early quantum theory ap physics chapter 27. early quantum theory 27.1 discovery and properties of...

Early Quantum Theory

AP Physics

Chapter 27


27.1 Discovery and Properties of the Electron


Glass tube filled with

a small amount of

gas

When a large voltage

was applied

A dark shape

seemed to

extend from

the cathode27.1


Name Cathode Rays

Deflected by electric or magnetic fields

Negative charge

JJ Thompson – discovered the electron

Believed that the electron was

a part of the atom

Robert Millikan – determined

the charge on an electron

27.1

Experiment Video

http://cwx.prenhall.com/petrucci/medialib/media_portfolio/text_images/004_MILLIKANOIL.MOV


27.2 Planck’s Quantum Hypothesis


Blackbody Radiation – all objects emit radiation proportional to T4 (in Kelvin)

Normal Temp – low intensity

Above 300K – we can sense

the IR as heat

At about 1000K objects glow

Above 2000K glow yellow

-white

27.2


As temperature increases

EMR emitted increases

increases toward higher frequencies

27.2


Blackbody – absorbs all the radiation that falls on it

Blackbody radiation – the EMR that a blackbody emits when hot and lumnous

Max Plank (1900) – purposed

his Quantum Hypothesis

Energy of any molecular vibration

could only be a whole number

multiple of a minimum value

27.2hfE


h is called Planck’s constant

Since energy has to be a whole number multiple

n – is a quantum number

It is quantized – occurs in only discrete quantities

27.2

hfE

sJxh 3410626.6

nhfE


27.3 Photon Theory of Light and the Photoelectric Effect

27.3 Photon Theory of Light

Einstein (1905) – when an object

emits light its energy must be

decreased by hf, so light is

emitted in quanta where

Where f is the frequency of

the quanta emitted

Light is transmitted as tiny

particles called photons

hfE

27.3


When light shines on metals – electrons are emitted from the surface

Called the photoelectric effect

Both photon theory and wave

theory are consistent with

this basic result

27.3


Wave theory predicts (for monochromatic light)

1. Increased light intensity should

a. Increase the number of electrons ejected

b. The maximum kinetic energy of the should be higher

2. Frequency of light should not affect kinetic energy, only the intensity

27.3


Photon theory predicts (for monochromatic light)

All photons of the same frequency would have the same energy

All the energy of a photon would be transferred to an electron

Since electrons are held in the metal by some force, a minimum energy must be reached before an electron can be emitted

27.3

hfE



This minimum energy is called the work function (W0)

Electrons that absorb less than W0 will not be ejected

Those that are ejected the energy will be

For the least tightly held electrons

27.3

WKEhf

0max WKEhf



1. Increase in intensity will result in

a. More electrons being ejected

b. The same maximum kinetic energy for all the electrons

2. If frequency is increased, the maximum kinetic energy increase linearly

27.3

0max WhfKE



3. Below a cutoff frequency no electrons will be ejected

Experiments have proven that emitted electrons follow the photon theory

27.3

0Whf


27.4 Energy, Mass, and Momentum of a Photon

27.4 Mass, Energy, and Momentum of a Photon

The momentum of a particle at rest is given by

(from relativity chapter)

Since a photon travels a c, either it has infinite momentum, or its rest mass is 0 (makes sense, the photon is never at rest)

The energy of a photon is

27.4

2

2

10

cv

vmp

hfEKE

27.4 Mass, Energy, and Momentum of a Photon

The momentum of a photon is developed from the relativistic formula

Since m0=0

Usually written

27.4

420

222 cmcpE

222 cpE pcE

h

c

hfp


27.6 Photon Interactions; Pair Production

27.6 Photon Interaction, Pair Production

Four interactions that photons undergo atoms

1. Photoelectric effect

2. Move an electron to

an excited state

3. Photon can be scattered

resulting in lower frequency

(energy) photon – called

the Compton Effect

27.6


Four interactions that photons undergo atoms

4. Pair production – a photon creates matter

The photon disappears and produces a electron-positron pair

Example of mass being

produced in accord with

The positron will quickly

collide with an electron

27.6

2mcE


Pair production must occur near a nucleus so that momentum can be conserved

Used in PET scanners (positron emission tomography)

27.6


27.7 Wave-Particle Duality

27.7 Wave-Particle Duality

Light properties can sometimes only be explained using particle theory (photons)

Sometimes the properties can only be explained using wave theory.

