Chapter 6 Electronic Structure of Atoms
1. Radiant Energy (Electromagnetic radiation)
Why the detour? Why must we study radiation in order
to understand the structure of the periodic table?
Types of Electromagnetic Radiation
heat, light, 'invisible' radiation (e.g.,
X-rays, UV-Vis, IR, microwave)
What defines the “types” of radiation?
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Characteristics of Electromagnetic Radiation
Moves through a vacuum at 3.00
x 108 m/s (c)
Wavelike behavior: wavelength
and frequency
Wavelength, ,
and frequency, ,
are related by the
speed of light, c:
c  λ
 typically expressed in units of s-1 (cycles/sec), or
Hertz (Hz)
 has units of length (nm, mm), etc. – wavelength
defines the type of radiation (UV-Vis, IR, etc.)
can vary from ~10-14 m (cosmic rays) to ~101 m
(radio waves)
visible region: ~10-9 m
violet light ~400 nm
red light ~700 nm
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e.g., An Ar ion laser emits radiation at 489 nm. What is the
frequency of this radiation?
According to classical physics, what is the nature of
electromagnetic radiation?
How is energy propagated by something which has
wavelike properties?
Three notable failures of classical physics (ca. 1890-1910):
Blackbody radiation
Photoelectric effect
Atomic emission spectra
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The blackbody radiation problem:
All objects above 0 K emit radiation
Objects at around room temperature emit mainly infrared
radiation (» 10mm) which is invisible. The sun emits most of
its radiation at visible wavelengths, particularly yellow ( » 0.5
mm)
The maximum wavelength of radiation emitted depends on
temperature:
As the temperature increases, the peak wavelength emitted by
the black body decreases.
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To solve the blackbody problem, i.e., to explain the
dependence of wavelength on temperature, Planck
assumed that energy is gained or lost by atoms in discrete
increments called quanta
If E is the amount of radiant energy gained/lost by an
atom, then
E = h
where h is called a quantum of energy
notice that h = 6.626 x 10-34 J-s (Planck's constant)
E.g., calculate the energy of a quantum that could be
absorbed or emitted at a wavelength of 703 nm
What does E=h tell us about the relation between
frequency and energy?
Which would have a higher energy: a quantum of violet
light (400 nm) or orange light (600 nm)?
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Applications of Planck’s quantum theory
Photoelectric effect: exposing the surface of a metal to
radiation above a certain frequency causes the metal to
lose electrons
Regardless of intensity, if the frequency of the radiation is
not above a certain threshold, an electron will not be
emitted by the metal
This phenomenon cannot be explained using the ‘wave’
notion of radiation
Einstein: assumes that radiation isn’t a continuous wave,
but exists as particles, or photons
photon: packet of radiant energy, with
E = h
e.g., calculate the energy of a 514.5 nm photon
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Atomic emission spectra
continuous spectra, emission/absorption spectra:
We’re mainly concerned with emission spectra (but
understand the origin of all three types)
Here’s a very nice demo…
Emission spectrum of hydrogen in the visible region:
How to explain the features of this spectrum? We assume that
the spectrum is related to the structure of the atom…..
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Balmer, 1885: Empirical formula to predict wavelengths of H
emission lines in the visible region:
1
 (1.096776x10 m

7
1
 1
1 
)  
n n 
2
1
2
2
1.096776x107 m-1 is known as Rydberg’s constant (RH)
Set n2 = 2, n1=3,4,5,6 and calculate wavelengths…..
n1
n2
(m)
1/ (m-1)
(nm)
This formula very accurate for H, but there is no
explanation of exactly why it works.
What models do we have (ca. 1910) of the structure of the
atom?
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Bohr model of hydrogen
Bohr assumed a 'planetary ' model for the H atom, i.e.,
the electron moved in a circular orbit about the proton
Bohr also assumed that:
'classical' laws of physics did not accurately
describe events at the atomic level
energies at the atomic level are quantized
Bohr proposed that:
the electron moves around the proton only in circular
'orbits' of certain allowed radii, which correspond to
certain definite energies
the electron can change from one allowed energy state to
another by absorbing/emitting radiation
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The radiant energy absorbed or emitted corresponds
exactly to the energy difference between the allowed
energy states:
E  E  E  h
f
i
Bohr was able to show that the energy of the electron in H
depends on the orbit it occupies:
1
En  (hc) RH  2 
n 
Notice that (hc)RH = 2.18 x 10-18 J
n = principal quantum number
n has only integer values; n=1 is closest to the
nucleus (and is called the ground state), n=2 is
further (and is called an excited state), and so on
So: an electron in an H atom has access to a
number of discrete energy levels, each described
by the n quantum number……
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Now, what happens when an electron changes
energy levels?
1
recall that E  (hc) R  
n
H
n 
2
and E  E  E  h
f
i
We can show that, for a transition from initial
state ni to final state nf,
 1
1 

E  En  En  (hc) RH  2  2 
ni 
 nf
f
i
(is this looking vaguely familiar?)
Recall that E  h , and  
1


 (hc) RH
hc
c
…….substitute

 1
1 
 2  2  , or
n
ni 
 f
1
 1.10x10 m

7
1
1
1 
  
n n 
2
i
2
f
If we set ni=2, and let nf vary from 3,4,5,6, does this
expression look familiar??
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E.g., calculate the energy, wavelength, and frequency of a
photon absorbed when H undergoes a transition from n=1
to n=4.
Bohr model very successful at predicting the spectrum of
H (and He+, Li2+, etc)
but this model failed for systems with more than one
electron
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Problems du Jour
What is the wavelength of radiation that has a
frequency of 93.1 MHz?
What distance does electromagnetic radiation
travel in 10.0 s?
Excited Li atoms emit visible light of frequency
4.47 x 1014 s-1. What is the wavelength of this
radiation? What is the color of this radiation?
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Problem du Jour
The Lyman series of emission lines of the hydrogen atom
are those for which nf=1.
(a) Calculate the wavelengths for the first three lines in the
Lyman series – those for which ni = 2, 3, and 4.
(b) Determine the region of the electromagnetic spectrum
in which the lines of the Lyman series are observed.
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