Modern Physics NCEA AS 3.5 Text Chapters:20,22. The Photoelectric Effect The photoelectric effect occurs when shining light (usually UV) onto a piece

Modern PhysicsModern Physics

NCEA AS 3.5NCEA AS 3.5

Text Chapters:20,22Text Chapters:20,22

The Photoelectric EffectThe Photoelectric Effect

The photoelectric effect occurs when The photoelectric effect occurs when shining light (usually UV) onto a piece of shining light (usually UV) onto a piece of metal causes electrons to be given off.metal causes electrons to be given off.

This effect can be used in a photoelectric This effect can be used in a photoelectric cell to produce small electric currents.cell to produce small electric currents.

Photoelectric cells are used inPhotoelectric cells are used inLightmetersLightmetersBurglar alarmsBurglar alarmsTV cameras etcTV cameras etc

Photoelectric CellsPhotoelectric Cells

Thin glass tube (evacuated)

Emitter – curved metal plate

Collector

A

LIGHT

Photoelectric ExperimentsPhotoelectric Experiments

When the photoelectric effect was studied When the photoelectric effect was studied in detail, the experimental results were in detail, the experimental results were very different to what was expected. A very different to what was expected. A new theory about the nature of light was new theory about the nature of light was needed to explain what happened.needed to explain what happened.

Scientists at the time considered light to Scientists at the time considered light to behave like a wave……behave like a wave……


What was expected:What was expected:Brighter light would cause electrons with more Brighter light would cause electrons with more

kinetic energy to be emittedkinetic energy to be emittedWhat actually happened:What actually happened:

Brighter light caused more electrons to be Brighter light caused more electrons to be emitted, but there was no change in the emitted, but there was no change in the amount of energy they hadamount of energy they had


What was expected:What was expected: If very dim light was used, it would take some If very dim light was used, it would take some

time before any electrons had absorbed time before any electrons had absorbed enough energy to escape from the metalenough energy to escape from the metal

What actually happened:What actually happened:With UV light, even the faintest light caused With UV light, even the faintest light caused

some electrons to be emitted instantlysome electrons to be emitted instantly


What was expected:What was expected:The frequency (or colour) of the light used The frequency (or colour) of the light used

would not affect the energy of the emitted would not affect the energy of the emitted electrons.electrons.

What actually happened:What actually happened:The higher the frequency, the higher the The higher the frequency, the higher the

energy of the electrons. Below a certain energy of the electrons. Below a certain frequency, no electrons were emitted.frequency, no electrons were emitted.


Einstein explained these results, using an Einstein explained these results, using an idea suggested by Max Planck, that said idea suggested by Max Planck, that said electromagnetic radiation comes in fixed electromagnetic radiation comes in fixed “packets” or “packets” or quantaquanta of energy called of energy called photonsphotons

The amount of energy each photon has The amount of energy each photon has depends on the frequency of the radiation.depends on the frequency of the radiation.


Each photon has a fixed amount of energy Each photon has a fixed amount of energy given by:given by:

h=Planck’s Constant = 6.63x10h=Planck’s Constant = 6.63x10-34-34JsJsThis suggested that light behaved like a This suggested that light behaved like a

moving particle, rather than a wavemoving particle, rather than a wave

hfE


The power supply The power supply provides an provides an opposing voltage opposing voltage to the p.e. cell.to the p.e. cell.

The variable The variable voltage is voltage is adjusted until the adjusted until the current in the current in the circuit is zerocircuit is zero

LIGHT

V


When the current was zero, the supply When the current was zero, the supply voltage was equal to the cut-off voltage of voltage was equal to the cut-off voltage of the cellthe cell

Different frequencies of light were tried, Different frequencies of light were tried, and the cut-off voltages measured:and the cut-off voltages measured:


These were the These were the results:results:

Below a certain Below a certain threshold threshold frequency ffrequency f00 no no

electrons were electrons were emittedemitted f

V

f0


The maximum EThe maximum Ekk of the electrons can be of the electrons can be

found from the voltage:found from the voltage:

Where e= electron charge = -1.6x10Where e= electron charge = -1.6x10-19-19

eVE

energyVoltage

k

charge


Another way Another way of looking at of looking at that last that last graph:graph:

f

Ek

f0

Intercept= Work function Φ (or B)

Gradient = h


By equating to y=mx+c:By equating to y=mx+c:

EEkk = max kinetic energy of emitted electrons = max kinetic energy of emitted electrons hf = energy of incoming photonshf = energy of incoming photons ΦΦ = The work function of the metal – the = The work function of the metal – the

minimum amount of energy required for the minimum amount of energy required for the electron to escape from the metal surface.electron to escape from the metal surface.

