Chapter 26 Quantum Physics

CAMBRIDGE A LEVELCAMBRIDGE A LEVEL

PHYSICS

QUANTUM PHYSICSQUANTUM PHYSICS

LEARNING OUTCOMESLEARNING OUTCOMES

NO. LEARNING OUTCOME

i R e l a t e t h e c o n c e p t o f p a r t i c u l a t e n a t u r e o f E M r a d i a t i o n . B ea b l e t o c a l c u l a t e t h e e n e r g y o f a p h o t o n .

ii U s e e v i d e n c e t o e x p l a i n t h e d u a l n a t u r e o f E M r a d i a t i o n .

iii U s e t h e p h o t o e l e c t r i c e f f e c t t o s u p p o r t t h e c l a i m t h a t E Mw a v e s e x h i b i t p a r t i c u l a t e n a t u r e .

iv U s e t h e f a c t t h a t e l e c t r o n s c a n b e d i f f r a c t e d t o e x p l a i n t h ew a v e b e h a v i o u r o f p a r t i c l e s . C a l c u l a t e t h e a p p r o p r i a t e d e

B r o g l i e w a v e l e n g t h .

v R e l a t e t h e e m i s s i o n a n d a b s o r p t i o n s p e c t r a t o t h e p r e s e n c eo f d i s c r e t e e n e r g y l e v e l s i n i s o l a t e d a t o m s . C a l c u l a t e t h e

a p p r o p r i a t e w a v e l e n g t h a n d f r e q u e n c y o f p h o t o n s a n d r e l a t e

i t w i t h t h e e n e r g y l e v e l d i a g r a m .

D UA L N AT U R E O F E M

R A D I AT I O N


R A D I AT I O N James Maxwell in 1864 proposed that James Maxwell in 1864 proposed that

EM radiation is made up of coupledelectric and magnetic oscillations thatmove at the speed of light and exhibitedwave behaviour.

Figure 2.1; Page 53, Chapter 2: Particle Properties of Waves; Concepts of Modern

Physics, by Beiser, Arthur; McGraw Hill Publications; New York, USA; 2003.

However, Maxwell had no physical

diffraction (wave properties).

However, Maxwell had no physicalevidence to support his claim.

Heinrich Hertz in 1988 byexperimentation, was able to produceEM radiation. In addition, Hertz was ableto show that the radiation he producedhad both electric and magneticcomponents, and these radiation couldundergo reflection, refraction anddiffraction (wave properties).


R A D I AT I O N


R A D I AT I O N

Thomas Young, using light, showed that Thomas Young, using light, showed thatEM radiation can undergo interferenceand diffraction, a property inherent towaves.


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R A D I AT I O N



The scientific community accepted that EM The scientific community accepted that EMradiation is made up of waves up till the endof the 19th century.

However, Maxwells theory failed whenradiation originating from matter was triedto be explained.

To analyse this radiation, it is assumed, withstrong justification that all objects beclassified as blackbodies.

A blackbody is an object that absorbs allradiation incident upon it.

Thus, the radiation emitted by objects isknown as blackbody radiation.


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A typical blackbody radiation spectrum is A typical blackbody radiation spectrum isshown below:


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R A D I AT I O N

Figure 2.6;

Page 58,

Chapter 2:

Particle

Properties of

Waves;

Concepts of

Modern

Physics, by

Beiser, Arthur;

McGraw Hill

Publications;

New York,

USA; 2003.

A radiation spectrum is a plot of spectral A radiation spectrum is a plot of spectralenergy density vs. frequency for aspecific material at differenttemperatures. The English duo of Rayleigh and Jeans at

the end of the 19th century proposed anequation for the shape of the radiationspectrum. However, the equation wasincorrect because it showed that thespectral energy density would approachinfinite values for high frequencies.


R A D I AT I O N


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In 1900, Max Planck (a German In 1900, Max Planck (a Germanphysicist), proposed a new formula torectify Rayleigh and Jeans formula athigher frequencies. However, any equation needs to be

justified by a physical explanation. Planck explained that the energy

changes inside a blackbody must havediscrete values, and not continuousvalues.


