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Chemistry

Optional Review Light and Matter

2015-10-27 www.njctl.org

Slide 3 / 63 Light and Sound

In 1905 Einstein derived an equation relating mass and energy. You should be familiar with this equation: E = mc

2

This equation has been changed a bit since, but a relationship has now, for the first time in history, been established between matter and energy, and between physics and chemistry.

Slide 4 / 63 Light and Sound

Because Einstein was able to prove a relationship between matter and energy, we today can understand more about matter by learning all about energy. We can see this relationship between energy and matter specifically when we look at some of the unusual properties of the wave nature of energy.

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The nature of light has been debated for thousands of years. In the 1600's, Newton argued that light was a stream of

• particles. Huygens countered that it was a wave.

Both had good arguments, but neither could prove their case.

The Nature of Light: Wave or Particle?

wave!

particle!

Slide 6 / 63 Young's Double Slit Experiment

In 1801, Thomas Young settled the argument (apparently) with his Double Slit Experiment. Later, when we look at the results of Young's experiment we will see one of the unusual properties of energy that we were talking about. But first, we must understand waves. To study the properties of waves we can look at any type of wave, from the waves in a body of water, to the sound waves produced by speakers. Waves are waves.

Click here to see a Veritasium video on Young's original Double Slit Experiment

Slide 7 / 63 Young's Double Slit Experiment

Young tested to see if light was a wave by seeing if it created an interference pattern when it went through two slits, like a wave would.

light source

d L

slit screen measurement screen

Slide 8 / 63 Young's Double Slit Experiment

This photo is of light (of one color) striking a distant screen after passing through 2 slits. This only makes sense if light is a wave.

d L

slit screen measurement screen x

light source

Slide 9 / 63 Diffraction and Interference

The double slit experiment relies on two properties of waves: Each slit generates a new wave due to diffraction. Those waves then either constructively or destructively interfere on a far away screen.

S1 S2 viewing screen

diffraction and interference

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1 What principle is responsible for light spreading as it passes through a narrow slit? A diffraction B polarization C dispersion D interference

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1 What principle is responsible for light spreading as it passes through a narrow slit? A diffraction B polarization C dispersion D interference

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Answer A

Slide 11 / 63 Double-Slit Maxima and Minima

Interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).

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The bright lines that appear on the screen are called maxima. The dark lines are called minima. Maxima are evenly spaced, and a minima occurs between each pair of maxima.

Double-Slit Maxima and Minima Slide 13 / 63

2 What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits? A diffraction B polarization C dispersion D interference

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2 What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits? A diffraction B polarization C dispersion D interference

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Answer D

Slide 14 / 63 If Light is a Wave… What exactly is waving?

In sound waves, we know it's the pressure in the air. In any simple harmonic motion there has to be two forms (or levels) of energy and a means to move between them. But what does that mean for light?

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A great way to start this up is to make a charge (like an electron) accelerate. That creates a changing electric field... which creates a changing magnetic field... which creates a changing electric field... which creates a changing magnetic field... which creates a changing electric field... which creates a changing magnetic field...

Accelerating Charges create E-M waves Slide 16 / 63 Accelerating Charges create E-M waves

Electromagnetic Wave Direction

Slide 17 / 63 James Maxwell

In Scotland in the late 1800's, James Maxwell, combined together the known equations of electricity and magnetism, and added one, to create Maxwell's Equations.

Slide 18 / 63 Maxwell's Equations

Gauss's Law Gauss's Law for Magnetism Faraday's Law of Induction Ampere's Law Maxwell's Equations

Slide 18 (Answer) / 63 Maxwell's Equations

Gauss's Law Gauss's Law for Magnetism Faraday's Law of Induction Ampere's Law Maxwell's Equations

Teacher Notes

[This object is a teacher notes pull tab] Maxwell’s equations are 4 mathematical equations that relate the electric field (E) and magnetic field (B) to the charge ( ρ ) and current (J) densities that determine the fields and produce electromagnetic radiation (light). Gauss's Law for Electricity : the rate of flow of an electric field out

• f any closed surface is proportional to the electric charge enclosed

within the surface. Gauss's Law for Magnetism : the net magnetic flux outside of any closed surface is 0. Faraday's Law of Induction : the generated voltage around a closed loops is equal to the rate of change of magnetic flux through the area

• f the loop.