BhfEk


Different Different metals have metals have different fdifferent f00’s ’s and work and work functions functions depending depending on how on how tightly they tightly they hold onto hold onto their their electronselectrons

f

Ek

f0 f0

Cu Pb

The ConclusionThe ConclusionSo the photoelectric effect could be So the photoelectric effect could be

explained by thinking of light as a stream explained by thinking of light as a stream of incoming particles that collided with of incoming particles that collided with electrons in the metal. If the photon had electrons in the metal. If the photon had enough energy, it could knock the electron enough energy, it could knock the electron free of the metal and send it across the free of the metal and send it across the cell to the collector.cell to the collector.

If photon was too small, it couldn’t hit If photon was too small, it couldn’t hit electrons hard enough (overcome work electrons hard enough (overcome work function) so no electrons emitted.function) so no electrons emitted.

Atomic SpectraAtomic Spectra

2 types2 typesEmission – certain frequencies of light given Emission – certain frequencies of light given

off by low pressure gases excited by heat or off by low pressure gases excited by heat or electricityelectricity

Absorption – certain frequencies absorbed Absorption – certain frequencies absorbed from a continuous spectrum by low pressure from a continuous spectrum by low pressure gasesgases

Spectra are unique to each element and Spectra are unique to each element and can be used to identify unknown elementscan be used to identify unknown elements

The Hydrogen SpectrumThe Hydrogen Spectrum

Balmer studied the emission spectrum Balmer studied the emission spectrum lines of Hydrogen, as it is the simplest lines of Hydrogen, as it is the simplest atom.atom.

He was limited by the fact that he could He was limited by the fact that he could only observe visible frequencies – we now only observe visible frequencies – we now know there are UV and IR spectral linesknow there are UV and IR spectral lines

The spectral lines are caused by the The spectral lines are caused by the movement of electrons between different movement of electrons between different energy shells in the atomenergy shells in the atom


In Balmer’s case he was looking at In Balmer’s case he was looking at spectral lines caused by electrons jumping spectral lines caused by electrons jumping from higher energy level (shells) down into from higher energy level (shells) down into the 2the 2nd nd shell. shell.

They would release their extra energy as a They would release their extra energy as a photon of light.photon of light.

Other Scientists later found series of Other Scientists later found series of spectral lines corresponding to jumps into spectral lines corresponding to jumps into the 1the 1stst, 3, 3rdrd, 4, 4thth, 5, 5thth etc etc


1 2 3 4 5 ∞

Lyman Series S=1 (UV)

Balmer Series S=2 (visible)

Paschen Series S=3 (IR)Bracket Series S=4 (IR)

Pfund Series S=5 (IR)

Nucleus

Shell no. / Energy level


A formula was worked out to calculate the A formula was worked out to calculate the wavelengths of these lines:wavelengths of these lines:

R=Rydberg’s Constant=1.097x10R=Rydberg’s Constant=1.097x10-7-7

S=Series no. (the shell jumped into)S=Series no. (the shell jumped into)L=Line no. (the shell jumped from)L=Line no. (the shell jumped from)

22

111

LSR


The formula worked perfectly for The formula worked perfectly for Hydrogen, but started to get more Hydrogen, but started to get more inaccurate the bigger and more complex inaccurate the bigger and more complex the atom gotthe atom got

Absorption spectra are produced by Absorption spectra are produced by electrons electrons absorbingabsorbing photons of energy photons of energy which allows them to jump which allows them to jump upup energy energy levelslevels

Bohr’s Model of the AtomBohr’s Model of the Atom

Rutherford’s student Niels Bohr proposed Rutherford’s student Niels Bohr proposed that:that:Electrons in H could only exist in stable orbits Electrons in H could only exist in stable orbits

with certain fixed amounts of energy, called with certain fixed amounts of energy, called energy levelsenergy levels

An electron moves from one energy level to An electron moves from one energy level to another by either emitting or absorbing a another by either emitting or absorbing a photon of light equal in energy to the photon of light equal in energy to the difference between the two energy levelsdifference between the two energy levels


The energy levels in the Hydrogen atom are The energy levels in the Hydrogen atom are given by :given by :

h=Plancks constant = 6.63x10h=Plancks constant = 6.63x10-34-34

c=speed of light = 3x10c=speed of light = 3x1088

R=Rydbergs constant = 1.097x10R=Rydbergs constant = 1.097x1077

n=energy level = 1,2,3,4…… (quantum number)n=energy level = 1,2,3,4…… (quantum number)

2n

hcREn


All energy values are negative – this All energy values are negative – this represents the fact that it is an energy represents the fact that it is an energy which which bindsbinds the electron to the nucleus the electron to the nucleus

The lowest energy state n=1 is called the The lowest energy state n=1 is called the ground stateground state

As nAs n∞, E∞, E0. This represents the 0. This represents the energy required to ionise the atom by energy required to ionise the atom by removing the electron completely.removing the electron completely.


