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Chemistry 1A Electronic Structure of Atoms 1

Chapter Six Learning Objectives

• describe the wave properties of radiant energy • understand the origin of light from excited atoms• understand the concept of quantization and the

quantum mechanical view of the atom• define the four quantum numbers and their

relation to electronic structure• write electron configurations for elements and

monatomic ions

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Electronic Structure

• Most of the evidence for our modern view of electronic structure came from studying the radiant energyemitted by excited atoms.

• When an atom absorbs energy in the form of heat, light, or electricity, why do we observe specific colors?

Colors of Excited Atoms

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Radiant Energy

• Although they appear quite different to our senses, visible light, microwaves, and X rays are all forms of radiant energy and are characterized by basic fundamental wave properties.

• Which one of the following waves has the longer wavelength (λ)? the lower frequency (ν)? What property is the same for both waves?

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Wave Properties

• The speed (c) of all forms of radiant energy is the product of the wavelength and the frequency of the wave:

λ (m) × ν (s−1) = c (m/s)where c (the speed of light) = 3.00 × 108 m/s

• The wavelength of radiant energy is inversely related to its frequency:

λνor

νλ cc

==

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Forms of Radiant Energy

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Practice Exercises

• If the temperature of stars is gauged by their colors, then do red stars have a higher or lower temperature than blue-white stars?

• While X rays can cause tissue damage, human skin is not penetrated by visible light. Which travels faster, X rays or visible light? Which form of radiant energy has the longer wavelength?

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Planck’s Equation: Quantized Energy

• Planck proposed that the energy (E) radiated by a heated object is emitted in discrete amounts called quanta, or whole-number multiples of hν:

E (J) = h (J ⋅ s) × ν (s−1) where h (Planck’s constant) = 6.626 × 10−34 J ⋅ s

• The quantized energy comes from the allowed vibrations of the heated atoms, which was unknown to Planck at the time.

• How does Planck’s equation explain the diverse effects of different forms of radiation?

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The Photoelectric Effect:Einstein and Photons

• Einstein proposed that light energymust come in packets, called photons,where the energy of a photon isproportional to its frequency, accordingto Planck’s equation:

Ephoton = hν

• As the frequency of light is increased past the threshold frequency, the excess energy of the photon is transferred to the electron in the form of kinetic energy.

The Photoelectric Effect

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Key Concept

The energy required to eject electrons from sodium metal via the photoelectric effect is 265 kJ/mol.

(a) What wavelength of light in nanometers has sufficient energy per photon to dislodge an electron from the surface of sodium?

(b) If sodium is irradiated with light of 439 nm, then what is the maximum possible kinetic energy of each emitted electron?

(c) How many electrons can be freed by a burst of 439 nm light whose total energy is 1.00 μJ?

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Practice Exercises

• The MRI (magnetic resonance imaging) body scanners used in hospitals operate with 400 MHz radiofrequency energy, much less energy than X rays used for medical imagining. How much energy does this correspond to in kilojoules per mole (assume three significant figures)?

• The watt (W) is the SI unit of power (the measure of energy per unit time) where 1 W = 1 J/s. If the laser in a CD player has an output wavelength of 781 nm and a power level of 0.10 mW, then how many photons strike the CD surface during the playing of a CD 69 minutes in length?

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Line Spectra of Excited Atoms

The emission of light from electronically excited gaseous atoms played a major role in developing the modern view of electronic structure.

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Bohr’s Model of the Hydrogen Atom

• A simple model was developed using the concept of quantization to explain the observed lines of the hydrogen emission spectrum.

• Bohr introduced the condition that the electron in a hydrogen atom could only occupy certain orbits or allowed energy levels, which he labeled using positive integers (n).

• Bohr’s orbits are like steps on a ladder: it is possible to stand on one step or another, but impossible to stand between steps.

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Bohr’s Model of the Hydrogen Atom

• Bohr showed that the potential energy of the single electron in the nth orbit or energy level of the hydrogen atom is given by the equation

• The energy (and therefore the wavelength) of the emitted light is quantized by the difference in energy between the two orbits in the transition.

172 m 10097.1 where1 −×=⎟⎠⎞

⎜⎝⎛−= HH R

nhcRE

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Energy Levels of the Hydrogen Atom

• For n = 1, the electron is in the ground state (lowest or most negative energy).

• For n > 1, the electron is in an excited state.

• Why does the energy of the electron increase (become less negative) with increasing n?

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Key Concept

In one transition, the electron in a hydrogen atom falls from the n = 3 to the n = 2 level. In a second transition, the electron falls from the n = 2 level to the n = 1 level. In comparing the two transitions, the radiation emitted in the second one will have

(a)a lower frequency.(b)a smaller energy per photon.(c) the same energy per photon.(d)a shorter wavelength.

