Lecture 6: Light and the
Electromagnetic Spectrum
Dr Harris
9/5/12
HW: Ch 4: 21, 22, 27-30
• The vast majority of our present understanding of the electronic structure
of atoms has come from the light that is absorbed and emitted by
substances
• For example, what happens when you switch on a
• Neon lights are glass chambers pressurized with Neon or other noble
gases
• When a voltage is applied, the gas is ionized. This ionization causes a
“glow”.
• Why does this phenomena occur?
• What further information can this provide us about the electronic
structure of atoms?
• Over the course of the next two lectures, we will be able to understand
exactly what’s happening, and what it means
EMR: Light and Energy
• The electric current that flows through the lights causes the gases
electrons to become excited, or “bumped up” in energy
• When the electron drops back down to its original, lower energy state, the
excess energy is released as light. This is called emission.
• But what exactly is light?
• The light that we see with our eyes is a type of electromagnetic
radiation (EMR)
• When we use the term radiation, we are referring to energy that is
propagated (moves and spreads outward) through space as waves
• Light, such as that which emits from a lamp is comprised of visible
waves
• Radio waves from a radio are another
• Invisible UV and Infrared rays from the sun are also EMR
Propagation of Waves
• The waves created in water when
an external force is applied are an
example of propagation.
• The energy transferred to the spot
of impact when the droplet strikes
the surface is spread and
transmitted throughout the water.
• EMR propagates through the
universe as oscillating,
perpendicular electric and
magnetic fields
Wavelength and Frequency
• The distance between local
maxima, or crests, is the
wavelength λ (units of
meters)
• If we picture these waves
moving across the page, the
number of crests that pass a
given point per second is the
frequency, ν (units of s-1)
• The speed of a wave is given
by the product of ν and λ:
λν = c
c is the speed of light, 3.0 x 108 m/s.
All EMR moves at this speed
through vacuum
Different Types of EMR Have Different
Wavelengths
• The electromagnetic spectrum below shows EMR listed by increasing
wavelength
• Wavelengths vary from the size of an atomic nucleus to the length of
a football field
The Visible Spectrum
ROY G. BIV
(increasing Energy)
Examples
• What is the frequency of orange (~650 nm) light?
• A certain type of radiation has a frequency of 1015 s-1. What is the
wavelength, in nm, of this radiation? What kind of radiation is it?
Continuous Spectra
• White light is comprised of all wavelengths of the visible spectrum.
Because the spectrum of white light has no gaps, it is a continuous
spectrum.
• Sunlight, for example, is
continuous over a long range of
wavelengths. The spectrum of
sunlight is shown.
• Just something to know:
Sunlight is actually white, but
absorption and scattering of light
by the atmosphere causes the sky
to appear blue and the sun to
appear yellow.
Line (Discontinuous) Spectra
• Light emitted from chemical samples exhibits a discontinuous spectrum.
The radiation consists of spectral lines at particular wavelengths. This type
of spectrum is a line spectrum, or atomic emission spectra
• Sodium burns very brightly and emits an orangishyellow color: Discontinuous spectrum
Max Planck
• The observation of spectral lines indicates that certain elements can
only emit certain wavelengths
• How can this be? Why can’t any element emit at any wavelength?
• Max Planck first began to answer this question with his interpretation
of a phenomena known as blackbody radiation.
Blackbody Radiation And The End Of Classical
Physics
• All solid objects, when heated, emit thermal
radiation.
• Just when an object is hot enough to glow, it
appears red. As you continue to heat the
material, it becomes “white hot”
• The old laws of physics (Classical
physics) would predict that if you
continued to heat a body, you would
produce higher and higher frequencies
at increasing intensity
• This means that light bulbs would
give off UV, gamma, X-rays, and so
on. Of course, this doesn’t happen
The Birth Of Quantum Physics
• The failure of Classical Physics to explain blackbody radiation lead to
the creation of Quantum Physics by Planck, Einstein, and others.