-1

-2

Energy

(x10-18J)

0

n=1

n=2

n=3n=4

n=∞

181

2

7834

1

1018.2

1

10097.11031063.6

E

E

Electron VoltsElectron Volts

Sometimes an alternative unit for energy is Sometimes an alternative unit for energy is used called the electron voltused called the electron volt

1eV is the energy gained by 1 electron 1eV is the energy gained by 1 electron when accelerated by a potential of 1 Voltwhen accelerated by a potential of 1 Volt

1eV=1.6x101eV=1.6x10-19-19JJUsing this unit:Using this unit:

eVn

En 2

6.13

Nuclear ReactionsNuclear Reactions

3 types:3 types:

Radioactive DecayRadioactive Decay – the spontaneous – the spontaneous emission of particles from the nucleus of emission of particles from the nucleus of an atoman atom

Nuclear FissionNuclear Fission – splitting one large – splitting one large nuclei into two smaller onesnuclei into two smaller ones

Nuclear FusionNuclear Fusion – combining two small – combining two small nuclei into one large one. nuclei into one large one.

RadioactivityRadioactivity

3 types:3 types:Alpha Alpha Beta Beta GammaGamma

Named in order of their discovery.Named in order of their discovery.Alpha and beta decay don’t usually occur by Alpha and beta decay don’t usually occur by

themselves, there is usually some gamma themselves, there is usually some gamma that occurs with them.that occurs with them.

The NucleusThe Nucleus

In small atoms, the number of protons and In small atoms, the number of protons and neutrons are usually the same (roughly)neutrons are usually the same (roughly)

In larger atoms, there are usually many In larger atoms, there are usually many more neutrons than protons, in order to more neutrons than protons, in order to keep the nucleus stable. keep the nucleus stable.

If a nucleus is unstable, it may If a nucleus is unstable, it may spontaneously decay to something more spontaneously decay to something more stable by emitting alpha, beta or gamma stable by emitting alpha, beta or gamma radiationradiation

Alpha ParticlesAlpha Particles

Helium nucleusHelium nucleusCharge of +2Charge of +2Mass of 4 (a.m.u)Mass of 4 (a.m.u)Travel slowly ie. 10% of light speedTravel slowly ie. 10% of light speedDon’t travel very far ie. A few cms in airDon’t travel very far ie. A few cms in airLow penetration power – can be stopped Low penetration power – can be stopped

by a piece of paperby a piece of paperVery good ionising power – because Very good ionising power – because

they’re big and slow.they’re big and slow.

Beta ParticlesBeta Particles

An electron from the nucleusAn electron from the nucleusCharge of -1Charge of -1Same mass as an electron (effectively 0)Same mass as an electron (effectively 0)Travel relatively fast – up to 95% of light Travel relatively fast – up to 95% of light

speed speed Travel about 30 cms in airTravel about 30 cms in airAverage penetration power – can be Average penetration power – can be

stopped by a few mm of Aluminiumstopped by a few mm of AluminiumAverage ionising powerAverage ionising power

Gamma RadiationGamma Radiation

A wave of electromagnetic radiation A wave of electromagnetic radiation (energy)(energy)

No chargeNo chargeNo massNo massTravels at light speed Travels at light speed Travels several metres in airTravels several metres in airHigh penetration power – Several cms of High penetration power – Several cms of

lead needed to stop itlead needed to stop itLow ionising power – because no massLow ionising power – because no mass

RadiationRadiationOne way that the different types of One way that the different types of

radiation can be distinguished is by radiation can be distinguished is by observing their behaviour in a magnetic observing their behaviour in a magnetic field:field:

The NucleusThe Nucleus

Writing nucleiWriting nuclei

X = element symbolX = element symbol

A = mass number or A = mass number or nucleonnucleon number (the number (the number of p+n)number of p+n)

Z = atomic number Z = atomic number (the number of (the number of protons)protons)

XAZ

IsotopesIsotopes

Atoms with the same atomic number but Atoms with the same atomic number but different mass numbersdifferent mass numbers

Eg:Eg:

)(

)(31

21

11

tritiumH

deuteriumH

H

C

C

C

146

136

126

Alpha DecayAlpha Decay

Example: Radium 226 decays to Radon 222 by Example: Radium 226 decays to Radon 222 by alpha decay:alpha decay:

Note: Both mass and charge must be conservedNote: Both mass and charge must be conserved

(ie 226=222+4, 88=86+2(ie 226=222+4, 88=86+2

HeRnRa 42

22286

22688

Beta DecayBeta Decay

Cobalt 60 decays by beta decay to Nickel Cobalt 60 decays by beta decay to Nickel 6060

Again, mass and charge are conservedAgain, mass and charge are conservedNB. the NB. the or or symbols can be used symbols can be used

instead of He or einstead of He or e

eNiCo 01

6028

6027

Half-lifeHalf-life

The time it take for the decay rate to have The time it take for the decay rate to have halved, or….halved, or….