R A D I AT I O N


R A D I AT I O N

Planck explained that the energy

Planck explained that the energychanges, that occur inside a blackbodyare like that in a oscillator. where , , , , ; . . When radiation of frequency is

absorbed, the oscillator jumps to ahigher state. When radiation offrequency is emitted, the oscillatorjumps to a lower state.


R A D I AT I O N


R A D I AT I O N

Each discrete bundle of energy has energy,

Each discrete bundle of energy has energy, and is known as a quantum (Latin for how much).

We now accept that EM radiation exhibits a particulate nature; i.e. EM radiation can also be said to be made up of discrete bundles of energy called photons as well as a wave nature; i.e behaving like waves.

This is called the dual nature of EM radiation.


R A D I AT I O N


R A D I AT I O N

EXAMPLESEXAMPLES Calculate the energy of one photon of Calculate the energy of one photon of

red light if the wavelength is 680 nm. 2.93 x 10-19 J

How many photons of red light are found in red light with energy of 4.39 x 10-18 J ? 15

Is it possible to have 6.00 x 10-18 J of energy of red light? No. It is not a multiple of quantum.

EXAMPLESEXAMPLES

Questions; Page 328, Chapter 9: Photons, Electrons and Atoms; Section 9.1: The

Photoelectric Effect, International A/AS Level Physics, by Mee, Crundle, Arnold and

Brown, Hodder Education, United Kingdom, 2008.

EXAMPLESEXAMPLES

Questions 8,9 and 10; Set 45: Wave Particle Duality of Electromagnetic Radiation ; page 113;

PROBLEMS IN PHYSICS ; E.D GARDINER, B.L McKITTRICK; McGraw Hill Book Company, Sydney

1985.

EXAMPLESEXAMPLESQuestion 12; Set 45:

Wave Particle Duality of

Electromagnetic

Radiation ; page 113;

PROBLEMS IN PHYSICS ;

E.D GARDINER, B.L

McKITTRICK; McGraw

Hill Book Company,

Sydney 1985.

The photoelectric effect provides us The photoelectric effect provides us with further evidence of the particulate nature of EM radiation.

This effect occurs when metal is illuminated (by EM radiation). Under certain conditions, electrons can be ejected from the surface of the metal.

T H E P H OTO E L EC T R I C

E F F EC T


E F F EC T


E F F EC T


E F F EC T Electrons in metal are bound

to the positive ions in the

metal.

To eject electrons, there must

be enough energy supplied.

If the illuminating EM

radiation has photons that

have enough energy, then

electrons will be ejected. Else,

no electrons will be ejected.

Diagram 38.1, page 1261, Chapter 38: Photons: Light Waves behaving as Particles; Sears and Zemanskys

University Physics, Young and Freedman, 13th edition, Pearson Education, San Francisco, 2012.

Electrons are ejected if the amount of Electrons are ejected if the amount of energy contained in the photons (of EM radiation) is at least equal to the work function energy, of the metal.

Definition: The work function energy is the minimum energy required by the electron to escape from the surface of the metal.

The table on the next slide gives some values of work function energy.


E F F EC T


E F F EC T

The interaction between photons and electrons are one to one; i.e. one electron interacts with one photon.

If an electron absorbs the photon, it will absorb all the energy of the photon.


E F F EC T


E F F EC TTable 38.1, page 1264, Chapter 38:

Photons: Light Waves behaving as

Particles; Sears and Zemanskys

University Physics, Young and

Freedman, 13th edition, Pearson

Education, San Francisco, 2012.


E F F EC T


E F F EC T



The diagram on the previous slide shows The diagram on the previous slide shows how the photoelectric effect may be observed.

Two conducting electrodes are separated in an evacuated tube and connected to a battery, and the anode is illuminated.

