Electromagnetic Radiation

Introduction

• Nearly all of our present understanding of the structure of atoms and the behavior of electrons has come from observing interactions of matter with light. Specifically, the light that is absorbed or 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 the light is turned on, a voltage is applied and the gas is ionized. This results in a “glow”. Why?

• When the electron is separated from the atom, its energy goes up. In this circumstance, we say that the electron has become excited.

• Excited electrons will quickly return to their original, lower energy state. The excess energy is released as light. This is called emission.

EMR: Light and Energy

Low energyState (ground)

𝒆𝒆−

Energy absorbed

High energyState (excited)

𝒆𝒆−

Energy emitted

𝒆𝒆−

𝒆𝒆−

1

2 4

3

Increasing E

• 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 pure energy that moves and spreads (propagation) outward through space as waves

• The waves created in water when an external force is applied is an example of propagation.

• EMR propagates through the universe as oscillating, perpendicular electric and magnetic fields

Wave Propagation

• For traveling waves, the distance between peaks is the wavelength (λ) (m)

• The number of complete wavelengths that pass a given point per second is the frequency, ν (units of s-1, also known as Hertz, Hz)

• Shorter wavelengths = higher frequencies!

• The speed of a wave, a constant value, 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 space

Wavelength and Frequency

• The electromagnetic spectrum below shows EMR listed left to right by increasing wavelength. High frequency = high energy

• Wavelengths vary from the size of a nucleus to the length of a football field

EMR is Classified By Wavelength

ROY G. BIV (increasing Energy)

Visible Radiation (Light)

A

• Radiation types ranging from radio to visible are considered non-ionizing radiation. This means that radiation of this type lacks the energy necessary to eject electrons from chemical bonds. As a result, these radiation types are harmless.

• UV, X-ray and Gamma radiation are ionizing radiations. These types can ionize compounds, causing the destruction of chemical bonds, which can initiate chain processes leading to burns, adverse reactions, and certain types of cancer.

Ionizing vs Non-Ionizing Radiation

• 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 nearly continuous over a long range of wavelengths.

Sunlight

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

No sunscreen Sunscreen

(C.I.R.L) The Greenhouse Effect

• Greenhouse gas (GHG) molecules scatter infrared radiation, essentially creating a “warm blanket” around the Earth’s surface that sustains life at night. Too much GHG enhances the effect to dangerous levels.

• Light emitted from chemical samples (ex. Neon light) 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

• Ex. Sodium burns very brightly and emits an orangish-yellow color.

Spectral Lines

• 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?

The Beginning of Quantum Mechanics

The Beginning of Quantum Mechanics

• 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 predicted that continuous heating would produce increasingly high frequencies with indefinite intensities. This failure led to the creation of quantum mechanics, the field of physics used today.

The Birth Of Quantum Physics

• Planck, Einstein and others explained blackbody radiation by asserting that radiation can only be emitted in small, exact amounts called quanta

• This means that electrons have exact, fixed energy values! (quantized)

• Light is believed to be comprised of tiny packets of energy called photons

Quantized vs Continuous

Imagine a person on a set of stairs. The person’s height abovethe floor is quantized, because he/she can only stand on thestairs, not between them. The person can only attain exact,specific heights above the ground level. The energies ofelectrons follow this same model.

A person on a ramp, however, can stand anywhere on the ramp,so the allowed heights are continuous, or non-quantized.

• The failure of classical physics is due mainly to the incorrect assumption that electron energies are continuous.

• Treating photons as waves, it was determined that the amount of energy contained in some number of photons is given by:

• This quantum model still required more evidence to be proven,and Einstein’s photoelectric effect experiment was able toprovide it.

Where n is the total number of photons, En is the total energy in joules of n photons, and h is Planck’s constant, 6.626 x 10-34 J•s

En = nhν

Energy of Radiation

Calculate the total energy in 10 photons of green light (~520 nm)

What are we given:λ = 520 nm

n = 10

Solve for En.

We can solve for ν. ν𝜆𝜆 = 𝑐𝑐 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇: 𝜈𝜈 = 𝑐𝑐𝜆𝜆

Apply SI units to λ!

Examples

𝐸𝐸𝑛𝑛 = 𝑛𝑛𝑇𝜈𝜈

E10 = nhcλ

= 10 6.626 x10−34 Js3.0 x108 m

s520x10−9m

E10 = 3.2 x 10−18J

A single pulse from a red laser (λ=690 nm) emits 0.1 mJ of energy.Calculate the number of photons in the pulse.

