Chapter 6 Electronic Structure of atoms

• 6.1 Electromagnetic radiation =c -frequency, hertz, s-1, -wavelength, meter, nm c=3.0x108

m/s) 1m=109nm

• Sample Exercise 6.1 Concepts of Wavelength and Frequency

• Two electromagnetic waves are represented below.

• (a) Which wave has the higher frequency? (b) If one wave represents visible light and the other represents infrared radiation, which wave is which?

Two electromagnetic waves are represented below.

(a) Which wave has the higher frequency? (b) If one wave represents visible light and the other represents infrared radiation, which wave is which?

• C= c=2.9979x108m/s, -nm, -1/s, s-1, hertz(hz), 1m=109nm

• Sample Exercise 7.1

• The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salts such as Sr(NO3)2 and SrCO3 are heated. (This can be easily demonstrated in the lab by dissolving one of these salts in methanol that contains a little water and igniting the mixture in an evaporating dish.) Calculate the frequency of red light of wavelength 6.50 X 102 nm.

• (4.61x1014 s-1)

Practice Exercise• (a) A laser used in eye surgery to fuse detached retinas

produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation. (b) An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4 MHz (megahertz; MHz = 106 s–1). Calculate the wavelength of this radiation. The speed of light is 2.998 × 108 m/s to four significant digits.

• Answers: (a) 4.688 × 1014 s–1, (b) 2.901 m

• 6.2 Quantized energy and photons

• E=h• h-Plank’s constant=6.626x10-34 J-s

• Ephoton=hv• Sample Exercise 6.3 Energy of a PhotonCalculate the energy of one photon of yellow light with a

wavelength of 589 nm.

Practice Exercise• (a) A laser emits light with a frequency of 4.69 × 1014 s–1.

What is the energy of one photon of the radiation from this laser? (b) If the laser emits a pulse of energy containing 5.0 × 1017 photons of this radiation, what is the total energy of that pulse? (c) If the laser emits 1.3 × 10–2 J of energy during a pulse, how many photons are emitted during the pulse?

• Answers: (a) 3.11 × 10–19 J, (b) 0.16 J, (c) 4.2 × 1016 photons

Atomic Spectra and Atomic Spectra and BohrBohr

Atomic Spectra and Atomic Spectra and BohrBohr

If e-’s are in quantized energy If e-’s are in quantized energy states, then ∆E of states can states, then ∆E of states can have only certain values. have only certain values. This explain sharp line This explain sharp line spectra.spectra.

n = 1

n = 2E = -C (1/2 2)

E = -C (1/1 2)n = 1

n = 2E = -C (1/2 2)

E = -C (1/1 2)

PLAY MOVIE

Energy Adsorption/Emission

Energy Adsorption/Emission

See Active Figure 6.9See Active Figure 6.9

Origin of Line SpectraOrigin of Line Spectra

Balmer seriesBalmer series

See Active Figure 6.10See Active Figure 6.10

• E=(-2.178x10-18 J)(Z2/n2) Z=nuclear charge=1 (hydrogen)

• =(-2.178x10-18 J)(1/n2) E=(-2.178x10-18 J)(1/n2

f- 1/n2i)

=hC/E

• 1/=RH(1/n2f- 1/n2

i) RH=Rydberg constant=1.096776x107 m-1

• Sample Exercise 7.4 Energy Quantization in Hydrogen

• Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

• (1.633x10-18)

Sample Exercise 6.4 Electronic Transitions in the Hydrogen Atom

Using Figure 6.14, predict which of the following electronic transitions produces the spectral line having the longest wavelength: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3.

Practice Exercise• Indicate whether each of the following electronic

transitions emits energy or requires the absorption of energy: (a) n = 3 to n = 1; (b) n = 2 to n = 4.

• Answers: (a) emits energy, (b) requires absorption of energy.

E=energy of level nfinal-energy of level ninitial

• =-2.178x10-18 J(1/nfinal2 -1/ ninitial2)

• Sample Exercise 7.5 Electron Energies

• Calculate the energy required to remove electron from a hydrogen atom in its ground state.

• 6.3 The wave behavior of matter

• E=mc2 h=6.626x10-34 J s or 6.626x10-34 kg m2/s

• 1 J= 1 kg m2/s2

• m=h/, or vina=h/m (de Brolie's equation) -velocity

• m -momentum

• Sample Exercise 7.3 Calculations of Wavelength

• Compare the wavelength for an electron (mass = 9.11 X 10-31 kg) traveling at a speed of 1.0 X 107 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s.

