electromagnetic radiation all electromagnetic radiation travels at the same velocity: the speed of...

Electromagnetic Radiation

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

• Therefore,

c =

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.

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 atoms 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.

E = hf

where h is Planck’s constant (6.63 x 10-34 J-s) and f is the frequency of the light

Planck’s Postulate


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 of stairs, the person cannot reach a certain height unless first raising his or her legs to the height of the specific steps.

Planck didn't believe this was a 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 one worked for some reason. Which brings us to our next mystery...


The Nature of Energy

• Einstein used this assumption to explain the photoelectric effect.

• He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.63 10−34 J-s.

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.

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 = hf

where h is Planck’s constant

(6.63 x 10-34 J-s)

voltagesource

Currentindicator

Radiant energy

metalsurface

e-

evacuated chamber

Photon 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 shows that light is made of particles (photons) and therefore light is not a wave.

KEm

ax o

f ele

ctro

ns

Frequency of light f

Wave-Particle Duality

Earlier we proved that light is a wave.

Now we've proven that light is a particle.

So which is it?

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?



Check out this animation about the Wave-Particle Duality

Like that?Here's one more to watch

Electron Microscopy

Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.

11 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 = hf

c = 3.00 x 108 m/s

h = 6.63 x 10-34 J-s

c = λf

12 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

13 The energy of a photon depends on

A its amplitude.

B its velocity.

C its frequency.

D none of the given answers

14 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

15 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 = hf

c = 3.00 x 108 m/s

h = 6.63 x 10-34 J-s

c = λf

16 The frequency of a photon that has an energy of 3.7 x 10-18 J is

A 5.6 × 1015 Hz

B 1.8 × 10-16 Hz

C 2.5 × 10-15 JD 5.4 × 10-8 J

E 2.5 × 1015 J

E = hf

c = 3.00 x 108 m/s

h = 6.63 x 10-34 J-s

c = λf

17 The energy of a photon that has a wavelength of 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 = hf

c = 3.00 x 108 m/s

h = 6.63 x 10-34 J-s

c = λf

18 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 = hf

c = 3.00 x 108 m/s

h = 6.63 x 10-34 J-s

c = λf

Energy, Mass, and Momentum of 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.

The Wave Nature of Matter

• Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was

=hmv

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!

Wave Nature of Matter

Electron wavelengths are often about 10-10 m, about the size of an atom, so the wave character of electrons is important.

In fact, the two-slit experiment that showed that light was a wave, has been replicated with electrons with the same result...electrons are particles and waves.

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!

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.

19 Assuming both balls are moving with a speed of 10 m/s, which ball has a longer de'Broglie wavelength?

A The tennis ball

B The bowling ball

C Both balls have the same wavelength

D It's impossible to tell

E I don't know the answer

bowling ball

tennis ball

20 Assuming both balls are not moving (ignoring molecular movement), which ball has a longer de' Broglie wavelength?

bowling ball

tennis ball

A The tennis ball

B The bowling ball

C Both balls have the same wavelength

D It's impossible to tell

E I don't know the answer

21 Which option correctly ranks the objects below in order of increasing de' Broglie wavelength, if each object is traveling at a speed of 10 m/s?

A golfball, tennis ball, baseball, basketball, bowling ball

B baseball, tennisball, golfball, basketball, bowling ball

C basketball, baseball,tennis ball, bowling ball, golf ball

D bowling ball, basketball, baseball, tennis ball, golfball

E tennis ball, bowling ball, basketball, golfball, baseball

bowling ball

baseball

basketball

tennis ballgolfball

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

h = 6.63 x 10-34 J-s

l = hmv=

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

h = 6.63 x 10-34 J-s

l = hmv=

24 What is the wavelength of the matter wave associated with an electron (me = 9.1 x 10-31kg) moving with a speed of 2.5 × 107 m/s?

h = 6.63 x 10-34 J-s

l = hmv=

25 What is the wavelength of the matter wave associated with an electron (me = 9.1 x 10-31kg) moving with a speed of 1.5 × 106 m/s?

h = 6.63 x 10-34 J-s

l = hmv=

Atomic Spectra

Small amount of gas heated in a discharge tube emits light only at characteristic frequencies.