Note that the ejected electrons would have to go against the direction of the electric force; hence they will lose kinetic energy.


E F F EC T


E F F EC T

Conclusions of the experiment:

,

Conclusions of the experiment:I. Electrons are ejected only if the

incident light had a minimum frequency, . This frequency is known as the threshold frequency,

II. The photoelectrons have a range of kinetic energies, from zero to ,,


E F F EC T


E F F EC T

III. If the frequency of the incident III. If the frequency of the incident radiation is increased, the value of , also increases.

IV. For constant frequency of incident radiation, the value of

, remains the same, even for increased intensity of radiation.


E F F EC T


E F F EC T

Aside on intensity:

,

Aside on intensity:

The intensity of EM radiation is proportional to , the number of photons being emitted. The more photons are emitted, the intensity of the radiation also increases. The less photons there are, the less intense will be the radiation.

Recall that !"#. This means that when the source of EM radiation is more intense, it contains more photons. No change occurs to the amount of energy in each photon.


E F F EC T


E F F EC T

Explanation:Explanation:

Electrons are ejected if the amount of energy contained in the photons (of EM radiation) is at least equal to the work function energy , of the metal (material from which anode is made).

The remainder of the absorbed energy (if there is) will be in the form of kinetic energy of the photoelectrons.


E F F EC T


E F F EC T

Some of the photoelectrons that are

$, %&'& ( )

Some of the photoelectrons that are ejected have sufficient kinetic energy ($,) to reach the cathode (overcoming the effect of the electric field).

The maximum kinetic energy of the ejected electrons, $, is the difference between the energy of the incident photon, %&'&and the work function energy, of the metal; i.e $, %&'& ( ).


E F F EC T


E F F EC T

If we were to plot the graph of $, vs.

If we were to plot the graph of $, vs. incident light frequency, , we would obtain a straight line.

The straight lines are unique to the type of metal used as seen in the next slide.

The horizontal axis intercept of each line corresponds to the threshold frequency, .


E F F EC T


E F F EC T

Note that no photoelectrons are ejected for

Note that no photoelectrons are ejected for frequencies lower than .

The lines for every metal are parallel to each other. This means that all lines will have the same slope. The slope gives the value of , Plancks constant.


E F F EC T


E F F EC T


E F F EC T


E F F EC T

Figure 2.12; Page 64, Chapter 2: Particle Properties of Waves; Concepts of Modern Physics, by

Beiser, Arthur; McGraw Hill Publications; New York, USA; 2003.

The electrons with , will reach the The electrons with , will reach the cathode and produce a photocurrent in the external circuit.

All the other photoelectrons will not reach the anode as they have kinetic energies less than $,.


E F F EC T


E F F EC T

If we are to increase the potential If we are to increase the potential difference between the electrodes, but keeping the frequency of the incident radiation constant, the amount of photocurrent will decrease.


E F F EC T


E F F EC T

We can actually reach a p.d. when the

$,

We can actually reach a p.d. when the photocurrent drops to zero. This p.d. is known as the stopping potential.

The stopping potential is the minimum potential difference between the electrodes necessary to stop electron flow.

The stopping potential helps us calculate the value of $,.


E F F EC T


E F F EC T

How? Notice that the work done on the How? Notice that the work done on the electrons is negative (it takes away kinetic energy from the electrons).

Some of the electrons have kinetic energy equal to $,. These are the fastest moving electrons.

We assume that these fastest electrons are stopped just before they reach the cathode.


E F F EC T


E F F EC T

Hence, $, *+ where + *

. ,

.

Hence, $, *+ where + stopping potential, V and * charge of an electron = . -,.

On simplification , we can also obtain

*.

*+ where * mass of an

electron = -. / and . speed of the fastest moving electron(s), .


E F F EC T


E F F EC T

One important thing to note is that the

One important thing to note is that the intensity of the incident light does not affect the value of $,.

If the incident light had a frequency lower than the threshold frequency, no photoelectrons will be detected.