Ampere's Law : in a constant electric field, the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

Slide 19 / 63 Speed of Light

He found they predicted that energy could move between two forms (electric and magnetic) and that disturbance must travel through space at a speed of 3.0 x 108 m/s. This very much agreed with the known speed of light. 3.0 x 10

8 m/s is the speed of light

in a vacuum.

Slide 19 (Answer) / 63 Speed of Light

He found they predicted that energy could move between two forms (electric and magnetic) and that disturbance must travel through space at a speed of 3.0 x 108 m/s. This very much agreed with the known speed of light. 3.0 x 10

8 m/s is the speed of light

in a vacuum.

Teacher Notes

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The speed at which an EM wave travels through a vacuum is related to the electric constant ε0 and the magnetic constant μ0 .

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In physics we learned that a changing magnetic field produces an electric field. Maxwell showed that a changing electric field produces a magnetic field as well. Once these changing fields are first started up, they keep creating each other...and travel on their own. These traveling fields are called electromagnetic waves.

Creating Electromagnetic Waves

Electromagnetic Wave Direction

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3 An electric field is produced by a A constant magnetic field. B changing magnetic field. C either a constant or a changing magnetic field. D gravitation

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3 An electric field is produced by a A constant magnetic field. B changing magnetic field. C either a constant or a changing magnetic field. D gravitation

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Answer B

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4 A changing electric field will produce a A current. B gravitational field. C magnetic field. D a gravitational field.

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4 A changing electric field will produce a A current. B gravitational field. C magnetic field. D a gravitational field.

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Answer C

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Young showed that light is a wave. Maxwell showed that electromagnetic waves exist and travel at the speed of light. Light was shown to be an electromagnetic wave. The frequency of an electromagnetic wave is related to its

• wavelength. For electromagnetic waves (including light), in

a vacuum: c = speed of light = wavelength (m) = frequency (Hz or s

• 1)

Light is an Electromagnetic Wave

c = λ

c= c=

λ

Slide 24 / 63 c = λ The Electromagnetic Spectrum

All electromagnetic radiation travels at the same velocity: the speed of light (c) c = 3.00 x 108 m/s.

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5 All electromagnetic waves travel through a vacuum at A the same speed. B speeds that are proportional to their frequency. C speeds that are inversely proportional to their frequency. D speeds too slow to measure.

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5 All electromagnetic waves travel through a vacuum at A the same speed. B speeds that are proportional to their frequency. C speeds that are inversely proportional to their frequency. D speeds too slow to measure.

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Answer A

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6 In a vacuum, the velocity of all electromagnetic waves: A is zero. B is 3.0 × 10

8 m/s.

C depends on the frequency. D depends on their amplitude.

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6 In a vacuum, the velocity of all electromagnetic waves: A is zero. B is 3.0 × 10

8 m/s.

C depends on the frequency. D depends on their amplitude.

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Answer B

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7 For a wave, the frequency times the wavelength is the wave's _______. A speed. B amplitude. C intensity. D power.

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7 For a wave, the frequency times the wavelength is the wave's _______. A speed. B amplitude. C intensity. D power.

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Answer A

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8 The wavelength of light that has a frequency of 1.20 x 1013 Hz is _______. A 25 m B 2.5 x 10

• 5 m

C 0.040 m D 2.5 m

c = λv c = 3.00 x 108 m/s

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8 The wavelength of light that has a frequency of 1.20 x 1013 Hz is _______. A 25 m B 2.5 x 10

• 5 m

C 0.040 m D 2.5 m

c = λv c = 3.00 x 108 m/s

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Answer B

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9 Electromagnetic radiation travels through a vacuum at a speed of __________. A 186,000 m/s B 125 m/s C 3.00 x 108 m/s D It depends on wavelength

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9 Electromagnetic radiation travels through a vacuum at a speed of __________. A 186,000 m/s B 125 m/s C 3.00 x 108 m/s D It depends on wavelength

