Phy Revision Quantham Physics

Topic

I.

11:

Quantum Physics

The photoelectric Effect

This is the phenomenon that when certain (clean) metal surfaces are illuminated by electromagnetic radiation (e.g. ultraviolet), electrons are emitted from the surfaces. Electrons emitted this way are called photoelectrons.

lf an electromagnetic radiation illuminates a metalsurface: Predictions of the classical wave

theory

Kinetic energy

Observations which are not in accordance with the p.gdictions of the classicalwave theory

of the

electron lncreas'ng the intensity of the radiation (by increasing the should depend on the intensity of rate of incidence of photons) increases the rate at which electrons are emitted, but has no effect on the maximum energy of the electrons. Above the threshold frequencv. the maximum energy of the

emitted electrons increases with the frequency

of

the

radiation, even with low-inten\ity radiatron.

[lectrons will be emitted at any frequency, provided the intensity of the radiation is high enough.

Electrons will require some time

No electron is emitted if the frequency of the radiation is below a certajn threshold frequencv. even with very intense radiation.

to Electrons are emitted as soon

as

the radiation is incident on

absort) incident radiation before the surface. they acquire enough kinetic energy 1o escape from the metal.

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

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Note 2: The intensity of the radiation depends on the rate at which the photons arrive. IRate of arrival of photons is proportional to rate of emission of photoelectrons. i.e. the greater the intensity of incident radiation (provided the frequency is above threshold), the Sreater the magnitude of the

photocurrent!l tntensity ot radiation,

-';::: 4

-

=

no*'*Ahr

[?

=(?),,",*,-""',

Photocurrent,i=

Note 3: Work function

0

is required to

lt

),,- [T]

where e = r.6xr'''c

,*[l) r /,,.,"",".^,,

l.

freethe electron from the surface of metal. tf,jfis less than

0, no electron is ejected.

lncreasing the intensity {by increasing the rate of incidence of photons) means more photons per second, but each photon is still unable to eject an electron.

Note 4: lf /rjtis greater than {}, the remainder is available to the electron as kinetic energy. (This is where the idea of stopping potential

the greater the

Illpllldg

of

4

4

comes in

-the

greater the KE of the photoelectron,

needed to prevent electrons from reaching the collector

electrode.) Decreasingthe intensity (by decreasing the rate of incidence of photons) means fewer photons per second, but each photon is still able to ejed an electron.

Note 5; The value ofd, for any metal is a constant. The reason why photoelectrons which are emitted have different KE or velocities is because ofthe different depth that the electrons were

initially situated within the metal. This leads to varying amount of ofenergy losses within the metal layers.

Commonly asked questions include asking on the effect of a given change on the stopping potential value, Vs, KEmax and/or saturatlon current. ln summary, To increase KEm." (or

to increase V,)

tE(by1for.l.i") JO(by.l,foortro) 2lPaee

To increase saturation current

1 the intensity ofthe

EM radiarion by photons rate of incidence of (ptovided E > 6)

a

the

saturation current

-v, lncreasing frequenry of radiation; rate of incidence of photons constant

Einstein's Equation for Photoelectric Emission

Energy

of

Work Function of Metal

Photon

0

or

.qr

hf.

hf

or

or hc

I

Remaining energy of emitted Photon

hc

i

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

+ at

EPE

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

you are given.

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2,

Wave

-

Particle Duality

Matter exhibiting its wave or particulate nature in different situation is known duality.

as

wave-particle

Experiment demonstrating wave-particle duality

Particle behave as wave Electron Diffraction Experiment Electrons passingthrough diffraction grating Bive rise to a diffraction pattern similar to that of a light diffraction pattern.

Wave behave as particle Photoelectric experiment Light behave as particle like photons, leading to immediate emission of electrons when it is incident on clean metalsurfaces.

Specific conclusion

Electrons demonstrate wave nature when undergoing diff raction.

Light demonstrates particulate nature in a photoelectric experiment.

6eneral

All particles can possiblv demonstrate wave nature-

Allwaves can possibly demonstrate particulate nature,

Note: lnterference ond dilftdction phenomeno ore evidences of wave noture of electromoanetic rodiotion. De Broglie's Equation

wherep = momentum of photon lRecallthat momentum

= mass

x velocity]

Note: This equation also applies to other particles or bodies which have a momentum. However, the wavelengths of more massive bodies are usually very short compared to their dimensions and so interference effects are usually not evident.

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3. A

Energy tevels in Atoms

typical energy level diagram in a single atom looks like this:

Er E3

n=3

Et

n=2

E1

.

An atom is said

to be in its ground state if none of its electrons

has an unoccupied energy level

beneath it.

.

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

.

lt

to be in an ionized state if one or more of its electrons have transited to above the highest energy level (n = infinity). i.e. the electrons have escaped_ is said

A photon is emitted when an electron transits.from a higher energy level

Ener8y of thjs photon is equal to the energy driJerence

hf

=LE-8:,

Ez

or

AI

to

a lower energy level.

between the 2 energy levels. hc

=aE=h

Ez

The same energy must be absorbed for the electron to transit from the lower energy level to the fiigher energy level.

Note: Commonly asked questions include the difference between exdtation of ground state eledrons by photons and incident electrons. Difference: incoming photon must have the exact amount of energy that corresponds to At (a photon cannot be sub-divided; it is a "packet of energy'' and is wholly absorbed) whereas incident electron can have any amoltnt of energy that is greaterthan A'' in order to bring about this transition-

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Une Spectra The existence of line spectra demonstrates the existence of discrete energv levels within atems.

Emission Spectrum

Absorption Spectrum

Description Lines of certain colours on a dark backgroundHot Bas.

Source

Explanation of spectra

The number of possible energy

differences is finite, so the number of possible frequencies of emitted photons is also finite. The frequency of each photon emitted coraesponds to a line.

Dark lines across a continuous band of colours.

White light passed through a coolgas. When white light passes through a cool gas, the atoms ofthe coolgas can only absorb photons of a finite number of frequencies. While these photons are eventually re-emitted when the excited electrons de excite, the radiat'on is in all directlons and so the intensity of the original direction ;s reduced.

Noter The direction of increasing frequency can be deduced by inspecting the line spacing. The lines get increasingly closer together as frequency increases {vice versa for wavelengths). e.g

lncreasing frequency lncaeasing wavelength

questions to Try

YJCi t1

:. ,:::.

P2

lr.:ri

SRJC

28,29!.30

' l:

.,3r',::-:i:rli;

P'' P2 P1

:,.-:8. cJc

P1

P2

MJc

P1

F

6lPase

27,28,29,30

''r'