This is because the electrons will only be ejected if they absorb photons with energy at least equal to the work function energy.


E F F EC T


E F F EC T


E F F EC T


E F F EC T The stopping potential remains

the same, regardless of

intensity for the same metal.

The value of 0,12 is

independent of incident

radiation intensity.

If the intensity of the incident

radiation is increased, the

amount of photocurrent

increases because more

photons hit the surface, and

more electrons can be ejected.




E F F EC T


E F F EC T The stopping potential, 34

depends on the frequency of

incident radiation, 5 for a

constant value of light

intensity.

This shows that the value of

0,12 depends on the

frequency of incident

radiation, 5.

The larger the value of 5, the

larger will be the value of the

stopping potential, 34.



Summary of the photoelectric experiment:Summary of the photoelectric experiment:


E F F EC T


E F F EC T

Page 1263, Chapter 38: Photons: Light Waves behaving as Particles, Section 38.1 : Light

Absorbed as Photons: The Photoelectric Effect; Sears and Zemanskys University Physics,

Young and Freedman, 13th edition, Pearson Education, San Francisco, 2012.


E F F EC T


E F F EC T

Page 1263, Chapter 38: Photons: Light Waves behaving as Particles, Section 38.1 : Light

Absorbed as Photons: The Photoelectric Effect; Sears and Zemanskys University Physics,

Young and Freedman, 13th edition, Pearson Education, San Francisco, 2012.


E F F EC T


E F F EC TFigure 38.4, Page 1264, Chapter 38:

Photons: Light Waves behaving as

Particles, Section 38.1 : Light

Absorbed as Photons: The

Photoelectric Effect; Sears and

Zemanskys University Physics,

Young and Freedman, 13th edition,

Pearson Education, San Francisco,

2012.

Let us go back to the graph of $, vs.

6,12

Let us go back to the graph of $, vs. incident light frequency, .

Plotting that relationship will give us a straight line of equation $, %&'& ( ).

On simplification, we may obtain

*.

( ).

Remember that the 6,12 the stopping potential, in eV or J.


E F F EC T


E F F EC T

This equation again tells us that the

( 7

This equation again tells us that the maximum kinetic energy of the photoelectrons is equal to the difference between the energy of the absorbed incident photon (EM radiation) and the work function energy.

Since, the value 0,12 can be zero, by setting the left side = 0, we will obtain ( 7.


E F F EC T


E F F EC T

This means that if EM radiation had

8

This means that if EM radiation had frequency equal to the threshold frequency, 8, the photoelectrons would have no kinetic energy.

We can then calculate 54 by using the

equation 7


E F F EC T


E F F EC T

EXAMPLESEXAMPLES

Examples; Page 243, Chapter 9: Photons, Electrons and Atoms; Section 9.1: The Photoelectric

Effect, International A/AS Level Physics, by Mee, Crundle, Arnold and Brown, Hodder

Education, United Kingdom, 2008.

EXAMPLESEXAMPLES

Questions 2 and 3; Page 244, Chapter 9: Photons, Electrons and Atoms; Section 9.1: The

Photoelectric Effect, International A/AS Level Physics, by Mee, Crundle, Arnold and Brown,

Hodder Education, United Kingdom, 2008.

EXAMPLESEXAMPLESQuestion 1; Set 45: Wave

Particle Duality of

Electromagnetic Radiation ; page

113; PROBLEMS IN PHYSICS ; E.D

GARDINER, B.L McKITTRICK;

McGraw Hill Book Company,

Sydney 1985.


Particle Duality of

Electromagnetic Radiation ;

page 113; PROBLEMS IN

PHYSICS ; E.D GARDINER, B.L

McKITTRICK; McGraw Hill

Book Company, Sydney 1985.

EXAMPLESEXAMPLESQuestions 4 and 5; Set

45: Wave Particle

Duality of

Electromagnetic

Radiation ; page 113;

PROBLEMS IN PHYSICS ;

E.D GARDINER, B.L

McKITTRICK; McGraw

Hill Book Company,

Sydney 1985.