• (7.27x10-11)

• Sample Exercise 6.5 Matter WavesWhat is the wavelength of an electron moving with a speed of

5.97 × 106 m/s? The mass of the electron is 9.11 × 10–31 kg.

Practice Exercise

• Calculate the velocity of a neutron whose de Broglie wavelength is 500 pm. The mass of a neutron is given in the table inside the back cover of the text.

• Answer: 7.92 × 102 m/s

SymbolSymbol ValuesValues DescriptionDescription

n (principal)n (principal) 1, 2, 3, ..1, 2, 3, .. Orbital size Orbital size (shell)(shell) and energy and energy

where E = -R(1/nwhere E = -R(1/n22))

ℓℓ (angular(angular 0, 1, 2, .. n-10, 1, 2, .. n-1 Orbital shape or Orbital shape or Azimuthal)Azimuthal) or type or type

(subshell) (subshell)

mmll (magnetic) (magnetic) --ℓℓ..0..+..0..+ℓℓ Orbital Orbital

orientation orientation

#orbitals in shell = n#orbitals in shell = n22 # of orbitals in subshell = 2 # of orbitals in subshell = 2 ℓℓ + 1 + 1

QUANTUM NUMBERSQUANTUM NUMBERS

QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERS

The The shape, size, and energyshape, size, and energy of each orbital of each orbital is a function of 3 quantum numbers:is a function of 3 quantum numbers:

nn (principal)(principal) ff shell shell

ℓℓ (angular or azimuthal) (angular or azimuthal) ff subshell subshell

mm ℓℓ(magnetic)(magnetic) ff designates an orbital designates an orbital within a subshellwithin a subshell

Subshells & Subshells & ShellsShells

Subshells & Subshells & ShellsShells

n = 1n = 1

n = 2n = 2

n = 3n = 3

n = 4n = 4

Types of Atomic Orbitals

See Active Figure 6.14

• s- SPHERICALSPHERICAL in shape-1 orbital in shape-1 orbital• p-p-“dumbbell” shaped-3 orbital“dumbbell” shaped-3 orbital• d-5 orbitald-5 orbital• f-7 orbitalf-7 orbital

• The angular momentum quantum number (l) indicates the shape of the orbital (subshell). (l value is from 0 to n-1)

       For specific main energy level, the number of orbital shapes possible is equal to n, number of orbitals is n2, the number of electrons is 2 n2

       Depending on its value of l, an orbital is assigned a letter (s,p,d,f).

• Value of l 0 1 2 3 4letter used s p d f g

• Sublevels in the atomPrincipal sublevel sublevel Level number, l letter 1 0 s 2 0, 1 s, p 3 0,1, 2 s, p, d 4 0,1,2,3 s, p, d, f

• Orbitals in the atomorbital number of number

of

n l Designation ml orbitals, electronsper

sublevel1 0 1s 0 1 22 0 2s 0 1 2

1 2p -1, 0, +1 3 63 0 3s 0 1 2

1 3p -1, 0, +1 3 6 2 3d -2, -1, 0, +1, +2 5 10

4 0 4s 0 1 21 4p -1, 0, +1 3 6 2 4d -2, -1, 0, +1, +2 5 10 3 4f -3, -2, -1, 0, +1, +2, +3 7 14

• Sample Exercise 6.6 Subshells of the Hydrogen Atom• (a) Without referring to Table 6.2, predict the number of

subshells in the fourth shell, that is, for n = 4. • (b) Give the label for each of these subshells. (c) How

many orbitals are in each of these subshells?• Practice Exercise• (a) What is the designation for the subshell with n = 5 and

l = 1? (b) How many orbitals are in this subshell? (c) Indicate the values of ml for each of these orbitals.

• Answers: (a) 5p; (b) 3; (c) 1, 0, –1

• Exercise 6.7 Using Quantum Numbers• Complete following Statements• (A) when n = 2, the values of l can be _____ and

_____.• (B) When l = 1, the values of ml can be_____,____,

and _____, and the subshell has the letter label ____.• (C) The subshell with l=2 is called a ______subshell• (D) when a subshell is labeled s, the value of l is

_____, and ml has the value_____.• (E) There are _______ orbitals in the p subshell• (F) When a subshell is labeled f, there are ___ values

of ml, corresponding to ___ orbitals

• Practice: 1. An electron with the following four quantum numbers may be an electron in an unfilled (outermost) sublevel of S, N, Ag, Ca, Eu, I, or Cu

a. 3, 2, -1,+1/2b. 4, 3, +2, -1/2c. 2, 1, 0, +1/2• 2. . All of the following sets of quantum numbers are

allowed EXCEPT• a. n = 1, ℓ= 0, mℓ= 0• b. n = 3, ℓ= 2, mℓ = +2• c. n = 4, ℓ= 3, mℓ = –1• d. n = 5, ℓ= 1, mℓ = 0• e. n = 6, ℓ= 2, mℓ = +3

• Sample Exercise 7.6 Electron Subshells

• For principal quantum level n = 5, determine the number of allowed subshells (different values of ℓℓ), and give the designation of each.

