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Topic 11: Quantum PhysicsI. The photoelectric EffectThis is the phenomenon that when certain (clean) metal surfaces are illuminated byelectromagnetic radiation (e.g. ultraviolet), electrons are emitted from the surfaces.Electrons emitted this way are called photoelectrons.lf an electromagnetic radiation illuminates a metalsurface:

Note 1: ln its interaction with matter to release an electron, an electromagnetic radiation behaveslike a stream of particleiike photons, each with energy proportionalto the frequency of radiation-This energy can be absorbed by an electron immediatelv_

Predictions of the classical wavetheory Observations which are not in accordance with thep.gdictions of the classicalwave theoryof the electronon the intensity ofKinetic energyshould depend

[lectrons will be emitted at anyfrequency, provided the intensityof the radiation is high enough.

lncreas'ng the intensity of the radiation (by increasing therate of incidence of photons) increases the rate at whichelectrons are emitted, but has no effect on the maximumenergy of the electrons.Above the threshold frequencv. the maximum energy of theemitted electrons increases with the frequency of theradiation, even with low-inten\ity radiatron.No electron is emitted if the frequency of the radiation isbelow a certajn threshold frequencv. even with very intenseradiation.

Electrons will require some time toabsort) incident radiation beforethey acquire enough kinetic energy1o escape from the metal.

Electrons are emitted as soon as the radiation is incident onthe surface.

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Note 2: The intensity of the radiation depends on the rate at which the photons arrive. IRate ofarrival of photons is proportional to rate of emission of photoelectrons. i.e. the greater the intensityof incident radiation (provided the frequency is above threshold), the Sreater the magnitude of thephotocurrent!ltntensityot radiation, -';::: = 4 - no*'*Ahr lt [ ? ),,- [T]

=(?),,",*,-""', where e = r.6xr'''chotocurrent,i=,*[l)

l. r /,,.,"",".^,,Note 3: Work function 0 is required to freethe electron from the surface of metal. tf,jfis less than0, no electron is ejected.lncreasing the intensity {by increasing the rate of incidence of photons) means more photons persecond, but each photon is still unable to eject an electron.

Note 5; The value ofd, for any metal is a constant. The reason why photoelectrons which areemitted have different KE or velocities is because ofthe different depth that the electrons wereinitially situated within the metal. This leads to varying amount of ofenergy losses within the metallayers.

Commonly asked questions include asking on the effect of a given change on the stopping potentialvalue, Vs, KEmax and/or saturatlon current. ln summary,

Note 4: lf /rjtis greater than {}, the remainder is available to the electron as kinetic energy.(This is where the idea of stopping potential 4 comes in -the greater the KE of the photoelectron,the greater the Illpllldg of 4 needed to prevent electrons from reaching the collectorelectrode.)Decreasingthe intensity (by decreasing the rate of incidence of photons) means fewer photons persecond, but each photon is still able to ejed an electron.

To increase KEm." (or to increase V,) To increase saturation currenttE(by1for.l.i") 1 the intensity ofthe EM radiarion by a therate of incidence of photons(ptovided E > 6)JO(by.l,foortro)2lPaee

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saturationcurrent

lncreasing frequenry of radiation; rate of incidence of photons constant

Einstein's Equation for Photoelectric Emission

-v,

Energy ofPhoton

oror

hfhcI

Work Functionof Metal

0.qr hf.or

hci

Remainingenergy ofemitted Photon

KE-".= y, m v^u"'

atEPE

+

This is a very useful equatton, for many calculation questions require you to make use of it. youhave to use the relevant alternate forms ior the terms jn the equation, depending on the quantitiesyou are given.

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3. Energy tevels in AtomsA typical energy level diagram in a single atom looks like this:

Et

E1

n=3n=2

hf =LE-8:, Ez

ErE3

. An atom is said to be in its ground state if none of its electrons has an unoccupied energy levelbeneath it.

. lt is said to be in an excited state if one or more of its electrons have transited to a higherenergy level, and so there are unoccupied energy levels beneath them.

. lt is said to be in an ionized state if one or more of its electrons have transited to above thehighest energy level (n = infinity). i.e. the electrons have escaped_A photon is emitted when an electron transits.from a higher energy level to a lower energy level.Ener8y of thjs photon is equal to the energy driJerence AI between the 2 energy levels.

or hc =aE=h EzThe same energy must be absorbed for the electron to transit from the lower energy level to thefiigher energy level.Note: Commonly asked questions include the difference between exdtation of ground stateeledrons by photons and incident electrons. Difference: incoming photon must have the exactamount of energy that corresponds to At (a photon cannot be sub-divided; it is a "packet ofenergy'' and is wholly absorbed) whereas incident electron can have any amoltnt of energy that isgreaterthan A'' in order to bring about this transition-

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