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Schrödinger’s Modelof the Hydrogen Atom

• The idea that the electron is a particle orbiting the nucleus in a fixed path proved to be an insufficient view of electronic structure.

• Bohr’s model was replaced with Schrödinger’s more complex model that highlighted the known wavelike properties of the electron.

• Schrödinger’s model resulted in an equation with solutions called orbitals, which describe a region of space in which an electron is most probably located for an allowed energy level.

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Key Concept

• Bohr’s orbits (defined paths) were replaced with Schrödinger’s orbitals (electron density maps).

• The energy of the electron is precisely known, but there is a large uncertainty in the position of the electron.

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Quantum Numbers

• Schrödinger’s model requires three integer (quantum) numbers, n, l, and ml, to describe each orbital in three-dimensional space.

• These numbers describe the energy and probable location of the electron and they may only have certain allowed combinations.

• Similar to Bohr’s model, the principle quantum number, n, is the primary factor in determining the energy of the electron: the higher the n, the higher the energy of the orbital.

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Quantum Numbers and Orbitals

• As n increases, so does the number and type of allowed orbitals: the collection of orbitals with the same value of nis called a shell.

• Complete the following table for the n = 3 shell:

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Orbital Shapes

• The shapes of orbitals are boundary surfaces that enclose 90% of the total electron density.

• What is the relationship between the radius of maximum probability and the value of n?

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Orbital Shapes

• Beginning with the n = 2 shell, each shell has a p subshell that contains three degenerate orbitals, all with the same dumbbell-like shape but with different orientations.

• Which quantum number, n, l, or ml, is different for each porbital?

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Many-Electron Atoms and theFourth Quantum Number

• The application of Schrödinger’s model to atoms other than hydrogen (many-electron atoms) requires a fourth quantum number, the spin magnetic quantum number, ms.

• It was shown empirically that an electron has an intrinsic magnetic spin with only two possible orientations: aligned with an external magnetic field (ms = +½) or opposed to that field (ms = −½).

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Many-Electron Atoms and thePauli Exclusion Principle

• The importance of the spin magnetic quantum number comes when electrons occupy specific orbitals in many-electron atoms.

• The Pauli exclusion principle states that no two electrons in an atom are allowed to have the same set of four quantum numbers n, l, ml, and ms.

• As a result, orbitals may hold no more than two electrons, which must have opposite spins.

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Key Concept

Indicate the maximum number of electrons that can be described using each of the following sets of allowed quantum numbers:

(a)n = 2, ms = −½

(b)n = 4, l = 1

(c)n = 6, l = 2, ml = −1

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Subshell Energy Levels inMany-Electron Atoms

• For a given value of n, the energy of a subshell increases with increasing value of l.

• The orbitals are filled in order of increasing energy, with no more than two electrons per orbital.

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Key Concept

Imagine a universe in which the value of ms can be +½, 0, and −½. Assuming that all other quantum numbers can take only the values possible in our world and that the Pauli exclusion principle applies, provide each of the following:

(a) the new electron configuration of neon

(b) the Z of the element with a completed n = 2 shell

(c) the number of unpaired electrons in fluorine

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Condensed Electron Configurations

• The core electrons can be represented by the nearest noble gas of lower atomic number.

• The electrons beyond the core electrons are the valence electrons, which determine the chemical properties of an element.

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Anomalous Electron Configurations

• There are some minor departures from the expected configurations, for example that of Cr and Cu.

• Both half-filled and fully-filled subshells have unusual stability.

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Electron Configurations and the Periodic Table

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Electron Configurations of Ions

• Main-group metals form cations with the electron configuration of the preceding noble gas whereas nonmetals form anions with the electron configuration of the following noble gas:

Al ([Ne]3s23p1) ⇒ Al3+ ([Ne]) Cl ([Ne]3s23p5) ⇒ Cl− ([Ar])

• Transition metals form cations by first losing their valence s electrons before losing any delectrons:

Fe ([Ar]4s23d6) ⇒ Fe2+ ([Ar]3d6) ⇒ Fe3+ ([Ar]3d5)

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Practice Exercises

• How many valence electrons, core electrons, and unpaired electrons are in a selenium atom? a copper atom?

• A group of students are considering the identity of the species that has the electron configuration 1s22s22p63s23p63d7. The students offer the following as possible answers: (a) a Mn atom; (b) a Co3+ ion; (c) a Ni2+ ion; and (d) a Cu2+ ion. Which, if any, is the correct identity?