This realization that light has both properties is called wave-particle duality

The principle of complementarity – to fully understand light, we must be aware of both its particle and its wave natures

27.7


27.8 Wave Nature of Light

27.8 Wave Nature of Matter

Louis de Broglie (1923) – proposed

all particles have wave

properties

The wavelength of a particle

is related to is momentum

This is called the de Broglie wavelength27.8

h

p p

h


The wavelength of a 0.20kg ball traveling at 15 m/s would be

This is ridiculously small

Interference and diffraction only occur if a slit is not much larger than the wavelength

So the wave properties of ordinary objects is not detectable

27.8

p

hmv

h mxsmkg

sJx 3434

102.2)/15)(20.0(

106.6


But atomic particles have small enough masses that their de Broglie wavelength is measureable

This is the

diffraction

pattern of an

electron

27.8


27.10 Early Models of the Atom


Plum Pudding Model (1890)

JJ Thomson – homogeneous sphere of positive charge embedded with negative electrons

27.10


Planetary Model (1911) Ernest Rutherford

Tiny positively charged nucleus contains most of the mass

Electrons orbit around the nucleus like planets around the sun

27.10


27.11 Atomic Spectra: key to the Structure of the Atom

27.11 Atomic Spectra

If a pure gas in a tube is

excited

It produces a discrete

spectrum

When looked at through a

spectrometer we can observe a emission spectrum unique to that element

If a continuous spectrum passes through a gas, dark lines, or an absorption spectrum, is visible

27.11


It is assumed that in low density gases, the spectrum is from individual atoms

Hydrogen is the simplest atom, and shows a regular pattern to its spectral lines

JJ Balmer – showed that four lines in the visible spectrum of hydrogen have wavelength that fit the formula

27.11

22

1

2

11

nR


R is called the Rydberg Constant

n = the integer values starting with 3

Later, the Lyman series was found to fit

Paschen series

27.11

22

1

2

11

nR

22

1

1

11

nR

22

1

3

11

nR


27.12 The Bohr Model

27.12 Bohr Model

Niels Bohr – electrons cannot lose

energy continuously, but in

quantum jumps

Light is emitted when an electron

jumps from a higher state to

a lower state

He compared a quantized angular momentum to the Balmer series

27.12

u lhf E E

27.12 Bohr Model

Although the results worked

n is an integer called the principle quantum number

It was simply chosen because it

worked

The lowest E1 – ground state

Higher levels – excited state27.12

L I 2( )( )vrL mr nL mvr2

hL n

27.12 Bohr Model

The minimum energy level required to remove an electron from the ground state is called the ionization energy

For hydrogen is it 13.6eV and precisely corresponds to the energy to go from E1 to E=0

Often shown in an Energy Level Diagram

Vertical arrows show transitions

Energy released or absorvedcan be calculated by the difference between energy at each level 27.12


27.13 de Broglie’s Hypothesis Applied to Atoms

27.13 de Broglie’s Hypothesis Applied to Atoms

Bohr could give no reason why electrons were quantized

Reason was purposed by de Broglie

A particle of mass moving with a nonrelativistic speed would have

a wavelength such that

If each electron orbit is treated as a standing wave we get

This is the quantum condition

purposed by Bohr27.13

h

mv

2n

hmvr n

early quantum theory ap physics chapter 27. early quantum theory 27.1 discovery and properties of...

Documents

photon theory of lighteinstein

quantum number

plancks quantum hypothesis27

plancks quantum hypothesish

quantum hypothesisenergy

plancks constantsince

maximum kinetic energy

frequency of light