Quantum Qualities 1 frequency, wavelength and momentum of photons and electrons.

Quantum Qualities

1

Quantum Qualitiesfrequency, wavelength and

momentum of photons and electrons

Quantum Qualities

2

In 1833, Michael Faraday observed evidence of electrons when he observed a gas discharge glow in an evacuated container. The container was a sealed glass tube with two electrodes.

In 1858, Julius Plucker proved the glow was charged. The glow cast a shadow and responded to a magnetic field. Casting a shadow meant the glow was comprised of rays, and responding to a magnet meant the glow was charged.

In 1876, Eugen Goldstein named the glow “cathode rays”.

Quick Trip Way Down Memory Lane

Quantum Qualities

3

In 1896, Jean-Baptist Perrin captured cathode rays and measured their charge, proving that the rays carry charge.

In 1885, Johann Balmer, a Swiss schoolteacher developed an equation that describes the photographs of emission light spectra of the elements (rainbow light patterns with dark spaces among the colors).

In 1883, Thomas Alva Edison observed that a sealed light bulb deposited carbon inside the bulb and modestly called it the Edison Effect.


In 1890’s, Max Planck used spectroscopic data to create a blackbody radiation law.

Quantum Qualities

4

In 1897, J. J. Thompson proved that:

• cathode rays were particles.

• the charged particles emitted by a heated cathode were the same as cathode rays.

• cathode rays acted as charged particles in both electric and magnetic fields.

• Later he measured the charge to mass ratio of the charged particles, later determined to be electrons.

Hear J. J. Thompson describe the relative size of an electron.

From the soundtrack of the film, Atomic Physics Copyright J. Arthur Rank Organization, Ltd., 1948,


Quantum Qualities

5

It was harder back then to get Edison’s bulbs to glow and certainly harder to keep them from burning out.

But, it was still possible to direct a light beam to a prism and then see the diffracted light on a screen on the other side of the grating.

The 19th Century Version of a Diffraction Experiment

Quantum Qualities

6

It was harder back then to get Edison’s bulbs (discharge tubes) to glow and certainly harder to keep them from burning out.

But, it was still possible to direct a light beam (from a discharge tube) to a prism (grating), and then see the diffracted light on a screen on the other side of the grating.

Filter

Current

On

OffVoltage

-1000 0 +1000

Voltage Generator

Discharge Tube

DiffractionGrating Screen

1

3

Today’s Version of a 19th Century Diffraction Experiment

Quantum Qualities

7

Johann Balmer found a mathematical series that predicts the wavelengths of the spectra lines when hydrogen is the gas in the glowing bulb.

657

n

m

486

n

m

434

n

m

410

n

m

375

n

m

2

2 4

k

364.56 nmk

He put different integers in the “k” position of the equation and then noticed that his answers matched the wavelengths of the spectra lines.

Unfortunately, Balmer did not have any idea why the equation worked or why there were colored lines in the first place.

Developing a Model: Matching Observations to Theory

Quantum Qualities

8

Any object that absorbs all the light that strikes it is called a blackbody.

Light Source

Max Planck performed his “blackbody radiation” experiment to figure out why the spectra lines occurred.

Blackbody Radiation

Quantum Qualities

9

A blackbody will emit (radiate) light as it heats up

Max Planck used this spectroscopic data to create a blackbody radiation law.

Screen

1

3

Blackbody Radiation

Quantum Qualities

10

Screen

1

3

• Planck believed that the separation of light into discrete lines meant that light energy was quantified as discrete energy levels. • If an unbroken spectrum had been observed, it would have meant a continuous energy distribution.

• Planck started with Balmer’s result and “quantized” the photon emissions from various blackbody radiators.

Blackbody Radiation

Quantum Qualities

11

Plank’s experiments produced a description of energy emitted from the blackbody as a function discrete frequency values. Frequency can be calculated from the wavelength,

f = c/ = (speed of light wave)/(wavelength of light)Planck’s Radiation Hypothesis states that:

Blackbody Radiation

The emitted or absorbed energy was quantized with the smallest possible value being when n =1 and that:

All other permitted values of the energy are integral multiples of h f.

E

n

=

n x h x f

Quantum Qualities

12

n = an integer

Remember that:

f = frequency of light associated with the heat energy

h = 6.63 x 10-34

Joule·seconds

En= is the dependent variable assigned to theenergy absorbed or emitted

hf is h multiplied by frequency and has units of energy (Joules).

