Electromagnetic RadiationElectromagnetic radiation () The nature of matter () Atomic spectrum ()
Quantum mechanics () Orbital ()
Electron spin () Periodic table ()
7.1 Electromagnetic Radiation ()
Radiant energy that exhibits wavelength-like behavior and travels through space at the speed of light in a vacuum.

Waves have 3 primary characteristics: ()
1. Wavelength (, λ): distance between two peaks in a wave.
()
2. Frequency (, ν): number of waves per second that pass a given point in space. ( )
3. Speed: speed of light (), c = 2.9979 × 108 m/s.
Figure 7.1: The nature of waves. Note that the radiation with the shortest wavelength has the highest frequency.


c = νλ
c = speed of light (m s−1) ν = frequency (Hzs−1)
λ = wavelength (m)

Microwave (MW):
Radio waves:
When a strontium salt is dissolved in methanol (with a little water) and ignited, it gives a brilliant red flame. The red color is produced by emission of light when
electrons, excited by the energy of the burning methanol, fall back to their ground states.
: Sample Exercise 7.1
7.2 The nature of matter
Energy is quantized and can occur only in discrete units, called quanta.
()

: Sample Exercise 7.2
ΔE = change in energy, in J h = Planck’s constant (),
6.626 × 10−34 J s ν = frequency, in s−1 (Hz) λ = wavelength, in m
ΔE h hc = = ν λ
Photoelectric effect ()
0 2
Energy has mass () E = mc2
E = energy m = mass c = speed of light
E hc photon =
(rest mass)
Photon:
λ = wavelength, in m h = Planck’s constant, 6.626 × 10−34 J s
(J s = kg m2 s−1) m = mass, in kg ν = velocity, in m s−1
de Broglie’s Equation ()
mv h
p h ==λ
Sample Exercise 7.3
me = 9.11×10-31 kg, v = 1.0×107 m/s m(ball) = 0.10 kg, v = 35 m/s λ = ?
mball
7.3 Atomic Spectrum of Hydrogen
Figure 7.7: A change between two discrete energy levels emits a photon of light.
ΔE = hν
7.4 The Bohr Model ()
The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.


Figure 7.8: Electronic transitions () in the Bohr model for the hydrogen atom.

(transition)
E = 2.178 10 J (18 2− × − z n/ )2
E = energy of the levels in the H-atom ()
z = nuclear charge (,for H, z = 1) n = an integer ()
Ground State ():

For an hydrogen-like atom, it is the state with n = 1. n = 1

ΔE = Efinal state − Einitial state
λ = hc EΔ
nm m
7.5 The quantum mechanical model of the atom
Node ()
Figure 7.10: The hydrogen electron visualized as a standing wave around the nucleus.

Quantum mechanics()
A specific wave function is often called an orbital.

Heisenberg Uncertainty Principle ()
x = position () p=mv = momentum () h = Planck’s constant ()
π4 hpx ≥Δ⋅Δ
The more accurately we know a particle’s position, the less accurately we can know its momentum, and vice versa.
()



1s
Probability Distribution ()
Ψ2
1s
7.6 Quantum Numbers (, QN)
1.Principal QN () n = 1, 2, 3, . . . related to size and energy of the orbital. ()
2. Angular Momentum QN () l = 0 to n − 1 relates to shape of the orbital.
()
:
s: sharp () p: principal () d: diffuse () f: fundamental ()
f
3. Magnetic QN () ml = l to −l
relates to orientation of the orbital in space relative to other orbitals. ()
4. Electron Spin QN () ms = +1/2, −1/2
relates to the spin states of the electrons. ()
= 2l + 1
Answer l = 0 1 2 3 4
5s 5p 5d 5f 5g
: 3d, 4f orbitals, n, l, ml = ?
Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.
7.7 Orbital shapes and energies
()

6s?
Answer: 5
+ - ++- --
2p
Figure 7.15: A cross section of the electron probability distribution for a 3p orbital.
3p
3d: dxy, dyz, dxz, dx2-y2, dz2
+ +
+ + ++ ++ +
+ -
- -
- - - - - -
Figure 7.17: Representation of the 4f orbitals in terms of their boundary surface
().
, (degenerate, )
7.8 Electron spin and the Pauli principle
Electron spin:
Pauli Exclusion Principle
In a given atom no two electrons can have the same set of four quantum numbers (n, l, ml, ms).
Therefore, an orbital can hold only two electrons, and they must have opposite spins. ()



11+
e-
e-
e-
the radial probability
2s2p
Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability
distribution for the 3s, 3p, and 3d orbitals
:3s > 3p > 3d
Penetration effect ():
Figure 7.22: The orders of the energies of the orbitals in the first three levels of polyelectronic atoms.
Ens < Enp < End < Enf

Figure 7.24: Mendeleev's early periodic table, published in 1872. Note the spaces left for missing elements with atomic masses 44, 68,
72, 100.

