noble gas core

    • Al = 1s2 2s2 2p6 3s2 3p1

    • First 3 terms are the same as Ne config.

    • Write it as [Ne] 3s2 3p1


    7 9 exceptions

    7.9 Exceptions

    • Particularly stable configurations

      • Full sublevel

      • Half-full sublevel

  • Some transition metals rearrange

  • Cr = [Ar] 4s2 3d4

    • Just missed the stable half-full 3d5

    • Kick one e- up to d to get [Ar] 4s1 3d5

  • What other family would do this?

  • Cu = [Ar] 4s2 3d9 Ar 4s1 3d10


  • 7 9 periodicity of electron configuration

    7.9 Periodicity of Electron Configuration


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