Blackbody Radiation

E

n

=

n x h x f

Quantum Qualities

13

Quick Trip a Shorter Distance Down Memory Lane

In 1905, Albert Einstein extended Planck’s concept to light and used it to explain the photoelectric effect.

In 1913, Niels Bohr proposed a model for the hydrogen

In 1911, Robert Millikan measured the charge of an electron.

atom that combined ideas about the nucleus and electrons that explained the spectra colors and the Balmer mathematical series as well.

Quantum Qualities

14

Eescape

=

is the energy an electron has when it leaves the surface of a metal.

E escape

(Shine a light on a metal and electrons will escape from the metal surface.)

hf

hf is the energy of the light shining on the metal

hfw-

is the energy used to move the electron away from the metal atom. (The work done to free the electron from the metal surface.)

hfw

Einstein said that when hf is greater than hfw an electron will leave the metal surface.

Einstein and the Photoelectric Effect (1905)

Light Source

Photons

Photoelectric Effect

Quantum Qualities

15

Current

On

Off

-1000 0 +1000

Voltage Generator

Electrode

Voltage

He selected the gravitational field and the electric field.

Gravity will pull oil drop down.

Electric field can pull oil drop up.

(Put a charged oil drop in two force fields and balance the forces so the oil drop does not move.)

Fg is the gravity force pulling the charged oil drop down.

Fe = -qE

Remember that:

Fg = mg

Fe is the electric force pulling the charged oil drop up. m is the mass of the the charged oil drop up. q is the amount of charge on the oil drop up. g and E are the gravity and electric field strengths, respectively.

Millikan Oil Drop Experiment (1911)

Quantum Qualities

16

Current

-1000 0 +1000

Voltage Generator

Voltage

An oil drop with a surface charge

• Electric field between electrodes can be adjusted to suspend the drop.• The mass of the oil drop is known.

•The oil drop floats because the force on the drop in the electric field exactly counteracted the force on the drop in the gravity field.

On

Off

Electrodes

m gq E

electron 1.602x1

0

-19Coulombs

(Put a charged oil drop in two force fields and balance the forces so the oil drop does not move.)

Millikan Oil Drop Experiment (1911)

Quantum Qualities

17

initial finalΔE = E - E = h × f

h = Planck’s constant

f = frequency of the photon

Bohr Hydrogen Atom Model (1913)

• Electrons reside in orbits and can absorb specific quantities of energy to move to another orbit.

• If an electron returns to its original orbit, the specific amount of absorbed energy could be returned to the world as a photon of light.

• The wavelength and frequency of that light could be calculated using the equation Balmer developed in 1885.

• The energy of that light could be calculated using the equation Planck developed in 1900.

PhotonE = h x f

Quantum Qualities

18

• Photons, packets of light with energy = hf, are an example of mass less particles.

• The particle wave duality of light can be shown by combining Planck’s Law and Einstein’s hypothesis.

• Planck stated that an atom can only emit and absorb energy of specific values.

initial finalE = E - E = h f • Einstein stated that the frequency times the wavelength of a photon is equal to the speed of light. f = c

Putting the two equations together yields .c

E = h

Particle Wave Duality

Quantum Qualities

19

The particle-wave nature of photons can be described using the work of Planck and Einstein.

photon

h cE = h f = = p c

This equation models the energy of a photon that is released when an electron returns from an outer orbit to its original orbit (closer to the nucleus).

Particle Wave Duality

It can be used to relate the energy of a photon to that photon’s:

•Frequency: Ephoton = h x f

•Wavelength: Ephoton = (h x c)/

•Momentum: Ephoton = p x c

Quantum Qualities

20

Your Great Grandfather’s Time

By 1920, engineers and scientists understood that:• photons existed• if photons ever stopped moving, they would have no

mass (a photon’s rest mass equals zero).

Since photons do move:

• their mass is related to the energy needed for movement as defined by Einstein’s famous equation!

•their mass is “relativistic” mass, m using E = mc2

•they have momentum, p , like all moving objects with mass using Pr = mrc

Quick Trip not so Long Ago

Quantum Qualities

21



In 1923, Louis De Broglie understood the properties of photons:

• Some photons can be seen by humans because they have a wave frequency (color) that is detected by human eyes and/or human instruments.

PhotonE = n(h)(v)

• all photons move and have a relative mass connected to the energy, Ephoton, they possess.

r r=p (m )c

• all photons obey Planck’s quantum energy equation:

• They, like all moving objects with mass, have momentum, pr

Quantum Qualities

22

He also believed that:

• all things including photons have wave properties.

• unlike photons, most things have a rest mass.