• Planck explained blackbody radiation by asserting that radiation can
only be emitted in small, exact amounts called quanta
• He then derived the amount of energy absorbed or released in a
single event is equal to:
E = nhν
where E is the total energy in J, n is the number of quanta, and h is
Planck’s constant, 6.626 x 10-34 Js
Examples
• Calculate the energy contained in a single quanta of blue light (~400 nm)
• Calculate the energy of contained in 10 quanta of green light (~520 nm)
• A laser beam of yellowish light (~550 nm) emits 1018 quanta per minute.
How much energy is emitted per hour?
Einstein and the Photon
• Like Planck, Einstein envisioned light as a beam of particles, each
consisting of equal energy. He called these particles photons.
• Borrowing from Planck’s theory, he asserted that each photon in the beam
is a little packet of energy E = hν
• Using this theory, Einstein sought to
understand a phenomena that had defied
physics for many years prior… the Photoelectric
effect
The Photoelectric Effect
• The photoelectric effect is the ejection of electrons
from metal surface under illumination.
• Photons of low frequency, no matter how intense the
beam, will not eject an electron from a metal surface.
• It is not until the threshold frequency (νT) is reached,
that a photon is just energetic enough to loosen an
electron.
• At energies beyond the threshold energy (ET = hvT), the
electron is ejected at higher and higher velocities.
Excess Energy is Converted to Kinetic Energy
• The energy of motion is called kinetic energy
(Ek)
• The kinetic energy of a body of mass is given
by:
𝑬𝒌 =
Plot of Ek vs. ν for sodium
slope of line = h
𝟏
𝒎𝑽𝟐
𝟐
• m is the mass in kg, and 𝑉 is the velocity
(speed) in meters per second (m/s). The
units of energy are Joules (J).
5.51 x 1014 s-1
• Einstein found that as you increase the energy of the photons striking the
metal, the energy beyond the threshold energy (excess) is converted into
kinetic energy. Thus,
𝑬𝒌 = 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬𝑻
http://phet.colorado.edu/en/simulation/photoelectric
Example
• Given that the threshold frequency of copper is 1.076 x 1015 s-1, calculate
the kinetic energy of an electron that will be ejected when a 210 nm
photon strikes the surface?
• What do we know?
νT = 1.076 x 1015 s-1
νphoton =
𝑐
λ
=
3.0 𝑥 108 𝑚 𝑠 −1
2.100 𝑥 10−7 𝑚
= 1.428 𝑥 1015 𝑠 −1
𝑬𝒌 = 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬𝑻
substitute:
𝐸𝑘 = ℎ𝑣𝑝ℎ𝑜𝑡𝑜𝑛 − ℎ𝑣𝑇 = ℎ(𝑣𝑝ℎ𝑜𝑡𝑜𝑛− 𝑣𝑇 )
𝐸𝑘 = (6.626 𝑥 10−34 𝐽𝑠)(3.52 𝑥 1014 𝑠 −1 )
𝑬𝒌 = 𝟐. 𝟑𝟑 𝐱 𝟏𝟎−𝟏𝟗 𝑱
Example Continued.
• From the example on the previous page, calculate the velocity of the
electron?
𝑬𝒌 =
• Mass of electron = 9.109 x
10-31
𝟏
𝒎𝑽𝟐
𝟐
kg.
𝑆𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝑉: 𝑉 =
𝑉=
Joule =
𝒌𝒈 𝒎𝟐
𝒔𝟐
2 𝐸𝑘
𝑚
2 (2.33 𝑥 10−19 𝑘𝑔 𝑚2 𝑠 −2 )
= 7.15 𝑥 105 𝑚/𝑠
−31
(9.109 𝑥 10 𝑘𝑔)
Section 2. Wave-Particle Duality
Intro
• Planck and Einstein were able to determine that energy transferred
to or from an electron must be quantized.
