Topic 26: Topic 26: Quantum PhysicsQuantum Physics

26.1 Energy of a photon26.1 Energy of a photon

26.2 Photoelectric emission of electrons26.2 Photoelectric emission of electrons

26.3 Wave-particle duality26.3 Wave-particle duality

26.4 Energy levels in atoms26.4 Energy levels in atoms

26.5 Line spectra26.5 Line spectra

What is Quantum Physics?What is Quantum Physics?

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Quantum PhysicsQuantum Physics

Quantum physics:Quantum physics:

the study of the the study of the behaviour of matter and energybehaviour of matter and energy at the molecular, atomic, nuclear and smaller at the molecular, atomic, nuclear and smaller microscopic levelsmicroscopic levels..

In the early 20th century, it was discovered that In the early 20th century, it was discovered that

the the laws that govern macroscopic objects do not laws that govern macroscopic objects do not function the same in such small realmsfunction the same in such small realms..

What is QuantumWhat is Quantum

"Quantum""Quantum"

comes from the Latin meaning comes from the Latin meaning "how much.""how much."

It refers to the It refers to the discrete units of matter and discrete units of matter and energyenergy that are predicted by and observed in that are predicted by and observed in quantum physics. quantum physics.

Even space and timeEven space and time, which appear to be , which appear to be extremely continuous, extremely continuous, have smallest possible have smallest possible valuesvalues..

Who Develop Quantum PhysicsWho Develop Quantum Physics

As scientists gained the technology to As scientists gained the technology to measure measure with greater precisionwith greater precision, , strange phenomena was strange phenomena was observedobserved..

The birth of quantum physics is attributed to The birth of quantum physics is attributed to Max Max

Planck'sPlanck's 1900 paper on blackbody radiation. 1900 paper on blackbody radiation.

Development of the field was done by Development of the field was done by Max Max PlanckPlanck, , Albert EinsteinAlbert Einstein, , Niels BohrNiels Bohr, , Werner Werner HeisenbergHeisenberg, , Erwin SchroedingerErwin Schroedinger, and many , and many others. others.

Particulate Nature of E/M RadiationParticulate Nature of E/M Radiation In 1900, Max Planck, a German physicists suggested In 1900, Max Planck, a German physicists suggested

that the that the electromagnetic waveselectromagnetic waves emitted from a blackbody emitted from a blackbody (a perfect absorber and emitter of radiation) was (a perfect absorber and emitter of radiation) was quantizedquantized. .

This means that the energy emitted is not continuous, This means that the energy emitted is not continuous, but instead but instead consists of discrete amount or packetsconsists of discrete amount or packets called called quantas.quantas.

In 1905, Einstein extended Planck’s idea and postulated In 1905, Einstein extended Planck’s idea and postulated that that lightlight is emitted in packets (quantas or is emitted in packets (quantas or photonsphotons) and ) and remains in packets till absorbed.remains in packets till absorbed.

This idea of This idea of quantization of electromagnetic wavesquantization of electromagnetic waves into into packets of energy called photons packets of energy called photons suggests a particulate suggests a particulate nature of electromagnetic radiationnature of electromagnetic radiation..

The Particulate NatureThe Particulate Nature

The PhotonThe Photon

The photon is a quantum or packet of energy of an electromagnetic radiation.

Energy of a PhotonEnergy of a Photon

E hf hcE

OR

Where:

h is Planck’s constant = 6.63 × 10-34 Js

f is the frequency of the electromagnetic wave

Is the wavelength of the electromagnetic wave

c is the speed of light in vacuum = 3.00 × 108 ms-1

Example 1Example 1

Solution:

Example 2Example 2

Solution:

Example 3Example 3

Solution:

Photoelectric EmissionPhotoelectric Emission

Photoelectric emissionPhotoelectric emission is the is the release release of electronsof electrons from the from the surface of a surface of a

metalmetal when when electromagnetic radiationelectromagnetic radiation is incident on its surfaceis incident on its surface

The Photoelectric EffectThe Photoelectric Effect

The Photoelectric EffectThe Photoelectric Effect

CollectorMetal

emitter

Photo-electrons

Evacuated tube

Electromagnetic radiation

The Photoelectric EffectThe Photoelectric EffectThe experiment was first carried out by Einstein in 1905.The experiment was first carried out by Einstein in 1905.

