Quantum Theory and the
Electronic Structure of Atoms
Chapter 7
Part 1
1
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Properties of Waves
Wavelength (l) 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 (n) is the number of waves that pass through a
particular point in 1 second (Hz = 1 cycle/s).
The speed (u) of the wave = l x n
2
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
lxn=c
3
4
A photon has a frequency of 6.0 x 104 Hz. Convert this
frequency into wavelength (nm). Does this frequency fall in
the visible region?
l
lxn=c
n
l = c/n
l = 3.00 x 108 m/s / 6.0 x 104 Hz
l = 5.0 x 103 m
l = 5.0 x 1012 nm
5
The wavelength of the green light from a traffic signal is
centered at 522 nm. What is the frequency of this
radiation?
6
Problem 1
What is the wavelength (in meters) of an
electromagnetic wave whose frequency is
3.64 x 107 Hz?
7
Mystery #1, “Heated Solids Problem”
Solved by Planck in 1900
When solids are heated, they emit electromagnetic radiation
over a wide range of wavelengths.
Radiant energy emitted by an object at a certain temperature
depends on its wavelength.
Energy (light) is emitted or absorbed in discrete
units (quantum).
E=hxn
Planck’s constant (h)
h = 6.63 x 10-34 J•s
blackbody-spectrum
8
Calculate the energy (in joules) of a photons with a wavelength
of 5.00 x 104 nm (infrared region).
l = 5.00 x 104 (nm) x (1 x 10-9 (m)/(nm) = 5.00 x 10-5 (m)
E=hxn
E=hxc/l
E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 5.00 x 10-5 (m)
E = 3.98 x 10 -21 J
9
Calculate the energy (in joules) of a photons with a wavelength
of 5.00 x 10-2 nm (x-ray region).
10
Problem 2
The energy of a photon is 5.87 x 10-20 J.
What is its wavelength in nanometers?
11
Mystery #2, “Photoelectric Effect”
Solved by Einstein in 1905
Light has both:
1. wave nature
2. particle nature
hn
KE e-
Photon is a “particle” of light
hn = KE + W
KE = hn - W
where W is the work function and
depends how strongly electrons
are held in the metal
12
photoelectric
When copper is bombarded with high-energy electrons, X rays
are emitted. Calculate the energy (in joules) associated with
the photons if the wavelength of the X rays is 0.154 nm.
E=hxn
E=hxc/l
E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m)
E = 1.29 x 10 -15 J
13
The work function of cesium metal is 3.42 x 10-19 J. Calculate
the minimum frequency of light necessary to eject electrons
from the metal.
14
The work function of cesium metal is 3.42 x 10-19 J. Calculate
the kinetic energy of the ejected electron if light of frequency
1.00 x 1015 s-1 is used for irradiating the metal.
15
Problem 3
The work function of titanium metal is 6.93 x
10-19 J. Calculate the energy of the ejected
electrons if light of frequency 2.50 x 1015 s-1 is
used to irradiate the metal.
KE = _____x 10-19 J
16
Mystery #3, “Emission Spectra”
Line Emission Spectrum of Hydrogen Atoms
17
18
Bohr’s Model of
the Atom (1913)
1. e- can only have specific
(quantized) energy
values
2. light is emitted as emoves from one energy
level to a lower energy
level
En = -RH (
1
n2
)
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
19
E = hn
E = hn
20
Ephoton = DE = Ef - Ei
ni = 3
ni = 3
ni = 2
nf = 2
1
Ef = -RH ( 2
nf
1
Ei = -RH ( 2
ni
1
DE = RH( 2
ni
)
)
1
n2f
nnf f==11
21
)
22
Calculate the wavelength (in nm) of a photon emitted
by a hydrogen atom when its electron drops from the
n = 5 state to the n = 3 state.
Ephoton = DE = RH(
1
n2i
1
n2f
)
Ephoton = 2.18 x 10-18 J x (1/25 - 1/9)
Ephoton = DE = -1.55 x 10-19 J
Ephoton = h x c / l
l = h x c / Ephoton
l = 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J
l = 1280 nm
23
Problem 4
What is the wavelength (in nm) of a photon
emitted during a transition from ni=6 to nf=4
in the H atom?
24
Mystery #1, “Heated Solids Problem”
Solved by Planck in 1900
When solids are heated, they emit electromagnetic radiation
over a wide range of wavelengths.
Radiant energy emitted by an object at a certain temperature
depends on its wavelength.
Energy (light) is emitted or absorbed in discrete
units (quantum).
E=hxn
Planck’s constant (h)
h = 6.63 x 10-34 J•s
blackbody-spectrum
25
Mystery #2, “Photoelectric Effect”
Solved by Einstein in 1905
Light has both:
1. wave nature
2. particle nature
hn
KE e-
Photon is a “particle” of light
hn = KE + W
KE = hn - W
where W is the work function and
depends how strongly electrons
are held in the metal
26
photoelectric
Mystery #3, “Emission Spectra”
Line Emission Spectrum of Hydrogen Atoms
27
Bohr’s Model of
the Atom (1913)
1. e- can only have specific
(quantized) energy
values
2. light is emitted as emoves from one energy
level to a lower energy
level
En = -RH (
1
n2
)
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
28
Why is e- energy quantized?
De Broglie (1924) reasoned
that e- is both particle and
wave.
2pr = nl
h
l = mu
u = velocity of em = mass of e29
Calculate the wavelength of the ‘particle’ in each of
the following two cases: (a) The fastest serve ever
recorded in tennis was about 150 miles per hour, or
68 m/s. Calculate the wavelength associated with a
6.0 x 10-2 kg tennis ball travelling at this speed.
h
l = mu
l =
6.63 x 10-34 J•s
(6.0 x 10-2 kg x 68 m/s)
2
kg
m
J=
s2
l = 1.6 x 10-34 m = 1.6 x 10-25 nm
Because the wavelength is so small compared to the size
of the tennis ball, the wave properties cannot be detected
by any existing measuring device.
30
Calculate the wavelength of the ‘particle’ in each of
the following two cases: (b) Calculate the wavelength
associated with an electron (9.1094 x 10-31kg)
travelling at this speed.
31
Problem 5
Calculate the wavelength (in nm) of a H
atom (mass = 1.674 x 10-27 kg) moving at
7.00 x 102 cm/s.
32
Chemistry in Action: Laser – The Splendid Light
Light Amplification by Stimulated Emission of Radiation
Laser light is (1) intense, (2) monoenergetic, and (3) coherent
33