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Answer C

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10 What is the frequency of red light whose wavelength is 600 nm? A 5.0 x 10

14 Hz

B 1.0 x 10

15 Hz

C 1.5 x 10

15 Hz

D 2.0 x 10

15 Hz

c = λv c = 3.00 x 108 m/s

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10 What is the frequency of red light whose wavelength is 600 nm? A 5.0 x 10

14 Hz

B 1.0 x 10

15 Hz

C 1.5 x 10

15 Hz

D 2.0 x 10

15 Hz

c = λv c = 3.00 x 108 m/s

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Answer A

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11 Plants absorb red light with a frequency of 5 x 1014 Hz while reflecting green light with a frequency of 5.5 x 1014 Hz. What must be true of green light compared to red light? A Green light has a longer wavelength than red light. B Green light has a shorter wavelength than red light. C Green light travels at a slower speed than red light. D Green light travels at a faster speed than red light. E Green and red light have the same wavelength.

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11 Plants absorb red light with a frequency of 5 x 1014 Hz while reflecting green light with a frequency of 5.5 x 1014 Hz. What must be true of green light compared to red light? A Green light has a longer wavelength than red light. B Green light has a shorter wavelength than red light. C Green light travels at a slower speed than red light. D Green light travels at a faster speed than red light. E Green and red light have the same wavelength.

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Answer B

Slide 32 / 63 Blackbody Radiation

All objects emit electromagnetic radiation which depends on their temperature: thermal radiation. A blackbody absorbs all electromagnetic radiation (light) that falls on it. Because no light is reflected or transmitted, the object appears black when it is cold. However, black bodies emit a temperature- dependent spectrum termed blackbody radiation. For example, the temperature of the above Pāhoehoe lava flow can be estimated by observing its color.

click here for a PHET simulation of the blackbody spectrum

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This figure shows blackbody radiation curves for three different temperatures. As can be seen the frequency and intensity changes depending on the temperature

• f the substance.

Classical physics couldn't explain the shape of these spectra.

Blackbody Radiation Slide 34 / 63

The wave nature of light could not explain the way an object glows depending on its temperature: its spectrum. In 1900, Max Planck explained it by assuming that the atoms that make up the objects only emit radiation in quantum amounts.

Planck’s Quantum Hypothesis

These days, this assumption is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck's career. Quantum: discrete quantity of electromagnetic radiation

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E = hv where h is Planck’s constant (6.63 x 10-34 J*s) and v is the frequency of the light

Planck’s Postulate

Energy and frequency are directly related

Slide 36 / 63 Planck’s Quantum Hypothesis

According to Planck's hypothesis, since only certain frequencies of light were emitted at varying temperatures, the amount of energy put into a substance triggered that substance to release a very specific type of light. In other words, if we think of this like a person walking up a flight

• f stairs, the person cannot reach a certain height unless first

raising his or her legs to the height of the specific steps.

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Planck didn't believe this was real...it just worked. It was like working from the answers in the book…you see that it works, but you have no idea why. Atoms only having steps of energy? This didn't make sense. Why couldn't they have any energy? Planck thought a "real" solution would eventually be found...but this

• ne worked for some reason. Which brings us to our next mystery...

Planck’s Quantum Hypothesis Slide 38 / 63

When light strikes a metal, electrons sometimes fly off causing an electric current.

The Photoelectric Effect

Classical physics couldn't explain some specific features about how the effect works. So Einstein used Planck's idea to solve it.

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If atoms can only emit light in packets of specific sizes, maybe light itself travels as packets of energy given by Planck's formula. He called these tiny packets of energy or light photons.

The Photon

E = hv

where h is Planck’s constant (6.63 x 10-34 J*s)

voltage source Current indicator Radiant energy metal surface

e- evacuated chamber

Slide 40 / 63 Particle Theory of Light

This particle theory of light assumes that an electron absorbs a single photon and made specific predictions that proved true. For instance, the kinetic energy of escaping electrons vs. frequency of light shown below: This shows clear agreement with the photon theory, and not with wave theory. This supports the proposition that light is made of particles (photons) and therefore light is not a wave.