The observations / conclusions :The observations / conclusions :

If photoemission takes place, it does so If photoemission takes place, it does so instantaneouslyinstantaneously. There is no . There is no delay between illumination and emissiondelay between illumination and emission

Photoemission takes place only if the frequency of the incident Photoemission takes place only if the frequency of the incident radiation is above a certain value called the radiation is above a certain value called the threshold frequency threshold frequency ff00

Different metals need radiation of different threshold frequencies

Whether or not emission takes place depends only on whether the frequency of the radiation used is above the threshold for that surface. It does not depend on the intensity of the radiation

For a given frequency, the rate of emission of photoelectrons is proportional to the intensity of the radiation.

ExplanationExplanationEmission is instantaneous if above threshold frequency:Emission is instantaneous if above threshold frequency:A single photon interacts only with a single electron. If the interaction is A single photon interacts only with a single electron. If the interaction is successful the entire energy successful the entire energy hfhf of the of the photon is absorbed by the electron photon is absorbed by the electron instantaneouslyinstantaneously and the photon ceases to exist. and the photon ceases to exist.

The rate of emission of photoelectrons is proportional to the intensity of the radiation:If N number of photons fall on the emitter in a time t, the intensity is

The increase in the number of incident photons per unit time increases the number of photoelectrons as each photon emits an electron. Therefore the photoelectric current increases proportionally with the intensity of the radiation.

Since and are kept constant:

E Nhf N hfItA tA t A

f A

NI

t

Kinetic Energies of PhotoelectronsKinetic Energies of Photoelectrons

CollectorMetal

emitter

Photo-electrons

Evacuated tube

Electromagnetic radiation

+

+

A

VAdjustable

p.d.Photoelectric current

Kinetic Energies of PhotoelectronsKinetic Energies of Photoelectrons

The The collector platecollector plate is made is made negativenegative so that when the photo-electrons so that when the photo-electrons move towards it, they will move towards it, they will lose their kinetic energieslose their kinetic energies and and gain potential gain potential energiesenergies

The current flowing through the circuit is measured with a micro-The current flowing through the circuit is measured with a micro-ammeter and the potential difference between the emitter and ammeter and the potential difference between the emitter and collector measured with a voltmetercollector measured with a voltmeter

The voltage between the emitter and collector plates is gradually The voltage between the emitter and collector plates is gradually increased until the current drops to zero.increased until the current drops to zero.

The minimum value of the potential difference necessary to stop the The minimum value of the potential difference necessary to stop the electron flow is known as the electron flow is known as the stopping potentialstopping potential..

If the experiment is repeated with If the experiment is repeated with radiation of greater intensityradiation of greater intensity but but same frequencysame frequency, the , the maximum currentmaximum current in the micro-ammeter in the micro-ammeter increasesincreases but the but the stopping potential is unchangedstopping potential is unchanged..

21

2mv eV

ExplanationExplanation

If If ff or or of radiation is of radiation is kept constantkept constant, , increasing the intensityincreasing the intensity of the radiation of the radiation does not change the maximum kinetic energydoes not change the maximum kinetic energy of the photoelectrons and the of the photoelectrons and the stopping potential:stopping potential:

Increasing the light intensity simply Increasing the light intensity simply increases the number of photons falling increases the number of photons falling on unit area in unit timeon unit area in unit time. This results in an increase in the emission of . This results in an increase in the emission of photoelectrons and the photocurrent. However, photoelectrons and the photocurrent. However, the incident photons still the incident photons still impart the same amount of energy impart the same amount of energy hfhf to every electron. to every electron.

If intensityIf intensity II of radiation is kept of radiation is kept constantconstant but frequency but frequency ff is increased is increased, , photoelectric current photoelectric current i i remainsremains constant but stopping potential increases: constant but stopping potential increases:

Increasing the frequency Increasing the frequency increases the kinetic energyincreases the kinetic energy of the photoelectrons. of the photoelectrons. It requires a larger stopping potential to reduce the photocurrent to zeroIt requires a larger stopping potential to reduce the photocurrent to zero

Work FunctionWork Function

Threshold frequencyThreshold frequency ff00 is the is the minimum frequencyminimum frequency of of electromagnetic radiation electromagnetic radiation that could emit photoelectrons that could emit photoelectrons from a materialfrom a material when the material is being irradiated. when the material is being irradiated.

The existence of the threshold frequency suggests that The existence of the threshold frequency suggests that electrons in the emitter are held weakly by electric forces electrons in the emitter are held weakly by electric forces within the material. In order to be ejected, within the material. In order to be ejected, the electron the electron must absorb a certain amount of energy must absorb a certain amount of energy ..

We call this energy the We call this energy the work functionwork function of the material and of the material and it can be defined as the it can be defined as the minimum energy necessary to minimum energy necessary to remove an electronremove an electron from the surface of the emitter from the surface of the emitter material.material.