The time taken for half of the original The time taken for half of the original atoms to have decayedatoms to have decayed

Usually shown on a graphUsually shown on a graph

Half-lifeHalf-lifeHalf Life

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 1 2 3 4 5

Time in days

No

. o

f A

tom

s

Detecting RadioactivityDetecting Radioactivity

Geiger Counter – detects electrical current Geiger Counter – detects electrical current caused by the ionisation of atoms in a gascaused by the ionisation of atoms in a gas

400V DC Supply

Counter or speaker- Anode: central wire

+Cathode: metal cylinderGeiger-Muller tube filled with low pressure Ar

End: thin mica window

Uses of RadioactivityUses of Radioactivity

Radiation therapy to treat cancerRadiation therapy to treat cancerSterilisationSterilisationCarbon datingCarbon datingNuclear medicine eg tracersNuclear medicine eg tracersSmoke detectorsSmoke detectors

Binding EnergyBinding Energy

If we put together a nucleus from If we put together a nucleus from individual protons and neutrons, we would individual protons and neutrons, we would find that the mass of the resulting nucleus find that the mass of the resulting nucleus is less than the total mass of the individual is less than the total mass of the individual nucleons.nucleons.

This reduction in mass is called a This reduction in mass is called a mass mass deficitdeficit


In order to break up a nucleus into In order to break up a nucleus into separate nucleons the mass deficit must separate nucleons the mass deficit must be restored by adding extra energy.be restored by adding extra energy.

This energy changes into mass according This energy changes into mass according to Einstein’s famous equation:to Einstein’s famous equation:

2mcE


This energy shortage has the effect of This energy shortage has the effect of holding the nucleus together so it is called holding the nucleus together so it is called the the binding energybinding energy..

Binding energy represents the amount of Binding energy represents the amount of “glue” holding the nucleus together.“glue” holding the nucleus together.

The more binding energy per nucleon, the The more binding energy per nucleon, the more stable an atom will bemore stable an atom will be


Mass number50 100 150 200

B.E per nucleon

(MeV)

2

4

6

8

56Fe

238U4He

7Li

Fusion Fission

Nuclear FissionNuclear Fission

Breaking large unstable nuclei into smaller Breaking large unstable nuclei into smaller ones.ones.

Lots of possible combinations of fragments Lots of possible combinations of fragments from one initial nucleusfrom one initial nucleus

Eg:Eg:

nKrBaUn 10

9236

14156

23592

10 3


When a large nucleus is split into smaller When a large nucleus is split into smaller fragments, the fragments have less mass fragments, the fragments have less mass per nucleonper nucleon

The lost mass is released as energy in the The lost mass is released as energy in the form of kinetic energy of neutrons and form of kinetic energy of neutrons and gamma raysgamma rays


Only one Only one neutron is neutron is needed to needed to start the start the reaction, but reaction, but several are several are producedproduced

This starts a This starts a “chain “chain reactionreaction””

n

UBa Kr

n n n

UBa Kr

n n n

UBa Kr

n n n

UBa Kr

n n n


If the chain reaction is controlled it can be If the chain reaction is controlled it can be used in a nuclear reactorused in a nuclear reactor

If it is uncontrolled it explodes as a nuclear If it is uncontrolled it explodes as a nuclear or atomic bombor atomic bomb

Nuclear FusionNuclear Fusion

The joining of two small nuclei to form one The joining of two small nuclei to form one larger onelarger one

This is the process that powers the sunThis is the process that powers the sunEg:Eg:

nHeHH 10

42

31

21


Fusing two light atoms together results in Fusing two light atoms together results in a nucleus with less mass per nucleona nucleus with less mass per nucleon

The lost mass results in a release of The lost mass results in a release of energyenergy


Fusion requires extreme temperature (eg Fusion requires extreme temperature (eg millions of degrees) to occur, and has not millions of degrees) to occur, and has not practically and economically been used in practically and economically been used in power generation (yet….)power generation (yet….)

Hydrogen bombs have been successfully Hydrogen bombs have been successfully made, but require a fission reaction to made, but require a fission reaction to provide the necessary temp.provide the necessary temp.

Documents

Modern Physics NCEA AS 3.5 Text Chapters:20,22. The Photoelectric Effect The photoelectric effect occurs when shining light (usually UV) onto a piece