Thus, a baseball’s mass is not zero when it is not being thrown but it does have a wave frequency and a wavelength associated with it when it is in motion.

Momentum and frequency values with corresponding wavelengths.

(m )object

(v )object velocity

hPlanck’s constant any object =




Quantum Qualities

23

• since the mass of a baseball (0.15 kg) is so large, the wavelength associated with a moving baseball is too short for humans to detect.

• since the mass of an electron (9.11 x10-31 kg) is so small, the wavelength associated with a moving electron is long enough for human instruments to detect.



He also believed that:


(m )object

(v )object velocity

hPlanck’s constant any object =

Quantum Qualities

24

In 1926, Erwin Schrodinger:

• wondered why De Broglie’s relationship only quantitatively worked when the moving particles where in a force-free environment.

• developed a general equation that:• described electrons moving with a wave motion

because they were under the influence of a force environment generated by the positive charge of the nucleus.

• gives the same momentum and frequency (wavelength) values that would be obtained by De Broglie if the electron was moving without the influence of the atom’s nucleus. Schrodinger’s equation is simply called the “wave

equation”. Unfortunately, it only works really well for the hydrogen atom.

Your Great Grandfather’s TimeQuick Trip not so Long Ago

Quantum Qualities

25

When De Broglie’s ideas were first applied to electron behavior, the topic was called quantum mechanics.

When Schrodinger’s ideas were applied to electron behavior, the topic was called wave mechanics.

The Mechanics of Electron/Atom Behavior

Quantum Qualities

26

The Mechanics of Electron/Atom Behavior

• the difficulties with quantum mechanics and/or wave mechanics is that there is no way to know both the position and speed of an electron at the same time.

In 1927, Werner Heisenberg suggested that:

• a probability perspective turns out to be a better way to describe electron behavior within an atom.

Heisenberg’s approach is known today as both:

statistical quantum mechanics and/or

statistical wave mechanics.

Quantum Qualities

27

Quantum Qualities

The major step forward in the understanding of light, electrons and atoms was the steady development of the ideas that:

• energy comes into and goes out of atoms but it does so in packets or quanta.

• each packet of energy can be associated with a frequency (wavelength).

• each packet of energy can interact with an electron within an atom.

• an electron will change orbits or even leave the atom if it interacts with the right packet of energy.

• energy packets, quanta, differ from each other by multiple integer values of Planck’s constant.

Quantum Qualities

28

Equation Summary of our Historical Trip

In 1885, Johann Balmer: 2

24

k364.56 nm

kAn equation that described the photographs of light spectra (rainbow light patterns with dark spaces among the colors).

In 1900, Max Planck: photonE = h f The quantum equation that describes the

relationship between the energy of a wave and the frequency of that wave.

In 1905, Albert Einstein: E escape

= hf hfw

-An equation that connects light energy to electrons leaving an atom.

Quantum Qualities

29

In 1911, Robet Millikan:

In 1913, Niels Bohr:

initial finalE = E - E = h fAn equation that explained the electron orbit quantum nature of hydrogen atom as seen from the hydrogen absorption spectrum and predicted the wavelength of the lines in that spectrum.

An equation that related the charge of an electron to BOTH its mass and the electric field its suspended in.

-mgqelectron

= E

An equation that connects the wavelength of a moving object to its mass and velocity.

(m )object (v )velocity

h object

In 1923, Louis De Broglie:

Equation Summary of our Historical Trip

Quantum Qualities

30

2.) For a photon with a wavelength of 700 nm, calculate the

Two Example Problems

a) frequency, b) the energy, and c) the momentum of the photon.

1.) Calculate the wavelength and the frequency of one photonof light that has an energy of 3.64 x 10-19

Joules.

Objectives: 1. to show the use of quantum equations 2. to illustrate unit manipulations

Quantum Qualities

31

Knowns:

Energy = J-193.64 10Planck’s constant = h =

-346.63 10 J ·s

Speed of light = c =

8 m3.0 10

s

Unknowns: Wavelength = = nmFrequency = f = s -

1

Equations:photon

h cE = h f = = p c

1.) Calculate the wavelength and the frequency of one photonof light that has an energy of 3.64 x 10-19 Joules.

Quantum Qualities

32

Unknowns: Wavelength = = nmFrequency = f = s -

1

Equations:photon

h cE = h f = = p c

1.) Calculate the wavelength and the frequency of one photon

photon

h c=

E

photonEf =

h

photon

h cE = photonE = h f

of light that has an energy of 3.64 x 10-19 Joules.