• 1.     Electron configuration-the arrangement of electrons in an atom.

       Rules governing electron configurations

• a.      Aufbau principle: an electron occupies the lowest-energy orbital that can receive it.

• b. Pauli exclusion principle: no two electrons in the same atom can have the same set of four quantum numbers.

• c.      Hundi’s rule: orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin.

       Representing electron configurations: orbital notation, electron-configuration notation and noble gas electron configuration.

• Core electrons (inner shell) and valence electrons (outer shell)

Sample Exercise 6.7 Orbital Diagrams and Electron Configurations

Draw the orbital diagram for the electron configuration of oxygen, atomic number 8. How many unpaired electrons does an oxygen atom possess?

• Practice Exercise

• (a) Write the electron configuration for phosphorus, element 15. (b) How many unpaired electrons does a phosphorus atom possess?

• Answers: (a) 1s22s22p63s23p3, (b) three

• Anomalous electron configuration (due to the closeness of the 3d and 4s orbitals)Chromium (Cr): [Ar]4s13d5 (Mo)Copper (Cu): [Ar]4s13d10 (Ag, Au)

• Palladium (Pd): [Kr]5s04d10

• Nb(Niobium) [Kr]5s14d4 -----Rh(Rhodium) [Kr]5s14d8

• Sample Exercise 7.7 Electron Configurations• Give the electron configurations for sulfur (s),

cadmium (Cd), hafnium (Hf), chromium (Cr), copper (Cu), and radium (Ra) using the periodic table inside the front cover of this book.

Sample Exercise 6.9 Electron Configurations from the Periodic Table

(a) Write the electron configuration for bismuth, element number 83. (b) Write the condensed electron configuration for this element. (c) How many unpaired electrons does each atom of bismuth possess?

Practice Exercise• Use the periodic table to write the condensed electron

configurations for (a) Co (atomic number 27) • (b) Te (atomic number 52).• Answers: (a) [Ar]4s23d7 or [Ar]3d74s2, (b) [Kr]5s24d105p4 or

[Kr]4d105s25p4

• The p block element together with the s block element are called the main group elements (or representative elements)

• The d- block element are metals with typical metallic properties and are often referred to as transition elements.

• Diamagnetism: no unpaired electrons, repelled from a magnetic field

• Paramagnetism: unpaired electrons, attracted to

• Sample exercise 7-7:an element has the electron configuration [kr]4d55s1. without looking at the periodic table, identify the period, block, and group inn which element is located. Then consult the periodic table to identify this element and the others in its group.

Exercise: An electron with four quantum numbers 3, 2, -1, -1/2 may be an electron in an unfilled sublevel of Ca, Fe, Al, Ar, Ag?

Sample Exercise 6.8 Electron Configurations for a GroupWhat is the characteristic valence electron configuration of

the group 7A elements, the halogens?

Practice Exercise• Which family of elements is characterized by an ns2np2

electron configuration in the outermost occupied shell?• Answer: group 4A

• Sample Integrative Exercise Putting Concepts TogetherBoron, atomic number 5, occurs naturally as two isotopes,

10B and 11B, with natural abundances of 19.9% and 80.1%, respectively. (a) In what ways do the two isotopes differ from each other? Does the electronic configuration of 10B differ from that of 11B? (b) Draw the orbital diagram for an atom of 11B. Which electrons are the valence electrons? (c) Indicate three major ways in which the 1s electrons in boron differ from its 2s electrons. (d) Elemental boron reacts with fluorine to form BF3, a gas. Write a balanced chemical equation for the reaction of solid boron with fluorine gas. (e) ΔH°f for BF3(g) is –1135.6 kJ mol–1. Calculate the standard enthalpy change in the reaction of boron with fluorine. (f) When BCl3, also a gas at room temperature, comes into contact with water, the two react to form hydrochloric acid and boric acid, H3BO3, a very weak acid in water. Write a balanced net ionic equation for this reaction.