Louis de Broglie, a French physicist in 1924, Louis de Broglie, a French physicist in 1924, asked this about nature. If EM waves can exhibit a dual nature, why cant objects (particles) behave likes waves?

As demonstrated in 1927 by electron diffraction (scattering) , this claim was indeed true.

The experiment that showed electrons can diffracted was done independently by Davisson and Germer (in USA) and G.P Thompson (In England).

WAV E N AT U R E O F

PA R T I C L E S


PA R T I C L E S


PA R T I C L E S


PA R T I C L E S

Diagram 39.2, page 1287, Section 39.1: Electron Waves, Chapter 39: Particles Behaving as Waves; Sears

and Zemanskys University Physics, Young and Freedman, 13th edition, Pearson Education, San Francisco,

2012.


PA R T I C L E S


PA R T I C L E S

Diagram 33.6(b), page 1288, Section 33.2: Reflection and Refraction, Chapter 33: The Nature and

Propagation of Light; Sears and Zemanskys University Physics, Young and Freedman, 13th

edition, Pearson Education, San Francisco, 2012.

The diagram on the previous slide shows the

set up for the Davisson and Germer

experiment.

The diagram on the left shows what the

initial results of the Davisson and Germer

experiment.

As expected, the electron beams underwent

diffuse reflection when it hit the surface of

the nickel crystal that behaved like a

polycrystalline material.

This scattering would have produced very

continuous readings of electron intensity at

any angle .


PA R T I C L E S


PA R T I C L E S

Diagram 39.3(a), page 1288, Section 39.1: Electron Waves, Chapter 39: Particles Behaving as Waves;

Sears and Zemanskys University Physics, Young and Freedman, 13th edition, Pearson Education, San

Francisco, 2012.

However, a certain error caused air to enter

the vacuum chamber. They had to heat the

nickel crystal sample. Heating, caused

rearrangement of the structure and now

the sample was like made up of single nickel

atoms.

On repetition, they did not obtain a

continuous distribution of intensity ( vs. ),

but obtained peaks and troughs; similar to

wave interference patterns. This is seen on

the diagram on the left.

This evidence was sufficient enough to

support de Broglies claim.


PA R T I C L E S


PA R T I C L E S

Diagram 39.3(b), page 1288, Section 39.1: Electron Waves, Chapter 39: Particles Behaving as

Waves; Sears and Zemanskys University Physics, Young and Freedman, 13th edition, Pearson


What had occurred?

The evenly separated atoms of nickel had

behaved similar to how slits respond when

EM radiation is incident on them.

The atoms cause the electron beams to

diffract and interfere.

Similar to waves, constructive interference

occurred if the phase difference was in even

integer multiples of , while destructive

interference occurred when the phase

difference was odd integer multiples of .

de Broglie also proposed a formula to help de Broglie also proposed a formula to help us calculate the wavelength, of a particle.

The de Broglie wavelength is given by

9

%

.where Plancks constant;

% momentum of the particle,inkgms>.


PA R T I C L E S


PA R T I C L E S

Notice the symmetry between de

? 5A.

Notice the symmetry between de Broglies equation and the wave equation (? 5A.

We can also calculate the frequency of a particle by using the equation


PA R T I C L E S


PA R T I C L E S

EXAMPLESEXAMPLES

Example 3.1; Page 94, Chapter 3: Wave Properties of Particles; Concepts of Modern Physics,

by Beiser, Arthur; McGraw Hill Publications; New York, USA; 2003.