Quantum Qualities

33

Solution:

-34 8

-19

6.63 10 J s 3.0 10 m/s=

3.64 10 J

Wavelength Value Calculation for Example #1Knowns:

Energy = J-193.64 10Planck’s constant = h =

-346.63 10 J ·s


8 m3.0 10

s

Equations: photonEf=

hphoton

h c=

E

-7 = 5.464 10 m The wavelength of light that has 3.64 x 10-19 J of energy is

Quantum Qualities

34

Solution:

-7 = 5.464 10 m

Units: Wavelength is typically reported in units of nanometers.

91 m = 1 10 nm

-7 9 nm = (5.464 10 m) (1 10 ) = 546.4 nm

m

Answer:

-19A photon with an energy of 3.64 10

J wavelengtoules has h of 54 a 6 nm

Wavelength Unit Conversion for Example #1

9 1 10 nm1 m

Remember:

or

546 nm

Quantum Qualities

35


h

Solution:

-19

-34

3.64 10 Jf=

6.63 10 J s

Frequency Calculation for Example #1

Knowns:

Energy = J-193.64 10

Planck’s constant = h =

-346.63 10 J ·s


8 m3.0 10

s

photon

h c=

E

14 1f = 5.49 10

s

The frequency of light that has 3.64 x 10-19 J of energy is

Quantum Qualities

36

Solution:

14 1f = 5.49 10

s

Units: Frequency is typically given in units of Hertz. 1

Hertz = Hz = second

14 141f = 5.49 10 = 5.49 10 Hz

s

Answer:

-19

14

A photon with an energy of 3.64 10

J frequency of 5.49 oul 10es has a Hz.

Frequency Unit Conversion for Example #1

Quantum Qualities

37

Summary for Problem #1 1.) Calculate the wavelength and the frequency of one

photon -193.64 10of light that has an energy of Joules.

Answer:

14and a frequency of 5.49 10 Hz.


Joules has a wavelength of 546 nm

Is this wavelength of light in the visible part of the spectrum?If so, what color is it?

?Yes, a 546 nm light wave is in the visible spectrum and will be green.

Quantum Qualities

38

Known: Wavelength = = 700 nm-34Planck's constant = h = 6.63 10 J s

8 mSpeed of light = c = 3.0 10

s

Unknown:Frequency = f in s

–1

Energy = Ephoton in J

2.) For a photon with a wavelength of 700 nm calculate theenergy, frequency, and the momentum.

Momentum = p in kg-m/s

Equations:

photon

h cE = h f = = p c

Quantum Qualities

39

Equations:photon

h cE = h f = = p c

photonEf =

h

h p =

photon

h cE = photonE = h f

h cp

c

h c

= p c

2.) For a photon with a wavelength of 700 nm calculate the

Unknown:

Frequency = f in s –

1



energy, frequency, and the momentum.

Quantum Qualities

40

Units:

-9 -91 10 m

700 nm = 700 nm = 700 10 m1 nm

Wavelength Unit ConversionKnown: Wavelength = = 700 nm

Wavelength = = 700 nmWavelength is usually reported in nm and the speed of light is given in m/s.

(For this problem the wavelength will be converted to meters from nanometers so the velocity can be used in meters/second.)

Unknown:

Frequency = f in s

–1




s

Quantum Qualities

41

photon

h cE =

Energy Calculation

Known: Wavelength = = 700 nm

-34Planck's constant = h = 6.63 10 J s


s

Unknown: Energy = Ephoton in Joules


h

h p =

photon

h cE =

Quantum Qualities

42

photon

h cE =

Solution:

-34 8

photon -7

m6.63 10 J s 3.0 10

sE = 7 10 m

-19photonE = 2.8 10 Joules

Energy Calculation

Equations:

Known: Wavelength = = 700 nm



s

Quantum Qualities

43

Units: Energy is typically reported in units of Joules.

Answer:

-19

A photon with a wavelength of 700 nm

has an energy of 3 10 Joules.

Energy Calculation

Is this wavelength of light in the visible part of the spectrum?If so, what color is it?

?Yes, a 700 nm light wave is in the visible spectrum and will be red.

Quantum Qualities

44

Frequency Calculation



s


h

Unknown: Frequency = f in s –

1

Energy =Ephoton in J


photon

h cE =

h

p =

Quantum Qualities

45

Equations: cf =

Solution:

8

-7

m3.0 10

sf = 7 10 m

14 1f = 4.3 10

s




s

h p =

Quantum Qualities

46

Solution:

14 1f = 4.3 10

s

Units: Frequency is typically reported in units of Hertz. 1

Hertz = Hz = second

14 141f = 4.3 10 = 4.3 10 Hz

s

Answer:

14

A photon with a wavelength of 700 nm

has a frequency of 4 10 Hz.