KEmax of electrons Frequency of light (v)

Slide 41 / 63 Wave-Particle Duality

Earlier we proved that light is a wave. Now we've proven that light is a particle.

So which is it?

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This question has no answer; we must accept the dual wave-particle nature of light. While we cannot imagine something that is both a wave and a particle at the same time; that turns out to be the case for light. Particle? Wave?

Wave-Particle Duality

Check out this animation about the Wave-Particle Duality Like that? Here's one more to watch

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12 The ratio of energy to frequency for a given photon gives A its amplitude. B its velocity. C Planck's constant. D its work function.

E = hv c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

Slide 43 (Answer) / 63

12 The ratio of energy to frequency for a given photon gives A its amplitude. B its velocity. C Planck's constant. D its work function.

E = hv c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

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Answer C

Slide 44 / 63

13 What is a photon? A an electron in an excited state B a small packet of electromagnetic energy that has particle-like properties C one form of a nucleon, one of the particles that makes up the nucleus D an electron that has been made electrically neutral

Slide 44 (Answer) / 63

13 What is a photon? A an electron in an excited state B a small packet of electromagnetic energy that has particle-like properties C one form of a nucleon, one of the particles that makes up the nucleus D an electron that has been made electrically neutral

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Answer B

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14 The energy of a photon depends on A its amplitude. B its velocity. C its frequency. D none of the given answers

Slide 45 (Answer) / 63

14 The energy of a photon depends on A its amplitude. B its velocity. C its frequency. D none of the given answers

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Answer C

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15 The photoelectric effect can be explained assuming A that light has a wave nature. B that light has a particle nature. C that light has a wave nature and a particle nature. D none of the above

Slide 46 (Answer) / 63

15 The photoelectric effect can be explained assuming A that light has a wave nature. B that light has a particle nature. C that light has a wave nature and a particle nature. D none of the above

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Answer B

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16 The energy of a photon that has a frequency 110 GHz is A 1.1 × 10-20 J B 1.4 × 10-22 J C 7.3 × 10-23 J D 1.3 × 10-25 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

Slide 47 (Answer) / 63

16 The energy of a photon that has a frequency 110 GHz is A 1.1 × 10-20 J B 1.4 × 10-22 J C 7.3 × 10-23 J D 1.3 × 10-25 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

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Answer C

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17 The frequency of a photon that has an energy of 3.7 x 10-18 J is A 5.6 × 10

15 Hz

B 1.8 × 10

• 16 Hz

C 2.5 × 10

• 15 J

D 5.4 × 10

• 8 J

E 2.5 × 10

15 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

Slide 48 (Answer) / 63

17 The frequency of a photon that has an energy of 3.7 x 10-18 J is A 5.6 × 10

15 Hz

B 1.8 × 10

• 16 Hz

C 2.5 × 10

• 15 J

D 5.4 × 10

• 8 J

E 2.5 × 10

15 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

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Answer A

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18 The energy of a photon that has a wavelength

• f 12.3 nm is

A 1.51 × 10-17 J B 4.42 × 10

• 23 J

C 1.99 × 10-25 J D 2.72 × 10-50 J E 1.61 × 10-17 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

Slide 49 (Answer) / 63

18 The energy of a photon that has a wavelength

• f 12.3 nm is

A 1.51 × 10-17 J B 4.42 × 10

• 23 J

C 1.99 × 10-25 J D 2.72 × 10-50 J E 1.61 × 10-17 J

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

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Answer E

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19 If the wavelength of a photon is halved, by what factor does its energy change? A 4 B 2 C 1/4 D 1/2

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

Slide 50 (Answer) / 63

19 If the wavelength of a photon is halved, by what factor does its energy change? A 4 B 2 C 1/4 D 1/2

E = h c = 3.00 x 108 m/s h = 6.63 x 10

• 34 J-s

c = λv

v

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Answer B

Slide 51 / 63

20 Compared to UV light with a wavelength of 300 nm, red light has half the energy. What must be the wavelength of this red light? A 150 nm B 300 nm C 600 nm D 900 nm E 450 nm

Slide 51 (Answer) / 63

20 Compared to UV light with a wavelength of 300 nm, red light has half the energy. What must be the wavelength of this red light? A 150 nm B 300 nm C 600 nm D 900 nm E 450 nm

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Answer C

Slide 52 / 63 Energy, Mass, and Momentum

• f a Photon

Clearly, a photon must travel at the speed of light, (since it is light) Special Relativity tells us two things from this: The mass of a photon is zero. The momentum of a photon depends on its wavelength.