Example 39.1, page 1289, Section 39.1: Electron Waves, Chapter 39: Particles Behaving as

Waves; Sears and Zemanskys University Physics, Young and Freedman, 13th edition, Pearson


EXAMPLESEXAMPLES

Examples; Page 245, Chapter 9: Photons, Electrons and Atoms; Section 9.2: Wave - particle

Duality, International A/AS Level Physics, by Mee, Crundle, Arnold and Brown, Hodder


EXAMPLESEXAMPLES

Questions; Section 9.2; Page 245, Chapter 9: Photons, Electrons and Atoms; Section 9.2: Wave -

particle Duality, International A/AS Level Physics, by Mee, Crundle, Arnold and Brown, Hodder


EXAMPLESQuestion 4;

Section 9.3:

Emission Spectra;

Page 253,

Chapter 9:

Photons,

Electrons and

Atoms;

International

A/AS Level

Physics, by Mee,

Crundle, Arnold

and Brown,

Hodder

Education,

United Kingdom,

2008.

M O D E R N ATO M I C M O D E L

The diagram on the left shows the change

in colour of the flame of a Bunsen burner

when a sample of sodium is placed in the

flame.

You are probably familiar with change in

Chemistry class.

The colour of the flame turns yellow

orange. The colour of the flames

correspond to wavelengths of 589.0 and

589.6 nm.

This also occurs to other metals when you

perform the flame test

Why does this occur?

Figure 39.19(b), page 1299, Section 39.3: Energy Levels and the Bohr Model of the Atom,

Chapter 39: Particles Behaving as Waves; Sears and Zemanskys University Physics, Young and

Freedman, 13th edition, Pearson Education, San Francisco, 2012.

Neils Bohr, in 1913, proposed a Neils Bohr, in 1913, proposed a model of the atom that changed the way physicists look at the atom.

He proposed that:

Atoms can only exist with certain specific levels of internal energy;

Each atom has a set of possible internal energies;


An atom can have an amount of An atom can have an amount of internal energy equal to any one of these levels, but cannot have an internal energy amount intermediate to these energy levels;All isolated atoms of the same

element have the same set of energy levels;Atoms of different elements have

different sets of energy levels.



Figure 9.9; Page 247, Chapter 9: Photons, Electrons and Atoms; Section 9.3: Emission Spectra,

International A/AS Level Physics, by Mee, Crundle, Arnold and Brown, Hodder Education,

United Kingdom, 2008.


The image on the previous slide shows the energy levels

present in an isolated atom of hydrogen.

Each of the horizontal lines represent a single internal energy

level.

The numbers on the left and right are the internal energies for

each level in Joules and eV respectively.

The lowest energy level is the ground state (B 0).

The ionisation energy level (B ) has internal energy = 0.

The isolated hydrogen atom (and its electrons) are only

allowed to have these specific energy levels.

According to Bohr, under normal

E%&'&

According to Bohr, under normal conditions, atoms are at their ground state.

Atoms can move up to a higher energy level by absorbing energy that is exactly equal to the difference between the new energy level, #FG and ground state, HIJ#K; i.e. *L /M&NO E%&'&


Excitation can occur either via heating,

internal energy.

Excitation can occur either via heating, electrical excitation (electron bombardement), or photon bombardment.

The excitation can bring the atom up to anywhere in , , , ., but not in between.

When the atom is excited, it becomes unstable, and thus has to lose the extra internal energy.


It loses the extra internal energy by

the old

It loses the extra internal energy by emitting a photon that has energy equal to the difference between the old energy level and the new energy level; i.e. *L &PO ( %&'&.

Note that absorption can only occur from ground level up, while emission can occur anywhere from a higher level to a lower one.


During emission, there will be at least During emission, there will be at least one photon emitted. The number of photons emitted depend on the path taken by the atom as it returns to the ground state.


Is there evidence for the emission? Is there evidence for the emission?


The image on the left

shows the line emission

spectra of several

elements.

These spectra are

produced by isolated

atoms of each element.

Each vertical line

corresponds to a particular

photon that was emitted.

Source:

http://www.mso.anu.edu.au/galah/images/emission_spec.png

Is there evidence for the emission? Is there evidence for the emission?


Figure 39.8, page 1293, Section 39.2: The Nuclear Atom and Atomic Spectra, Chapter 39:

Particles Behaving as Waves; Sears and Zemanskys University Physics, Young and Freedman,

13th edition, Pearson Education, San Francisco, 2012.


