The EMR Spectrum (Ch 4.4-4.9)
Lecture 5
Suggested HW
13, 19, 20, 21, 22, 28, 29,
31, 37
Introduction
• 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?
– What further information can this provide us about the
electronic structure of atoms?
EMR: Light and Energy
• The applied voltage cause the electrons to become excited, or
“bumped up” in energy
• When the electrons drop back down to their 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 low energy
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, like that which emits from a lamp, is comprised of
visible waves
– Radio waves from a radio are another type of EMR
Wave Propagation
• The waves created in water
when an external force is
applied are an example of
propagation.
• The energy transferred to the
spot of impact 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 peak, is
the wavelength (λ) (m)
• If we picture these
waves moving across
the page, the number of
peaks that pass a given
point per second is the
frequency, ν (units of s-1
or 1/s or Hertz, Hz)
λν = c
• The speed of a wave is
given by the product of ν
and λ:
c is the speed of light, 3.0 x 108 m/s.
All EMR moves at this speed
through vacuum
EMR is Classified By Wavelength
• 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
Visible Radiation (Light)
ROY G. BIV
(increasing Energy)
(C.I.R.L) Dangers of UV Exposure.
No sunscreen
Sunscreen
Group Work
• 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?
Spectra (Continuous)
• 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.
(C.I.R.L) The Greenhouse Effect
• CO2 molecules absorb and re-release infrared radiation,
essentially creating a “warm blanket” around the Earth’s
surface that sustains life at night. Too much CO2 enhances
the effect to dangerous levels.
Spectra (Line)
• 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
orangish-yellow color: Discontinuous
spectrum
Blackbody Radiation….Solving the Mystery
• 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
radiation.
• When an object is just hot enough to glow,
it appears red. As you continue to heat
the material, it becomes “white hot”
• Classical physics predicts that continuous
heating 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 photons (or quanta)
• He then derived the amount of energy absorbed or
released in a single event is equal to:
En = nhν
where En is the total energy in J, n is the number of
photons, and h is Planck’s constant, 6.626 x 10-34 J•s
Failure of Classical Physics and the Birth of
Quantum Physics
Group Work
1. Calculate the energy contained in a single photon of violet
light (~400 nm)
2. Calculate the energy of contained in 10 photons of green
light (~520 nm)
Einstein and the Photon
• Einstein envisioned light as
a beam of particles.
• 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 a metal surface under
illumination following the absorption of a
photon’s energy.
• Photons too low in frequency (energy), no
matter how intense the beam, will not
eject an electron from a metal surface.
• The minimum frequency required to free
an electron is called the threshold
frequency
• For energies beyond the threshold energy
(ET = hvT), the excess energy is converted
into kinetic energy and is ejected.
Electrons Convert Excess Photon Energy Into
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 incident
photon, the velocity of the ejected electron increases equally:
𝑬𝒌 = 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬𝑻
Photoelectric Effect Schematic
Ep = hνp
Ek
Electrons bound by energy E= hvT
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
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, contd.
• From the example on the previous page, calculate the velocity
of the electron?
𝑬𝒌 =
𝟏
𝒎𝑽𝟐
𝟐
• Mass of electron = 9.109 x 10-31 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)
Understanding the Physical Make-Up of Photons
• 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
Light as Waves?
• 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)
https://phet.colorado.edu/en/simulation/wave-interference
Constructive
and
Destructive
Constructive
and
DestructiveInterference
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. Higher amplitude = more
brightness. This is called constructive interference (a).
• Waves that are out of phase
will deconstruct (b), yielding a
lower amplitude (destructive
interference).
Light As Waves? Young’s Slit Experiment (1799)
Waves or Particles?
• Einstein’s Photoelectric effect suggested that photons had
momentum, a property of particles. This directly conflicted
with the findings of Young.
• 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
Waves or Particles?
• 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
Wave-Particle Duality
• 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, are wave-like.
Einstein (particle like): E = pc (p is momentum, p= m𝑉)
Planck (wave like) : E = hν
DeBroglie (both) : pc = hν
pc =
ℎ𝑐
λ
p=
ℎ
λ
pλ = h
λ𝐷 = ℎ/(𝑚𝑉)
• The value, λD is the DeBroglie
wavelength, or the wavelength of
any mass m with velocity 𝑉.
Louis DeBroglie (1892-1987)
Wave-Particle Duality
• 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 EMR and electrons behave in wave-like
manners
Both exhibit
the wave-like
ability of
diffraction
(C.I.R.L.) Scanning Electron Microscope Images
• Very high resolution images can be obtained from scattered and
diffracted electrons
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
• DeBroglie combined Bohr’s model with his theories 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, some whole number of electron
wavelengths, n, must fit around the
circumference (2πr) of the orbit !!
The Bohr Model Of the Atom
• Therefore:
2𝜋𝑟 = 𝑛λ
n = 1,2,3….
• We define n as the principle quantum number, the number
of electron wavelengths in a given shell. Bohr was able to
show that an electron in a HYDROGEN atom can only have
the following energies:
𝐸𝑛 =
−2.1799 𝑎𝐽
𝑛2
n =3
• Energies of electrons in each
level are quantized (set, exact).
n =2
n =1
• Each orbit represents an
allowed state in which an
electron can reside.
Transitions
• The lowest energy state is called the ground state. States
beyond the ground state are called excited states.
• Now, we can understand why certain elements can only
emit at certain wavelengths….
– because only specific transitions exist
When an electron absorbs energy, it is promoted to an
excited state, followed by rapid relaxation back to the
ground state. The excess energy must be released. To
do so, the atom emits a photon. The energy of the
photon is the difference in energy between the initial and
final states.
Example
Increasing Energy
• 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?
n=4
n=2
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸𝐼 − 𝐸𝐹
= 𝐸4 − 𝐸2
=
n=1
λ=
ℎ𝑐
𝐸
=
−2.1799 𝑎𝐽
−2.1799 𝑎𝐽
−
42
22
= 𝟎. 𝟒𝟎𝟖𝟖 𝒂𝑱
(6.626 𝑥 10−34 𝐽𝑠)(3.0 𝑥108 𝑚𝑠 −1 )
(.4088 𝑥 10−18 𝐽)
= 486 𝑛𝑚
Atomic Emission Spectra of Hydrogen
There it is!!!
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