Slide 53 / 63 Energy, Mass, and Momentum

• f a Photon

m = 0 p = hv c and since c = λv p = h λ This last equation turned out to have huge implications.

Slide 53 (Answer) / 63 Energy, Mass, and Momentum

• f a Photon

m = 0 p = hv c and since c = λv p = h λ This last equation turned out to have huge implications.

Teacher Notes

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Defining variables: m = mass (kg) p = momentum (kg-m/s) h = Planck's constant v = frequency (Hz)

λ = wavelength (m)

c = speed of light (m/s)

Slide 54 / 63 Matter as a wave?

Taking all of this into account, in 1924, French physicist Louis de Broglie asked: "If light can behave like a wave or a particle, can matter also behave like a wave?" He found that amazingly, it does!

Slide 55 / 63 Wavelength of Matter

de Broglie combined p = h/ with p = mv to get The wavelength of matter This wavelength is really small for normal objects, so it had never been noticed before. But it has a dramatic impact on the structure of atoms. l = h mv

= λ

in other words WAVE = PARTICLE λ

Slide 56 / 63 Wave Nature of Matter

The de-Broglie hypothesis that particles have wave-like properties needed to be supported by experiment. In fact, in a Nobel prize winning experiment, Davisson and Germer of Bell Labs found that electrons could be diffracted (remember the two slit experiment) just like waves. Electron wavelengths are often about 10-10 m, about the size of an atom, so the wave character of electrons is important.

Slide 57 / 63 Wave Nature of Matter

Electrons fired one at a time towards two slits show the same interference pattern when they land on a distant screen. The "electron wave" must go through both slits at the same time...which is something we can't imagine a single particle doing...but it does.

Click here for a video with more explanation of all this!

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These photos show electrons being fired one at a time through two slits. Each exposure was made after a slightly longer

• time. The same pattern emerges as was found

by light. Each individual electron must behave like a wave and pass through both slits. But each electron must be a particle when it strikes the film, or it wouldn't make one dot on the film, it would be spread out.

The most amazing experiment ever!

This one picture shows that matter acts like both a wave and a particle.

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21 What is the wavelength of a 0.25 kg ball traveling at 20 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

Slide 59 (Answer) / 63

21 What is the wavelength of a 0.25 kg ball traveling at 20 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

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Answer 1.26 x 10

• 34 m

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22 What is the wavelength of a 80 kg person running 4.0 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

Slide 60 (Answer) / 63

22 What is the wavelength of a 80 kg person running 4.0 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

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Answer 2.0 x 10

• 36 m

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23 What is the wavelength of the matter wave associated with an electron (m e = 9.1 x 10-31kg) moving with a speed of 2.5 × 10 7 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

Slide 61 (Answer) / 63

23 What is the wavelength of the matter wave associated with an electron (m e = 9.1 x 10-31kg) moving with a speed of 2.5 × 10 7 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

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Answer 2.9 x 10

• 11 m

Slide 62 / 63

24 What is the wavelength of the matter wave associated with an electron (m e = 9.1 x 10-31kg) moving with a speed of 1.5 × 10 6 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

Slide 62 (Answer) / 63

24 What is the wavelength of the matter wave associated with an electron (m e = 9.1 x 10-31kg) moving with a speed of 1.5 × 10 6 m/s?

h = 6.63 x 10

• 34 J-s

l = h mv

=

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Answer 4.9 x 10

• 11 m

Slide 63 / 63 Why does all this "Matter"?

Since matter and energy are now understood to share certain properties (wavelength for example) the interaction of matter with light has allowed us to probe the nature of matter itself, from the structure

• f the atom to the unique behavior of molecules. The structure and

behavior of matter is the domain of the chemist! "Are not the gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition?"

• Newton