Electromagnetic Radiation
Electromagnetic energy is energy carried through
space or matter by means of wavelike oscillations.
These oscillations are systematic fluctuations in the
intensity of electrical and magnetic forces.
Electromagnetic radiation - The rhythmic changes
with time and the successive series of these
oscillations through space. These oscillations are
popularly called the Light wave.
maximum
0
minimum
frequency Number of crests or troughs
pass this point in one second.
-1
crest
1Hz = 1 per second = 1/s = s
crest
trough
Time
υ = frequency
0
Time
Amplitude
wavelength
λ = wavelength
0
Distance
Electromagnetic spectrum
Visible light
Properties of Waves
traveling waves - wave crests and troughs move
across the surface of an ocean or lake
standing waves - wave crests and troughs do not
change position such as the string of a musical
instrument
The crest or point of maximum amplitude occur at
one position
points of zero amplitude or nodes occur at the
ends of the string
standing waves lead naturally to “quantum
numbers”
 
L = n  λ
 2
L = length of string
2L
=
λ n
constructive interference
In phase
Destructive Interference
out of phase
wavelength x frequency = speed
λ x Hz = m/s
The speed of light in a vacuum is
c = 3.00 x 108 m · s -1
or
λx υ = c
Example: What is the frequency in Hz of yellow light that
has a wavelength of 625 nm.
υ =
8
-1
3.00 x 10 m · s
c
625 nm
=
625. x 10 -9 m
14
= 4.80 x 10
s-1
Energy of Electromagnetic Radiation
Light travels in tiny quantized packets of energy.
These packets are called photons. Each photon pulses
with a frequency, υ, and travels at the speed of light, c.
Energy of a photon = E = h υ
h is called Planck’s constant and has a value of
-34
h = 6.626 x 10
J·s
Energy of Electromagnetic Radiation
In 1900, the German physicist MaxPlanck, theorized that
light travels in tiny quantizedpackets of energy and that
these packets travel at the speed of light,c , and pulse with
a frequency, υ. Later in the century these packets were
given the name photon
.
Using the ideas of Planck, Albert Einstein confirmed that
the energy of a photon is proportional to its frequency.
E=hυ
The h is calledPlanck’s constant and has the value
h = 6.626 x 10 -34 J · s
Example: Calculate the energy of 532 nm green light.
-34
hc
E = hυ =
=
532 nm
8
(6.626 x 10 J · s) 3.00 x 10 m · s
= 3.74 x 10
532. x 10
-19
J
-9
m
-1
Atomic Spectra and the Bohr Model of the Hydrogen Atom
Continuous spectrum - Is the continuous unbroken
distribution of all wavelengths and frequencies.
Atomic or Emission spectrum - a series of lines at only a
few wavelengths. Atoms absorb or emit radiation at
specific wavelengths.
Hydrogen line spectra - hydrogen is the simplest element.
A proton and an electron. Its spectrum actually consists of
several series of lines. Figure 1 (a similar series is shown
in Figure 7.7 of the text) shows a portion of the series
which occurs in the visible region. Other series occur in
the ultraviolet and Infrared. What we see from this is that
the transitions are between quantized energy levels. In
1885 J. J. Balmer found an equation which could fit all the
hydrogen lines in all the series.
 1
1
= RH  2  2 

 n1 n2 
1
The Rydberg constant is an empirical constant meaning it
was chosen to give values for lambda which are close to
-1
the experimentally determined ones. R H = 109,678
. cm
n 2 must be larger than n1 (to give a positive value for lambda).
n 2 can be any value from 2 to infinity and n 1 can be any
value from 1 to infinity.
The Bohr Model of the Hydrogen Atom
In 1913 the German physicist NielsBohr, proposed the
first theoretical model of the hydrogen atom. He likened
his model to that of a planet circling about the sun. What
was important about this model is that it placed restrictions
on the orbits and energies of that an electron could have in
a given orbit
One electron
system
+
Energy of the electron is
2 2me 4
E=n 2h 2
2 2me 4
b=
h2
E = -
b
n2
b = 2.18 x 10 -18 J
Absorption
of Energy
Emission of Energy
DE = Eh  E1 =
-b -b
 2
2
n h n1
 1
1 
DE = b 


