AP Chemistry Page 1 of 9Mr. Markic

Chapter 7 - Quantum Theory and the Electronic Structure of Atoms

Properties of WavesWavelength () is the distance between identical points on successive waves.

Amplitude is the vertical distance from the midline of a wave to the peak or trough.

Frequency (ν) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s).

Review of ConceptsWhich of the waves shown here has:

(a) The highest frequency

(b) The longest wavelength

(c) The greatest amplitude

Electromagnetic Radiation• Visible light consists of electromagnetic waves

• Electromagnetic wave has an electric field component and a magnetic field component

• these two components have the same wavelength and frequency (same speed, but travel in mutually perpendicular planes

• Electromagnetic waves travel 3.00 x 108 m/s

• The higher the frequency, the more energetic the radiation

• Maxwell (1873), proposed that visible light consists of electromagnetic waves.

• Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.

Speed of light (c) in vacuum = 3.00 x 108 m/s

All electromagnetic radiation ν x = c

AP Chemistry Page 2 of 9Mr. MarkicPractice Exercise

The wavelength of the green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation?

What is the wavelength (in meters) of an electromagnetic wave whose frequency is 3.64 x 107 Hz?

Review of ConceptsWhy is radiation only in the UV but not the visible or infrared region responsible for sun tanning?

Plank’s Quantum Theory• Atoms and molecules could emit (or absorb) energy only in discrete quantities, like small

packages or bundles

• Energy changes does not occur smoothly, but in specific steps

• Quantum – the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation

• Energy (E) of a single quantum equals a constant times its frequencyE = hv

• E = energy• h = Planck’s constant (6.63 x 10-34 J-s)• v = frequency

• Mystery #1, “Black Body Problem” Solved by Planck in 1900

• Energy (light) is emitted or absorbed in discrete units (quantum).

Mystery #2, “Photoelectric Effect” Solved by Einstein in 1905

The Photoelectric Effect We accept the idea that light possesses both particle-like and wavelike

properties Light behaves either as a wave or as a stream of particles.

Dual nature (particles and waves) is not unique to light but is characteristic of all matter, including electrons

hn = KE + W

where W is the work function and depends how strongly electrons are held in the metal

AP Chemistry Page 3 of 9Mr. MarkicSample ExerciseCalculate the energy (in joules) of(a) A photon with a wavelength of 5.00 x 104 nm (infrared region)

(b) A photon with a wavelength of 5.00 x 10-2 nm (X ray region)

The energy of a photon is 5.87 x 10-20 J. What is the wavelength (in nanometers)?

The work function of cesium metal is 3.42 × 10−19 J. (a) Calculate the minimum frequency of light required to release electrons from the metal.

(b) Calculate the kinetic energy of the ejected electron if light of frequency 1.00 × 1015 s−1 is used for irradiating the metal.

The work function of titanium metal is 6.93 x 10-19 J. Calculate the kinetic energy of the ejected electrons if light of frequency 2.50 x 1015 s-1 is used to irradiate the metal.

AP Chemistry Page 4 of 9Mr. MarkicBohr’s Theory of the Hydrogen AtomEmission Spectra• Either continuous or line spectra of radiation emitted by

substances• Can be seen by energizing a sample of material either with

thermal energy or with some other form of energy• Line spectra – the light emission only at a specific

wavelength • Every element has a unique emission spectrum.• The characteristic lines in atomic spectra can be used in

chemical analysis to identify unknown atoms, similar to fingerprints are used to identify people

Emission Spectrum of the Hydrogen Atom• The emission of radiation by an energized atom to the electron dropping

from a higher-energy orbit to a lower one and giving up a quantum of energy (a photon) in the form of light

• The brightness of a spectral line depends on how many photons of the same wavelength are emitted

• The emission process in an excited hydrogen atom, according to Bohr’s theory. An electron originally in a higher-energy orbit (n = 3) falls back to a lower-energy orbit (n = 2). As a result, a photon with energy hv is equal to the difference in energies of the two orbits occupied by the electron in the emission process. For simplicity, only three orbits are shown.

• e- can only have specific (quantized) energy values

• light is emitted as e- moves from one energy level to a lower energy level

En = -RH(1n2

) E = RH (1ni2 - 1nf2 )

n (principal quantum number) = 1,2,3,…

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

A mechanical analogy for the emission process. The ball can rest on any step, but not between steps

The energy levels in the hydrogen atom and the various emission series. Each energy level corresponds to the energy associated with an allowed energy state for an orbit, as postulated by Bohr. The emission lines are labeled according to the scheme in table 7.1

AP Chemistry Page 5 of 9Mr. Markic

Sample ExercisesWhat is the wavelength of a photon (in nanometers) emitted during a transition from the ni = 5 state to the nf = 2 state in the hydrogen atom?

What is the wavelength (in nanometers) of a photon emitted during a transition from ni = 6 to nf = 4 state in the H atom?

