Lecture 5Suggested HW

13, 19, 20, 21, 22, 28, 29, 31, 37

The EMR Spectrum (Ch 4.4-4.9)

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?

Neon light ?

• 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

EMR: Light and Energy

• 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

Wave Propagation

• 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)

• 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

Wavelength and Frequency

• 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

EMR is Classified By Wavelength

ROY G. BIV (increasing Energy)

Visible Radiation (Light)

(C.I.R.L) Dangers of UV Exposure.

No sunscreen Sunscreen

• 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?

Group Work

• 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.

Spectra (Continuous)

(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.

• 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

Spectra (Line)

• 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….Solving the Mystery

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

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)

Group Work

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:

• m is the mass in kg, and is the velocity (speed) in meters per second (m/s). The units of energy are Joules (J).

𝑬𝒌=𝟏𝟐𝒎𝑽𝟐

• Einstein found that as you increase the energy of the incident photon, the velocity of the ejected electron increases equally:

𝑬𝒌=𝑬𝒑𝒉𝒐𝒕𝒐𝒏−𝑬𝑻

Plot of Ek vs. ν for sodium

slope of line = h

5.51 x 1014 s-1

Ep = hνpEk

Electrons bound by energy E= hvT

Photoelectric Effect Schematic

http://phet.colorado.edu/en/simulation/photoelectric

• 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 =

𝑬𝒌=𝑬𝒑𝒉𝒐𝒕𝒐𝒏−𝑬𝑻

𝐸𝑘=h𝑣 h𝑝 𝑜𝑡𝑜𝑛−h𝑣𝑇=h (𝑣 h𝑝 𝑜𝑡𝑜𝑛−𝑣𝑇 )𝐸𝑘=(6.626 𝑥10− 34 𝐽𝑠)(3.52𝑥1014𝑠− 1)

𝑬𝒌=𝟐 .𝟑𝟑𝐱 𝟏𝟎−𝟏𝟗 𝑱

Example

• From the example on the previous page, calculate the velocity of the electron?

• Mass of electron = 9.109 x 10-31 kg Joule

𝑬𝒌=𝟏𝟐𝒎𝑽𝟐

Solving for𝑉 :𝑉=√ 2 Ekm𝑉=√ 2(2.33 𝑥10−19𝑘𝑔𝑚2𝑠− 2)

(9.109 𝑥10− 31𝑘𝑔)=7.15 𝑥105𝑚/ 𝑠

Example, contd.

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

• 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?

Light As Waves? Young’s Slit Experiment (1799)

https://phet.colorado.edu/en/simulation/wave-interference

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. 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).

Constructive and Destructive Interference

Light As Waves? Young’s Slit Experiment (1799)

• 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

λλ’

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

Waves or Particles?

• 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= m) Planck (wave like) : E = hν DeBroglie (both) : pc = hν pc = p = pλ = h

Louis DeBroglie (1892-1987)

• The value, λD is the DeBroglie wavelength, or the wavelength of any mass m with velocity .

Wave-Particle Duality

λ𝐷=h /(𝑚𝑉 )

• 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

Wave-Particle Duality

(C.I.R.L.) Scanning Electron Microscope Images

• Very high resolution images can be obtained from scattered and diffracted electrons

• Calculate the DeBroglie wavelength of an electron travelling at 1.00% of the speed of light.

• 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

λ𝐷= h𝑝

= 6.626𝑥 10−34 𝐽 𝑠

[ (9.109 𝑥10− 31𝑘𝑔 ) (𝟑 .𝟎𝟎𝒙𝟏𝟎𝟔𝒎𝒔−𝟏 ) ]=2.43 x10−10𝑚

𝑉=120𝑚𝑖h𝑟

𝑥5280 𝑓𝑡𝑚𝑖

𝑥.3048𝑚

𝑓𝑡𝑥

h𝑟3600 𝑠

=53.6m /s

λ𝐷= h𝑝

= 6.626 𝑥10− 34 𝐽 𝑠

[ (.0459𝑘𝑔 ) (53.6𝑚𝑠−1 ) ]=2.69x 10− 34𝑚

• DeBroglie wavelength of large objects is negligible

Examples

• 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 !!

Quantum Condition

• Therefore:

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=−2.1799𝑎𝐽

𝑛2

n =1

n =2

n =3• Energies of electrons in each

level are quantized (set, exact).

• Each orbit represents an allowed state in which an electron can reside.

The Bohr Model Of the Atom

• 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.

Transitions

• 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=1

Incr

easi

ng E

nerg

y 𝐸 h𝑝 𝑜𝑡𝑜𝑛=𝐸 𝐼−𝐸𝐹

¿−2.1799𝑎𝐽

42−(−2.1799𝑎𝐽22 )

¿𝟎 .𝟒𝟎𝟖𝟖𝒂𝑱

λ

n=2

Example

There it is!!!

Atomic Emission Spectra of Hydrogen

• 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

Conclusions