2
2
 n1 n h 
DE =
hc

b 1
1 
 2  2
=

hc  n1 n h 
1
Rh= 109,678 cm
-1
b =
109730
,
cm -1
hc
Photons (Light packets) are quantized, travel at the speed
of light, c , and travel with a frequency, υ .
Energy is proportional to frequency E = .h υ
Atoms absorb or emit radiation at specific wavelengths
The Bohr model is similar to a planet orbiting the sun and
satisfies the Rydberg equation fairly well.
The Bohr model is useless for any atom larger than
hydrogen.
Wave Properties of Matter and Wave Mechanics
Bohr’s model fails because the classical laws of
physics do not apply to particles as tiny as the
electron.
Classical physics fails because atomic particles are
not as our senses perceive them
Under the appropriate circumstances small particles
behave not as particles, but as waves
In 1924 Louis De Broglie proposed the idea of matter
waves, where their wavelength is give by
λ = h
mv
Example: What is the wavelength of a 100 kg person
running at 3.0 meters per second
J =
kg m
2
s2
kg m
-34
λ = h =
mv
-36
m
s 2 · s) = 2.21 x 10
-1
3.00 m · s
(6.626 x 10
100 kg
2
Electron waves in Atoms
Wave mechanics - the theory concerning wave
properties of matter
Serves as the basis of all current theories of
electronic structure
Quantum mechanics- the term is used because
wave mechanics predicts quantized energy levels
Erwin Schrödinger, an Austrian, is the first to
applied the concept of the wave nature of matter
to the explanation of electronic structure. (1926)
Quantum mechanics says that the electron waves in
an atom are standing waves and like the violin these
standing waves can have many waveforms or wave
patterns. We will call these waveforms orbitals
Orbitals are described by a wave function usually
represented by the symbol, ψ ( Greek letter, psi )
Wave function describes the shape of the electron
wave and its energy
Energy changes within an atom are simply the
electron changing from one waveform and energy to
another
The lowest energy state is called the ground state
The Principle Quantum Number,n
The principle quantum number is called n. All orbitals
which have the same value of n are said to be in the
same shell.
n ranges from n = 1 to n = ∞
shells are also sometimes related by letter
beginning for no particular reason with K .
n is related to the size of the of the electron wave
(how far it extends from the nucleus). The higher
the value of n, the larger is the electrons average
distance from the nucleus.
As n increases the energies of the orbitals
increase
Bohr’s theory only took n into account, and
worked because hydrogen is the only element in
which all the orbitals have the same value of n
The Secondary Quantum Number, l
The secondary quantum number divides the shells
into groups of orbitals called subshells
n determines the values allowed for l
for a give value of n l can range from
l = 0 to l = (n - 1) when n = 1 l = 0
n=1
n=2
n=3
n=4
n=5
n=6
n=7
l=0
l = 0, 1
l = 0, 1, 2
l = 0, 1, 2, 3
l = 0, 1, 2, 3, 4
l = 0, 1, 2, 3, 4, 5
l = 0, 1, 2, 3, 4, 5, 6
Subshells could be identified by their value of l, but to
avoid confusion between n and l they are given letter
codes
l determines the shape of the subshell
subshells within a shell differ slightly in energy
Energy —>
l =
0 1
s p
2
d
3
f
4
g
5
h
The Magnetic Quantum Number , ml
m divides the subshells into individual orbitals
l
m has values from l- to +l
l
when l = 0
m =0
l
when l = 1
m = -1, 0, +1
l
when l = 2
m = -2, -1, 0, +1, +2
l
when l = 3
m = -3, -2, -1, 0, +1, +2, +3
l
Electron Spin Quantum Number , m
s
Electron spin is based on the fact that electrons
behave like tiny magnets
Spin can be in either of two directions
Spin quantum number m s can have values of +1/2 or -1/2
Quantum
Number
n
l
ml
ms
Allowed Values
1, 2, 3, ...…,
∞
(n-1), (n-2), ...., 0
Name and Meaning
Principal quantum number: orbital
energy and size
Secondary Quantum number:
orbital shape (and energy in a
multi-electron atom), letter name
for subshell (s, p, d, f)
l, (l -1), ..., 0, ..., (-l +1), -l Magnetic quantum number:
orbital orientation
1/2, -1/2
Electron spin quantum number:
spin up (+1/2) or spin down (-1/2).
Pauli Exclusion principle- The Pauli exclusion principle
states that no two electrons in the same atom can have
the same values for all four quantum numbers (n, l, ml, ms)
Aufbau - Add electrons 1 at a time, tp the lowest
available orbital.
Hund’s Rule - When electrons are placed in orbitals of
the same energy they try to move as far away away from
each other as possible.
Approximate energy level diagram
6d
7s
6p
5d
6s
5p
5s
4d
4p
3d
4s
3p
3s
n = 2, l = 1, ml = 1
n = 2, l = 1, ml = 0
n = 2, l = 1, ml = -1
2s
2p
n = 2, l = 1, ml = -1
n = 2, l = 1, ml = -1
1s
5f
4f
Electron Configuration
2s
H
2s
1
1s
1s
2
He
1s
Be
1s 2s
1s
2s
Li
2
1s 2s
2s
1
1s
2
1s
2p
2s
2
2
2p
2s
1
B 1s 2s 2p
2
2
1s
2p
2
2
3
2p
2s
N 1s 2s 2p
1s
2
2
1s
2
2
5
2p
2s
F 1s 2s 2p
1s
4
O 1s 2s 2p
2p
2s
2
C 1s 2s 2p
1s
2s
2
2
2
6
Ne 1s 2s 2p
1s
Magnetic properties of Atoms
When two electrons occupy the same
orbital the must have different values of ms.
Atoms with more electrons spinning in one direction
than in the other are said to contain unpaired electrons.
The magnetic effects do not cancel and these atoms
behave as tiny magnets which can be attracted to an
external magnetic field. These atoms are said to be
paramagnetic.
Diamagnetic substances are those in which all the
electrons are paired.
Paramagnetism is a measurable property.