What are we given:En = 0.1 mJλ = 690 nm

Solve for n.

As was shown in the previous example, we will substitute for ν andapply SI units for En and λ.

𝑛𝑛 =𝐸𝐸𝑛𝑛𝑇𝜈𝜈

𝑛𝑛 =(0.1 𝑥𝑥 10−3 𝐽𝐽)

6.626 𝑥𝑥 10−34𝐽𝐽𝐽𝐽3.0 𝑥𝑥 108 𝑚𝑚𝐽𝐽

690 𝑥𝑥 10−9𝑚𝑚

= 3.5 𝑥𝑥 1014

The Photoelectric Effect

• Einstein was awarded the Nobel Prize in 1921 for his discovery ofthe photoelectric effect, which laid the foundation for solarpowered devices.

• This phenomena describes the ejection of electrons from a metalsurface following the absorption of a photon’s energy.

The Photoelectric Effect

• Photons too low in frequency (energy),no matter how intense the beam, willnot eject an electron from a metalsurface.

• The minimum frequency of a photonthat can excite an electron is calledthe threshold frequency, vo.

• For an electron to be ejected, it mustabsorb enough photon energy toovercome its attraction to the nucleus.This energy is called the workfunction, Φ

Φ = hνo

Electrons Convert Excess Photon Energy Into Kinetic Energy

• If the energy of the absorbed photon exceeds the work function, the extra energy is converted to kinetic energy (Ek), allowing the freed electron to move.

• As you increase the energy of the incoming photon, the kinetic energy of the ejected electron increases linearly, as shown in the graph above. The slope of this plot is h, thus, proving the quantum mechanical correct.

𝑬𝑬𝒌𝒌 = 𝑬𝑬𝒑𝒑 − Φ = (𝒉𝒉𝝂𝝂)− (𝒉𝒉𝝂𝝂𝒐𝒐) = 𝒉𝒉(𝝂𝝂 − 𝝂𝝂𝒐𝒐)

energy of incoming photon(n=1)

energy needed to free electron

excess energy remaining

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?𝝼𝝼o (frequency needed to free electron) = 1.076 x 1015 s-1

λ (wavelength of incomoing photon) = 210 nm

𝝼𝝼 (frequency of incoming photon)= 𝑐𝑐λ

= 3.0 𝑥𝑥 108𝑚𝑚 𝑠𝑠−1

210 𝑥𝑥 10−9𝑚𝑚= 1.428 x 1015 s-1

Ek = (6.626 x 10−34 Js)(1.428 x 1015s−1 − 1.076 x1015s−1)

ExamplePhotoelectric Effect

𝑬𝑬𝒌𝒌 = 𝒉𝒉𝒉𝒉 − 𝒉𝒉𝒉𝒉𝒐𝒐 = 𝒉𝒉(𝒉𝒉 − 𝒉𝒉𝒐𝒐)

𝐄𝐄𝐤𝐤 = 𝟐𝟐.𝟑𝟑𝟑𝟑 𝐱𝐱 𝟏𝟏𝟎𝟎−𝟏𝟏𝟏𝟏 𝐉𝐉

• From the example on the previous page, calculate the velocityof the electron? The mass of an electron is 9.109 x 10-31 kg. – Hint: you will need to break the unit JOULE into its basic SI

units. Also, recall that 𝐄𝐄𝐤𝐤 = 𝟏𝟏𝟐𝟐𝐦𝐦𝐕𝐕𝟐𝟐

Continued…

2𝐸𝐸𝑘𝑘𝑚𝑚 = 𝑉𝑉

2 2.33 𝑥𝑥 10−19 𝑘𝑘𝑘𝑘𝑚𝑚2

𝐽𝐽29.109 𝑥𝑥𝑥0−31 𝑘𝑘𝑘𝑘 = 𝟕𝟕.𝟏𝟏𝟏𝟏 𝒙𝒙 𝟏𝟏𝟎𝟎𝟏𝟏

𝒎𝒎𝒔𝒔

• 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 IssacNewton

• To test his hypothesis, Young conducted the ‘slit experiment’

Understanding the Physical Make-Up of Photons

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

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

Constructive and Destructive Interference

• The observed pattern can be explained by treating light as waves • Waves that are out of phase will destruct (a), yielding a lower

amplitude, which explains the dark lines. Low amplitude = low brightness

• Waves of light that are in phase, can interact, forming a single wave of high amplitude. High amplitude = high brightness. This is called constructive interference (b).

