Lecture 6: Light and the Electromagnetic Spectrum

Dr Harris9/5/12HW: 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

Neon light ?

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 orangish-yellow 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:

• 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 photons striking the metal, the energy beyond the threshold energy (excess) is converted into kinetic energy. Thus,

𝑬𝒌=𝑬𝒑𝒉𝒐𝒕𝒐𝒏−𝑬𝑻

Plot of Ek vs. ν for sodium

slope of line = h

5.51 x 1014 s-1

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 =

𝑬𝒌=𝑬𝒑𝒉𝒐𝒕𝒐𝒏−𝑬𝑻

substitute: 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 Continued.

• 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=√ 2𝐸𝑘

𝑚

𝑉=√ 2(2.33 𝑥10−19𝑘𝑔𝑚2𝑠− 2)(9.109 𝑥10− 31𝑘𝑔)

=7.15 𝑥105𝑚/ 𝑠

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 = hνphotonEk

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

λλ’

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 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 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 λD = h/p

DeBroglie’s Approach

Louis DeBroglie (1892-1987)

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

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.

• 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 𝑥 5280 𝑓𝑡𝑚𝑖 𝑥 .3048𝑚𝑓𝑡 𝑥 h𝑟

3600 𝑠=53.6m /s

λ𝐷=h𝑝=

6.626 𝑥10− 34 𝐽 𝑠[ (.0459𝑘𝑔 ) (53.6𝑚𝑠−1 ) ]

=2.69 x 10− 34𝑚

• 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:

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=−2.1799𝑎𝐽

𝑛2

n =1n =2n =3

• 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:

𝐸 h𝑝 𝑜𝑡𝑜𝑛=𝐸 𝐼−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?

n=4

n=1

E 𝐸 h𝑝 𝑜𝑡𝑜𝑛=𝐸 𝐼−𝐸𝐹

¿−2.1799𝑎𝐽

42−(−2.1799𝑎𝐽22 )

¿𝟎 .𝟒𝟎𝟖𝟖𝒂𝑱

λ

n=2

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