The image on the left

shows the line

emission spectrum of

hydrogen in the

visible spectrum.

Each emission line

has an associated

wavelength (of

photon).Source: http://intro.chem.okstate.edu/1314f00/Lecture/Chapter

7/Hemission1.GIF


Diagram 39.7, page 1292, Section 39.2: The Nuclear Atom and Atomic Spectra, Chapter 39:

Particles Behaving as Waves; Sears and Zemanskys University Physics, Young and Freedman,

13th edition, Pearson Education, San Francisco, 2012.

How do we obtain a line emission

The diagram on the previous slide shows

How do we obtain a line emission spectrum?

The diagram on the previous slide shows a method of obtaining a line emission spectrum for any element.

A sample of gas is heated. Heating excites the ground state electron, moving it to an excited state.


When the atom returns to its ground When the atom returns to its ground state, it may emit one or more photons, depending on the path take.

Note that the discrete lines present indicate the photons that have been emitted.


Is there evidence for the absorption? Is there evidence for the absorption?


The image above shows the line absorption spectrum of

atomic hydrogen.

Each vertical black line corresponds to a particular photon that

was absorbed.

All other photons are present, except the ones that were

absorbed.Source:http://ch301.cm.utexas.edu/atomic/#H-atom/line-spectra.html


Source: http://www.green-planet-solar-energy.com/images/spectrum_abs_1.jpg


The image on the previous slide shows how we can obtain the

line absorption spectrum of a particular sample. For example,

if we wanted to obtain the absorption spectrum of atomic

hydrogen, we would use a sample of cool atomic hydrogen

gas.

White light (all photons within the visible light region present)

is incident upon the sample of cool gas.

The sample of cool gas acts as a filter by absorbing only

certain photons. The photons that were absorbed will be

missing from the spectrum.


Source: http://astronomy.nmsu.edu/tharriso/ast110/1322_0613.jpg

The image on the previous slide shows how we can compare

the line emission, absorption and continuous spectra for a

particular element.

Note that the photons that were absorbed will also be

emitted but in a different direction.

EXAMPLES

EXAMPLES

Example 39.5, page 1299, Section 39.3: Energy Levels and the Bohr Model of the Atom, Chapter

39: Particles Behaving as Waves; Sears and Zemanskys University Physics, Young and

Freedman, 13th edition, Pearson Education, San Francisco, 2012.

EXAMPLES

Examples; Page 251, Chapter 9: Photons, Electrons and Atoms; Section 9.3: Emission Spectra,



EXAMPLES

Questions; Section 9.3: Emission Spectra; Page 252, Chapter 9: Photons, Electrons and Atoms;



EXAMPLESQuestion 5; Section 9.3:

Emission Spectra; Page

253, Chapter 9: Photons,

Electrons and Atoms;

International A/AS Level

Physics, by Mee, Crundle,

Arnold and Brown,

Hodder Education, United

Kingdom, 2008.

EXAMPLESQuestion 6; Section 9.3: Emission

Spectra; Page 253, Chapter 9: Photons,

Electrons and Atoms; International

A/AS Level Physics, by Mee, Crundle,

Arnold and Brown, Hodder Education,


EXAMPLESQuestion 7; Section 9.3:

Emission Spectra; Page

253, Chapter 9: Photons,

Electrons and Atoms;

International A/AS Level

Physics, by Mee, Crundle,

Arnold and Brown,

Hodder Education, United

Kingdom, 2008.

HOMEWORKHOMEWORK1. Question 7, Paper 4, Winter 2008 (E).1. Question 7, Paper 4, Winter 2008 (E).

2. Question 8, Paper 4, Summer 2009.

3. Question 7, Paper 42, Winter 2009.



6. Question 7, Paper 41, Summer 2011 (E).

7. Question 7, Paper 42, Summer 2011.



Chapter 26 Quantum Physics

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