Constructive and Destructive Interference

• 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 waves are particle-like and visa versa.

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

Wave-Particle Duality

λ𝐷𝐷 = 𝑇/(𝑚𝑚𝑉𝑉)

• 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

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

• We see that an electron moving at this speed has a similar wavelength as X-ray radiation.

2. 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?– Convert to SI units

λ𝐷𝐷 =𝑇𝑚𝑚𝑉𝑉

=6.626 𝑥𝑥 10−34 𝐽𝐽 𝐽𝐽

9.109 𝑥𝑥 10−31𝑘𝑘𝑘𝑘 𝟑𝟑.𝟎𝟎𝟎𝟎 𝒙𝒙𝟏𝟏𝟎𝟎𝟔𝟔 𝒎𝒎𝒔𝒔−𝟏𝟏 = 2.43 x 10−10𝑚𝑚

�𝑉𝑉 =120 𝑚𝑚𝑚𝑚𝑇𝑇𝑇 𝑥𝑥

5280 𝑇𝑇𝑓𝑓𝑚𝑚𝑚𝑚 𝑥𝑥

.3048 𝑚𝑚𝑇𝑇𝑓𝑓 𝑥𝑥

𝑇𝑇𝑇3600 𝐽𝐽 = 53.6 m/s

λ𝐷𝐷 =𝑇𝑝𝑝 =

6.626 𝑥𝑥 10−34 𝐽𝐽 𝐽𝐽.0459 𝑘𝑘𝑘𝑘 53.6 𝑚𝑚𝐽𝐽−1 = 2.69 x 10−34 𝑚𝑚

• DeBroglie wavelength of large objects is negligible

Examples

• Let’s revisit the nuclear model of the atom. Consider an atom with 1-electron. The electron will “orbit” around the nucleus. Depending on the energy of the electron, it can exist in different orbits, or “energy states” at increasing distances from the nucleus.

• In the expression below, we define n as the principle quantum number, corresponding to the quantized energy state of the electron. Bohr showed that for 1-electron species (H, He+, Li2+….), the electron can ONLY have the following energies:

𝐸𝐸𝑛𝑛 =−2.1799 𝑥𝑥 10−18 𝐽𝐽

𝑛𝑛2

n =1

n =2

n =3

• Each orbit represents an allowed state, or energy level in which an electron can reside.

The Bohr Model Of the Atom

• The lowest possible energy state of an electron is called the ground state. States beyond the ground state are called excited states.

When an electron absorbs energy, it transitions into an excitedstate, followed by rapid relaxation back to the ground state(although this transition may not necessarily be direct). Theexcess energy must be released. To do so, the atom emits aphoton. The energy of the photon is the difference in energybetween the higher and lower state.

Transitions

• What color of light is emitted when an excited electron in a hydrogen atom relaxes from the n=4 state to the n=2 state?

1. Solve for the energy of the photon

2. Using that energy, solve for wavelength.

n=4

n=1

En

erg

y

Ephoton = E4 −E2

= −2.1799 𝑥𝑥 10−18𝐽𝐽42

− −2.1799 𝑥𝑥 10−18𝐽𝐽22

= 𝟒𝟒.𝟎𝟎𝟎𝟎𝟎𝟎 𝒙𝒙 𝟏𝟏𝟎𝟎−𝟏𝟏𝟏𝟏 𝑱𝑱

λ = ℎ𝑐𝑐𝐸𝐸

= (6.626 𝑥𝑥 10−34𝐽𝐽𝑠𝑠)(3.0 𝑥𝑥108𝑚𝑚𝑠𝑠−1)(4.088 𝑥𝑥 10−19 𝐽𝐽)

= 486 𝑛𝑛𝑚𝑚

n=2

Example

BLUISH GREEN!!!

Ephoton = hν = hcλ

There it is!!!

Atomic Emission Spectra of Hydrogen

• The work of Planck, Einstein, DeBroglie and Bohr hasprovided much information into the relationship betweenEMR and electronic structure.

• From the understanding that energies are quantized, and thatphotons and electrons are both wave and particle like, theBohr model of the atom was able to explain the line spectraof hydrogen

• We now know that emission is the result of transitions fromquantized energy states. Different atoms have differentallowed transitions.

• The allowed wavelengths of light that can be absorbed andemitted by an atom give insight into the energy statesinvolved in a given process in an atom

Conclusions