Einstein’s TheoryEinstein’s Theory A single A single photonphoton has a quantum of energy has a quantum of energy hfhf. In a photoelectron . In a photoelectron

interaction, the entire quantum interaction, the entire quantum hfhf is is transferred to the electrontransferred to the electron in the in the emitter.emitter.

The The work functionwork function is dependent on the type of metal is dependent on the type of metal When a photon of When a photon of threshold frequencythreshold frequency ff00 is absorbed by an electron, is absorbed by an electron,

the electron is released from the surface with zero kinetic energy. the electron is released from the surface with zero kinetic energy. Therefore Therefore hfhf00 ==

When a photon of frequency When a photon of frequency ff ( (ff > > ff00) is absorbed by an electron, it is ) is absorbed by an electron, it is released from the surface with a velocity that could range from the released from the surface with a velocity that could range from the smallest smallest vvminmin to the largest to the largest vvmaxmax. .

Therefore, Einstein’s photoelectric equation is:Therefore, Einstein’s photoelectric equation is:

hfhf == + ½ + ½mvmv22 == + + eVeV00 VV00 = = stopping potentialstopping potential

hfhf / e / e = = / e + / e + VV00

VV0 0 = (h/e) f - = (h/e) f - / e / e

Example 4Example 4

Solution:

Example 5Example 5

Example 5Example 5

Exercise 6Exercise 6

Solution:

Example 7Example 7

Solution 7Solution 7

Wave-Particle DualityWave-Particle Duality The The photoelectric effectphotoelectric effect shows that electromagnetic shows that electromagnetic

radiations have radiations have particulate natureparticulate nature..

Observations show that Observations show that moving particlesmoving particles also display also display interferenceinterference and and diffraction patternsdiffraction patterns which are which are wave wave propertiesproperties

De Broglie proposed that a particle with mass De Broglie proposed that a particle with mass mm and and velocity velocity vv (for momentum (for momentum pp) also has wave properties) also has wave propertiesDe Broglie’s wavelength:De Broglie’s wavelength: == h h / / p p == h h // mv mvEinstein theory of relativity:Einstein theory of relativity: p p == E / c E / c == hf / c hf / c == h / h /

Wave-Particle DualityWave-Particle Duality

Moving electrons display diffraction pattern. Particles exhibit wave properties.

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Wave-Particle DualityWave-Particle Duality

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Example 8Example 8

Solution 8Solution 8

The Atomic StructureThe Atomic StructureRutherford’s Planetary Model:Rutherford’s Planetary Model:In 1911, after the famous In 1911, after the famous alpha alpha scattering experimentscattering experiment, Rutherford , Rutherford proposed that proposed that electrons revolve at electrons revolve at high speed in circular orbits around high speed in circular orbits around the positively charged nucleusthe positively charged nucleus. .

The Drawback:

According to classical electromagnetic theory, if a charged particle were accelerated around another charged particle then there would be a continuous radiation of energy. The loss of energy would slow down the speed of the electron and eventually the electron would fall into the nucleus. But such a collapse does not occur. Rutherford's model was unable to explain it.

Neil Bohr’s Atomic ModelNeil Bohr’s Atomic Model Niels BohrNiels Bohr,, in 1913 in 1913 applies applies

quantum theoryquantum theory to to Rutherford's atomic structure Rutherford's atomic structure

He proposed that He proposed that electrons electrons travel in stationary orbitstravel in stationary orbits defined by their angular defined by their angular momentum. momentum.

This led to the calculation of This led to the calculation of possible energy levelspossible energy levels for for these orbits andthese orbits and

He postulated that the He postulated that the emission of lightemission of light occurs occurs when an electron moves into when an electron moves into a lower energy orbit.a lower energy orbit.

Bohr’s PostulationBohr’s PostulationElectrons can move only in certain allowed orbits round the Electrons can move only in certain allowed orbits round the nucleus:nucleus:

Bohr’s Bohr’s circular orbitscircular orbits are also called are also called stationary statesstationary states.. Electrons in these stationary states behave very much like Electrons in these stationary states behave very much like

stationary waves fitted into the circumference of the orbit. This stationary waves fitted into the circumference of the orbit. This means: means: 22rr = = nnwhere where r r is the radius of the orbitis the radius of the orbit

is the wavelength of the electron waveis the wavelength of the electron wavenn is the integer called the quantum number of the orbit is the integer called the quantum number of the orbit

Electrons can exist in stationary states Electrons can exist in stationary states ( ( nn = 1, 2, 3 …) but = 1, 2, 3 …) but not in between not in between these statesthese states..