Which transition in the hydrogen atom would emit light of a shorter wavelength?(a) ni = 5 nf = 3

or

(b) ni = 4 nf = 2

The Dual Nature of the ElectronLouis de Broglie• Light can behave like a stream of particles (photons), and particles like electrons can possess

wave properties• An electron bound to the nucleus behaves like a standing wave (i.e. guitar string)• Waves are stationary because they do not travel along the string• Nodes - the amplitude of the wave at these points is zero (they don’t move at all)• The length of the wave must fit the circumference of the orbit exactly, if not the wave would cancel

itself on each successive orbit

The de Broglie Hypothesis• Radiation can have either a wavelike or particle – like (photon)

character• Hypothesis is useful for small particles like e- • For larger particles the wavelength becomes too small• All matter has wave characteristics

(a) The circumference of the orbit is equal to an integral number of wavelengths. This is an allowed orbit.

(b) The circumference of the orbit is not equal to an integral number of wavelengths. As a result, the electron wave does not close in on itself. This is a nonallowed orbit.

AP Chemistry Page 6 of 9Mr. Markic

Why is e- energy quantized?De Broglie (1924) reasoned that e- is both particle and wave.

2πr = n = h/muu = velocity of e-

m = mass of e-

Sample ExerciseCalculate the wavelength of the “particle” in the following two cases:

(a) The fastest serve in tennis is about 150 miles per hour, or 68 m/s. Calculate the wavelength associated with a 6.0 x 10-2 kg tennis ball traveling at this speed.

(b) Calculate the wavelength associated with an electron (9.1094 x 10-31 kg) moving at 68 m/s.

Calculate the wavelength (in nanometers) of a H atom (mass = 1.674 x 10-27 kg) moving at 7.00 x 102 cm/s.

Schrodinger Wave EquationIn 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- Wave function (ψ) describes:

1 energy of e- with a given ψ2 probability of finding e- in a volume of space

Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

A representation of the electron density distribution surrounding the nucleus in the hydrogen atom. It shows a high probability of finding the electron closer to the nucleus

AP Chemistry Page 7 of 9Mr. Markic

Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers.

Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

“Fill up” electrons in lowest energy orbitals (Aufbau principle)

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom.

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s…

Diamagnetism• Elements that have all of their e- spin paired• Not affected by magnetic fields

Paramagnetic• Elements that don’t have all of their e- spin paired• Strongly affected by magnetic fields

(a) Antiparallel pins of two electrons.(b) The two magnetic fields cancel each other

AP Chemistry Page 8 of 9Mr. Markic

Sample ExerciseWhat is the maximum number of electrons that can be present in the principal level for which n = 3?

Calculate the total number of electrons that can be present in the principal level for which n = 4.

Write a complete set of quantum numbers of each of the electrons in boron (B).

What is the electron configuration of S?

What is the electron configuration of Palladium (diamagnetic)

What is the electron configuration of Phosphorus?

Identify the atom that has the ground-state electron configuration: [Ar] 4s23d6.

AP Chemistry Page 9 of 9Mr. Markic

Big Idea 1: The chemical elements are fundamental building materials of matter, and all matter can be understood in terms of arrangements of atoms. These atoms retain their identity in chemical reactionsDuration: Middle NovemberTextbook Chapter: 7Enduring Understanding Essential Knowledge1.B: The atoms of each element have unique structures arising from interactions between electrons and nuclei.

1.B.1: The atom is composed of negatively charged electrons, which can leave the atom, and a positively charged nucleus that is made of protons and neutrons. The attraction of the electronsto the nucleus is the basis of the structure of the atom. Coulomb’s law is qualitatively useful for understanding the structure of the atom.1.B.2: The electronic structure of the atom can be described using an electron configuration that reflects the concept of electrons in quantized energy levels or shells; the energetics of the electrons in the atom can be understood by considerationof Coulomb’s law.

1.C: Elements display periodicity in their properties when the elements are organized according to increasing atomic number. This periodicity can be explained by the regular variations that occur in the electronic structures of atoms. Periodicity is a useful principle for understanding properties and predicting trends in properties. Its modern-day uses range from examining the composition of materials to generating ideas for designing new materials.

1.C.1: Many properties of atoms exhibit periodic trends that are reflective of the periodicity of electronic structure.1.C.2: The currently accepted best model of the atom is based on the quantum mechanical model.

1.D: Atoms are so small that they are difficult to study directly; atomic models are constructed to explain experimental data on collections of atoms.

1.D.1: As is the case with all scientific models, any model of the atom is subject to refinement and change in response to new experimental results. In that sense, an atomic model is not regarded as an exact description of the atom, but rather a theoretical construct that fits a set of experimental data.1.D.3: The interaction of electromagnetic waves or light with matter is a powerful means to probe the structure of atoms and molecules, and to measure their concentration.

Learning Objective1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data.1.6 The student is able to analyze data relating to electron energies for patterns and relationships.1.7 The student is able to describe the electronic structure of the atom, using PES data, ionization energy data, and/or Coulomb’s law to construct explanations of how the energies of electrons within shells in atoms vary.1.8 The student is able to explain the distribution of electrons using Coulomb’s law to analyze measured energies.1.9 The student is able to predict and/or justify trends in atomic properties based on location on the periodic table and/or the shell model.1.10 Students can justify with evidence the arrangement of the periodic table and can apply periodic properties to chemical reactivity.1.12 The student is able to explain why a given set of data suggests, or does not suggest, the need to refine the atomic model from a classical shell model with the quantum mechanical model.1.13 Given information about a particular model of the atom, the student is able to determine if the model is consistent with specified evidence.1.14 The student is able to use data from mass spectrometry to identify the elements and the masses of individual atoms of a specific element.