• However, the question yet to be answered is: What determines the
allowed energies of emission of a given element.
• The physical nature of photons and electrons needed to be
understood before this issue could be addressed
• Many years prior to Einstein’s photoelectric effect experiment, it had
been proposed that light was comprised of waves
• Thomas Young was the first physicist to propose that light was of
wave-like character, not particle like as proposed by Issac Newton
• To test his hypothesis, Young conducted the ‘slit experiment’
Light As Waves? Young’s Slit Experiment (1799)
• If light were made of only particles, then light passing through a slight of
height X would appear on a screen with the size and shape of the slit
• What Young observed, however, was a series of light and dark fringes
• This was the first indication of the wave-like character of light
Constructive and Destructive Interference
• The observed diffraction pattern of light can be explained by treating light
as waves with certain wavelengths and amplitudes.
• Waves of light that are in phase, can interact, forming a single wave of
larger amplitude. This is called constructive interference (a).
• Waves that are out of phase
will deconstruct (b), yielding
a lower amplitude
(destructive interference).
• Remember:
• wavelength determines
color
• amplitude dictates
brightness
Double Slit Experiment
• To confirm his hypothesis and prove his idea of constructive
interference, Young repeated the experiment using two slits.
• If light were indeed composed of waves, and the fringes due to
constructive interference, then the light fringes should be twice
as bright. The dark ones should be more defined. He was correct.
Young’s sketch of the interference, 1807.
Real Example
Back To the Photoelectric Effect
• In class yesterday, we described the photoelectric effect (Einstein, 1905)
• Electrons are bound to the metal atoms. The energy of this bond is the
threshold energy. In other words, it takes this much energy to ‘loosen’ the
electron
• When photons strike a metal surface, one of three scenarios can occur:
1. The photon has an energy which is less than the threshold energy.
So, the photon is not absorbed and nothing happens.
2.
The photon has EXACTLY enough energy to separate an electron
from the metal atom. However, there is no energy left for the
electron to move. Motion REQUIRES kinetic energy
3.
The photon has EXCESS energy. The excess energy is converted to
kinetic energy, and the electron moves away at some velocity
(speed) v.
Schematic
E = hνphoton
Ek
Compton Scattering
• Einstein’s Photoelectric effect suggested that photons had momentum, a
property of particles
• Compton asserted… “If EMR is made of particles, lets hit something with
it”
• This lead to the discovery of the ‘Compton Scattering’
• X-rays were found to ‘bounce’ off of
electrons at calculated angles, like pool
balls, and with an energy lower than
the initial energy
• This further supported particle-like
behavior
λ’
λ
What now?
• Young’s slit experiments did not mean that Newton was wrong
about the particle nature of EMR
• Einstein’s and Compton’s work did not prove that Newton was
correct
• What these experiments DID prove, was that physicists had to
develop a new theory that fused both the wave and particle-like
aspects of EMR into a single theory
DeBroglie’s Approach
• DeBroglie combined Einstein’s special theory of relativity with Planck’s
quantum theory to create the DeBroglie relation. In short, he summates
that if waves are particle-like, then particles, and hence, mass, is wavelike.
E = pc (p is momentum, p= m𝑉)
E = hν
pc = hν
Einstein (particle like):
Planck (wave like) :
DeBroglie (both) :
pc =
ℎ𝑐
λ
p=
ℎ
λ
pλ = h
λD = h/p
• The value, λD is the DeBroglie wavelength,
or the wavelength of any mass m with
momentum p.
Louis DeBroglie (1892-1987)
DeBroglie’s Hypothesis Confirmed
• Below are diffraction patterns of Aluminum foil. The left image is formed
by bombarding Al atoms with X-rays. The right image is formed with an
electron beam.
•
• As shown, both the EMR and electrons behave in the same wave-like
manner
Both exhibit
the wave-like
ability of
diffraction
Examples
• Calculate the DeBroglie wavelength of an electron travelling at
1.00% of the speed of light.