Quantum Qualities

47

Equations:

Momentum Calculation



s

Unknown:

Frequency = f in s –

1

Energy =Ephoton in J


photonEf=

hphoton

h cE =

h

p =

Quantum Qualities

48

Equations:

h p =

Solution:

-34

-7

6.63 10 J sp =

7 10 m

-28 J sp = 9.5 10

m

Momentum Calculation

note: 1 Joule

of energy

(1 kg)

(1 m)

(1 second)

2

2 kg s

2 m

2= 1

This momentum unit is also the same as the units of energy divided by velocity.

=

Quantum Qualities

49

Units:

2

2

kg m s 1 =

s m

-28 -28J s kg m9.5 10 = 9.5 10

m s

Answer: -27

A photon with an wavelength of 700 nm

has a momentum of 1 10 kg m/s.

Momentum CalculationThere are several popular choices for momentum units, but the usual units are (mass)(velocity).

For metric calculations these units would be kg m/s.

12

2

J s kg m s = 1

m s m

kg m1

s

Quantum Qualities

50

Summary for Example Problems 1 and 21.) Calculate the wavelength and the frequency of one photon -193.64 10of light that has an energy of Joules.

Answer:

14and a frequency of 5.49 10 Hz.


Joules has a wavelength of 546 nm

2.) For a photon with a wavelength of 700 nm calculate theenergy, frequency, energy and the

momentum.

Answer:

-27a momentum of 1 10 kg m/s.

14a frequency of 4 10 Hz, and

A photon with a wavelength of 700 nm has -19an energy of 3 10 Joules, and

Quantum Qualities

51

De Broglie’s equation connects the wavelength of a moving object to the mass and velocity of that moving object.

(m )

object(v )

velocity

h object =

3a.) What is the wavelength value associated with a 0.15 kg baseballmoving with a velocity of 30 meters/second?

Two De Broglie Wave Equation Examples

3b.) What is the wavelength associated with a 9.11 x10 kg electron

-31

moving with a velocity of 1.47 x 10 meters/second?

7

Objectives: 1. to show the use of quantum equations 2. to illustrate unit manipulations

Quantum Qualities

52

Wavelength CalculationKnowns

:


Unknowns:

bWavelength of baseball = in nm

Equations:

1 mSpeed of baseball = v = 3.0 10

s

7 mSpeed of electron = v = 1.4 10

s

-1Mass of baseball = m = 1.5 10 kg

-31Mass of electron = m = 9.11 10 kg

eWavelength of electron = in nm

object velocity

h = (m )(v )

Quantum Qualities

53

Wavelength CalculationKnowns:

-34h = 6.63 10 J s

Equations:

ball1 m

v = 3.0 10 s

electron7 m

v = 1.4 10 s

ball-1m = 1.5 10 kg electron

-31 m = 9.11 10 kg

bball ball

h = (m )(v )

electron e e

h =

(m )(v )

34

1 1) )b

6.64 x 10 Jsmeters

(1.5 x 10 kg (3.0 x 10 m/s

34

31 7) )e

6.64 x 10 Jsmeters

(9.11 x 10 kg (1.4 x 10 m/s

Quantum Qualities

54

Wavelength Calculation

Equations:

b -341.5 x 10 meters

e -34

-31 7

6.64 x 10 Js

(9.11 x 10 kg) (1.4 x 10 m/s)

e -34

-24

6.64 x 10 Js

(12.8 x 10 kg m/s)

b -34

-1 1

6.64 x 10 Js

(1.5 x 10 kg) (3.0 x 10 m/s)

e -10

6.64 x 10 meters

12.8

Quantum Qualities

55

Wavelength Calculation

b -34baseball wavelength = 1.5 x 10 meters

eelectron wavelength = = -115.19 x 10 meters

3a Answer:

A baseball does travel on a wave path like water but going 30 meters per second the ball goes through one complete wave after it has gone 1.5 x10-34 meters.

3b Answer:

An electron does travel on a wave path like water but going 1.4 x 107 meters per second the electron goes through one complete wave after it has gone 5.19 x10-11 meters.

Quantum Qualities

56

Quantum Qualities 1 frequency, wavelength and momentum of photons and electrons.

Documents

Transcript of Quantum Qualities 1 frequency, wavelength and momentum of photons and electrons.