7.11 The Aufbau Principle () and the periodic table
As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these hydrogen-like () orbitals.
Hund’s Rule ()
The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals. ()
:
Electron configuration
: (1s), (2s, 2p), (3s, 3p), (4s, 3d, 4p), (5s, 4d, 5p)…
: s(2), p(6), d(10), f(14) H: 1s1
He: 1s2
Li: 1s22s1
(: Be…Ne)
Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18
elements.
Atom Valence Electrons Ca 2 N 5 Br 7
The electrons in the outermost principle quantum level of an atom. (n )
Inner electrons are called core electrons ().
K: 1s22s22p63s23p64s1 or [Ar] 4s1
Ca: [Ar]4s2
(: 24Cr, 26Fe, 29Cu)
: Cr: [Ar]3d54s1; Cu: [Ar]3d104s1
Broad Periodic Table Classifications
Representative Elements (main group): filling s and p orbitals (groups 1,2,13-18)
sp
d
58-71)4f
90-103)5f
Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.
Figure 7.28: The periodic table with atomic symbols, atomic numbers, and partial electron configurations.
Figure 7.29: The positions of the elements considered in Sample Exercise 7.7
: Sample Exercise 7.7
Ionization energy (): The quantity of energy required to remove an electron from the gaseous atom or ion. X(g) → X+(g) + e-



Periodic Trends First ionization energy:
increases from left to right across a period ( ,);
decreases going down a group (, ,).
Figure 7.30: The values of first ionization energy for the elements in the first six periods.

Figure 7.31: Trends in ionization energies (kJ/mol) for the representative elements.
Sample Exercise 7.8
Answer P: 3s23p3
: Sample Exercise 7.9
Electron Affinity
The energy change associated with the addition of an electron to a gaseous atom. X(g) + e− → X−(g)

(, ,)
Figure 7.32: The electron affinity values for atoms among the first 20 elements that form
stable, isolated X- ions.
C-(1s22s22p3); N- (1s22s22p4), p
,(,)
Atomic Radii (): decrease going from left to right across
a period;
Liquid bromine (, Br2) in equilibrium with its vapor.
Figure 7.33: The radius of an atom (r) is defined as half the distance between the nuclei in a molecule
consisting of identical atoms.
Sample Exercise 7.10
, , ,
Figure 7.34: Atomic radii (in picometers, 10-12 m) for selected atoms.
7.13 The properties of a group: The alkali metals ()
The number and type of valence electrons primarily determine an atom’s chemistry. ()
,
Figure 7.35: Special names for groups in the periodic table.

: Cs > Rb > K > Na > Li
: Li > K > Na
, ,,

Questions and Exercises 19, 33, 37, 41, 45, 53, 55, 57, 61, 67, 71, 79, 85, 87, 97, 103
Chapter 7
7.1 Electromagnetic Radiation ()
Figure 7.1: The nature of waves. Note that the radiation with the shortest wavelength has the highest frequency.
Wavelength and frequency can be interconverted.
Figure 7.2: Classification of electromagnetic radiation.
When a strontium salt is dissolved in methanol (with a little water) and ignited, it gives a brilliant red flame. The red colo
7.2 The nature of matter
Photoelectric effect ()
Energy and Mass
Sample Exercise 7.3
Figure 7.7: A change between two discrete energy levels emits a photon of light.
7.4 The Bohr Model ()
Figure 7.8: Electronic transitions () in the Bohr model for the hydrogen atom.
Energy Changes in the Hydrogen Atom
Sample Exercise 7.4
Figure 7.9: The standing waves ()
Figure 7.10: The hydrogen electron visualized as a standing wave around the nucleus.
Quantum mechanics()
Probability Distribution ()
7.6 Quantum Numbers (, QN)
Sample Exercise 7.6
Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.
Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary s
Figure 7.15: A cross section of the electron probability distribution for a 3p orbital.
Figure 7.16: Representation of the 3d orbitals.
Figure 7.17: Representation of the 4f orbitals in terms of their boundary surface ().
Figure 7.18: Orbital energy levels for the hydrogen atom.
Figure 7.19: A picture of the spinning electron.
Pauli Exclusion Principle
Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution
Figure 7.22: The orders of the energies of the orbitals in the first three levels of polyelectronic atoms.
Figure 7.24: Mendeleev's early periodic table, published in 1872. Note the spaces left for missing elements with atomic masse
7.11 The Aufbau Principle () and the periodic table
Hund’s Rule ()
Electron configuration
Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.
Valence Electrons
Broad Periodic Table Classifications
Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.
Figure 7.28: The periodic table with atomic symbols, atomic numbers, and partial electron configurations.
Figure 7.29: The positions of the elements considered in Sample Exercise 7.7
Periodic Trends
Figure 7.30: The values of first ionization energy for the elements in the first six periods.
Figure 7.31: Trends in ionization energies (kJ/mol) for the representative elements.
Sample Exercise 7.8
Electron Affinity
Figure 7.32: The electron affinity values for atoms among the first 20 elements that form stable, isolated X- ions.
Liquid bromine (, Br2) in equilibrium with its vapor.
Figure 7.33: The radius of an atom (r) is defined as half the distance between the nuclei in a molecule consisting of identic
Sample Exercise 7.10
Figure 7.34: Atomic radii(in picometers, 10-12 m) for selected atoms.
7.13 The properties of a group: The alkali metals ()
Figure 7.35: Special names for groups in the periodic table.
Alkali metals ()