Bohr’s PostulationBohr’s PostulationElectrons in each orbit have a definite energy and they move in that orbit without radiating energy:

A ‘free’ electron at n = has zero potential energy.

All energy levels are negative indicating a loss of potential energy as the electron draws nearer to the nucleus.

The energy level at n = 1 has the lowest potential energy and is called the ground state of the atom.

Ground state for H atom = -13.6 eV

Historically, the quantum number n is called a shell where n = 1 is known as the K shell.Energy levels for a hydrogen atom

Electronic TransitionElectronic Transition

Electronic TransitionElectronic Transition

An electronic transition from one energy level to another requires An electronic transition from one energy level to another requires the absorption or emission of a photon:the absorption or emission of a photon:

This is represented by This is represented by vertical arrowsvertical arrows drawn between the energy drawn between the energy levels.levels.

An electron must An electron must absorb energyabsorb energy before it can be excited from a before it can be excited from a lower to a higher energy level. This can be achieved in 3 ways:lower to a higher energy level. This can be achieved in 3 ways:

An atom collides with an atomAn atom collides with an atom An electron absorbs a photon of a certain frequencyAn electron absorbs a photon of a certain frequency An electron absorbs energy from a bombarding electronAn electron absorbs energy from a bombarding electron

An electron in an upper energy level or excited state will fall back to An electron in an upper energy level or excited state will fall back to a lower level after a short interval. This downward transition a lower level after a short interval. This downward transition corresponds to the corresponds to the emission of a photonemission of a photon whose energy is the same whose energy is the same as the energy difference between the levels.as the energy difference between the levels.

hfhf = = EEHH – – EELL

where where EEHH = Energy of the upper state = Energy of the upper state EELL = Energy of the lower state= Energy of the lower state

Energy differenceEnergy difference between adjacent states are between adjacent states are not equalnot equal..

Example 9Example 9

Solution 9Solution 9

Line SpectraLine Spectra

Emission line spectraEmission line spectra are are discontinuous coloured linesdiscontinuous coloured lines superimposed on a superimposed on a dark backgrounddark background..

Absorption line spectraAbsorption line spectra are are discontinuous dark linesdiscontinuous dark lines superimposed on a superimposed on a continuous spectrum of coloured continuous spectrum of coloured lightslights..

Emission Line SpectraEmission Line Spectra

Emission line spectraEmission line spectra are obtained by are obtained by passing lightpassing light, , emitted from aemitted from a heated heated gasgas at low pressure in a discharge tube through a spectroscope. at low pressure in a discharge tube through a spectroscope.

The light is separated into different frequenciesThe light is separated into different frequencies by a prism and brought to by a prism and brought to focus on different sections of a white screen by lenses.focus on different sections of a white screen by lenses.

In total darkness, the screen will In total darkness, the screen will show coloured linesshow coloured lines which are actually the which are actually the images of the rectangular slit through which the light passes.images of the rectangular slit through which the light passes.

Different elements have different configurations of energy levels. In a Different elements have different configurations of energy levels. In a discharge tube at low pressure, discharge tube at low pressure, electrons in their excited states fall back to electrons in their excited states fall back to lower energy levelslower energy levels by emitting photons of specific frequencies seen on the by emitting photons of specific frequencies seen on the line spectra. This provides useful information for scientists line spectra. This provides useful information for scientists to identify to identify elements and study their atomic structureelements and study their atomic structure

Absorption Line SpectraAbsorption Line Spectra

Absorption line spectraAbsorption line spectra are produced when are produced when white lightwhite light from an incandescent from an incandescent lamp lamp passes through a container of cool gaspasses through a container of cool gas..

Electrons from the ground state in the Electrons from the ground state in the cool gascool gas absorb some photonsabsorb some photons and and transmit to the excited states. transmit to the excited states.

The continuous spectrum obtained on the screen The continuous spectrum obtained on the screen has missing frequencieshas missing frequencies due to the due to the absorption of photons by the cool gasabsorption of photons by the cool gas.They appear as .They appear as dark linesdark lines superimposed superimposed on a bright coloured backgroundon a bright coloured background..

The absorption line spectra can be The absorption line spectra can be observed in the continuous spectrum of observed in the continuous spectrum of the sunthe sun. The hottest central core emits white light but photons of some . The hottest central core emits white light but photons of some frequencies are absorbed by the cooler gases in the chromosphere (outer frequencies are absorbed by the cooler gases in the chromosphere (outer rim of the sun) rim of the sun)

Physics is Great!Physics is Great!

Enjoy Your Study!Enjoy Your Study!