ℎ
λ𝐷 = =
𝑝
6.626 𝑥 10−34 𝐽 𝑠
9.109 𝑥 10−31 𝑘𝑔 𝟑. 𝟎𝟎 𝒙𝟏𝟎𝟔 𝒎𝒔−𝟏
= 2.43 x 10−10 𝑚
• What is the DeBroglie wavelength of a golf ball which weighs 45.9 g
and is traveling at a velocity of 120 miles per hour?
• First, convert velocity to meters per second
120 𝑚𝑖 5280 𝑓𝑡 .3048 𝑚
ℎ𝑟
𝑉=
𝑥
𝑥
𝑥
= 53.6 m/s
ℎ𝑟
𝑚𝑖
𝑓𝑡
3600 𝑠
ℎ
λ𝐷 = =
𝑝
6.626 𝑥 10−34 𝐽 𝑠
.0459 𝑘𝑔 53.6 𝑚𝑠 −1
= 2.69 x 10−34 𝑚
• DeBroglie wavelength of large objects is negligible
Quantum Condition
• Recall the Bohr model of the atom. Bohr used DeBroglie’s theory to
justify why electrons are restricted to certain orbits around the nucleus.
• As shown above, if the waves of the electron do not match after a
revolution, you will have progressive destructive interference, and the
waves will cancel.
• Thus, the orbits will only be stable if some whole
number of orbits, n, around the nucleus fit the
circumference (2πr) of the orbit.
Quantum Condition
• Therefore:
2𝜋𝑟 = 𝑛λ
n = 1,2,3….
• We define n as the principle quantum number. Bohr showed
that an electron in a given orbit can ONLY have the following
energy:
𝐸𝑛 =
−2.1799 𝑎𝐽
𝑛2
n =3
n =2
n =1
• We say that the energy of
the electrons in each level is
quantized.
• Each orbit represents an
allowed state, or energy level
in which an electron can
reside.
Transitions
• The lowest energy state is called the ground state. When an
electron is transitioned to a higher state, the electron is said to be
excited, or in an excited state.
• Now, we can understand why certain elements can only emit at
certain wavelengths….
• because only certain transitions exist depending on the
circumference of the orbits around the nucleus
• Thus, when atoms absorb energy, electrons move to an excited
state. When they return to the ground state, the atom emits a
photon to release the energy. The energy of the photon is the
difference in energy between the initial and final states:
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸𝐼 − 𝐸𝐹
Example
• What would the wavelength of emitted light be, in nm, if an excited
hydrogen electron in the n=4 state relaxes back to the n=2 state?
E
n=4
n=2
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸𝐼 − 𝐸𝐹
= 𝐸4 − 𝐸2
−2.1799 𝑎𝐽
−2.1799 𝑎𝐽
=
−
42
22
n=1
λ=
ℎ𝑐
𝐸
=
= 𝟎. 𝟒𝟎𝟖𝟖 𝒂𝑱
(6.626 𝑥 10−18 𝐽𝑠)(3.0 𝑥108 𝑚𝑠 −1 )
(.4088 𝑥 10−18 𝐽)
= 486 𝑛𝑚
Atomic Emission Spectra of Hydrogen
There it is!!!
Transitions for a Hydrogen Atom
Emission in
the visible
region.
Conclusions
• The work of Planck, Einstein, DeBroglie and Bohr has provided much
information into the relationship between EMR and electronic
structure.
• From the understanding that energies are quantized, and that
photons and electrons are both wave and particle like, the Bohr
model of the atom was able to explain the line spectra of hydrogen
• We now know that emission is the result of transitions from
quantized energy states. Different atoms have different allowed
transitions.
• The allowed wavelengths of light that can be absorbed and emitted
by an atom give insight into the energy states involved in a given
process in an atom