+_

_

_

_

+_

+-Cathode Anode

High Voltage

try and think about listening to hydrogen

Atomic Spectra

An atomic spectrum is a line spectrum – only certain frequencies appear. If white light passes through such a gas, it absorbs at those same frequencies.

Atomic Spectra

Why don't atoms radiate, or absorb, all frequencies of light?

Why do they radiate light at only very specific frequencies, and not at others?

Atomic Spectra: Key to the Structure of the Atom

A portion of the complete spectrum of hydrogen is shown here. The lines cannot be explained by the Rutherford theory.

Lyman Balmer Paschen

ultraviolet

infrared

The Bohr Atom

Bohr proposed that electrons could orbit the nucleus, like planets orbit the sun...but only in certain specific orbits.

He then said that in these orbits, they wouldn't radiate energy, as would be expected normally of an accelerating charge. These stable orbits would somehow violate that rule.

Each orbit would correspond to a different energy level for the electron.

Bohr's Model

n represents the energy level where n=1 is the lowest naturally occupied level or "ground state"

+

n=1

n=2

n=3

The Bohr Atom

These possible energy states for atomic electrons were quantized – only certain values were possible. The spectrum could be explained as transitions from one level to another.

upper

lower

e-

Electrons would only radiate when they moved between orbits, not when they stayed in one orbit.

upper

lowere-

Absorption

Absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom.

The electromagnetic energy is transformed to other forms of energy for example, to heat.

Electromagnetic Radiation Absorption

Emission

Emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon, resulting in the production of light.

When the electrons in the atom are excited, for example by being heated, the additional energy pushes the electrons to higher energy orbitals. When the electrons fall back down and leave the excited state, energy is re-emitted in the form of a photon.

Electrons Produce Light!!

• Electrons (e-) move within atoms– (e-) movement is caused by

energy– (e-) move in different orbits

Photons

• A particle form of light or electromagnetic radiation

A photon walks into a hotel and checks in. "Do you want a hand with your luggage?" asks the receptionist. "No thanks", replies the photon, " I’m travelling light".

Excited state

1. Electrons jump to a higher orbit

2. Caused by atoms absorbing energy

Ground state

• Electron falls back to lower level (ground state)

• Energy is released as electromagnetic radiation (E.R) (photon)

Transition of n 3→2 4→2 5→2 6→2 7-2

Wavelength (nm) 650 500 450 425 400

color red blue green violet UV

Quantum or jump

• when an e_ jumps orbits it transports to the next orbit!!!

<>

A photon can be released as any electromagnetic energy

Spectral lines summed up

1. e- are in fixed orbits

2. e- can get excited, and jump to a higher orbit, if they absorb the appropriate energy

3. e- will fall back to lower level (ground state) and release a photon of similar energy (visible light)

5 points of the Bohrs Model

– 1. elements produce spectral lines also known as energy levels

2. Energy levels are represented by letters

– 3. Energy levels get larger the farther away they are from the nucleus

–4. larger the energy level more electrons they can hold

–5 Each energy level can only hold so many electrons


• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h


• One does not observe a continuous spectrum, as one gets from a white light source.

• Only a line spectrum of discrete wavelengths is observed.


• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:1. Electrons in an atom can only

occupy certain orbits (corresponding to certain energies).


• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:2. Electrons in permitted orbits

have specific, “allowed” energies; these energies will not be radiated from the atom.


• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:3. Energy is only absorbed or

emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

Line Spectra of Hydrogen• Balmer, Rydberg, and Ritz deduced an empirical

formula that predicted the observed wavelengths of lines in the hydrogen emission spectrum:

– RH = Rydberg constant = 1.0973732 107 m–1

– n, k are integers– k > n (always)– Understanding this equation theoretically was a hot topic in

the early 20th Century

22

111

knRH

The Nature of EnergyThe energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = −RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.

electromagnetic radiation all electromagnetic radiation travels at the same velocity: the speed of...

Documents