Phy Revision Quantham Physics

Topic

11:

_Quantum

Physics

I.

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:

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

radiation-This energy can be absorbed by an electron immediatelv_ Predictions of

the

classical wave

theory

Observations which are

not

in accordance

with the

p.gdictions of

the

classicalwave

theory

of

the

electron

on

the

intensity

_of

Kinetic

energy

should depend

[lectrons

will

be

emitted

at

any

frequency, provided

the

intensity

of the radiation is high enough.

lncreas'ng

the

intensity

of the

radiation (by

increasing

the

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.

No electron is

emitted if the

frequency

of the

radiation

is

below a certajn threshold frequencv. even

with

very intense

radiation.

Electrons

will

require some

time

to

absort)

incident radiation

before they acquire enough kinetic energy

1o escape

from the

metal.

Electrons are

emitted

as soon as

the

radiation is incident on the surface.

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

lt

[

?

),,-

[T]

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

where

e =

r.6xr'''c

Photocurrent,i=

,*[l)

l.

r

_{/,,.,"",".^,,}

Note 3: Work function

₀

is required to

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 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,

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

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.

To increase KEm." (or

to

increase V,) To increase

saturation current

tE(by1for.l.i")

1

the

intensity

ofthe

EM radiarion by

a

the

rate

of

incidence of photons (ptovided E >

6)

JO(by.l,foortro)

2lPaee

saturation current

lncreasing frequenry of radiation; rate of incidence of photons constant

Einstein's Equation

for

Photoelectric Emission

-v,

Energy

of

Photon

or

or

hf

hc

I

Work

Function

of

Metal

0

.qr

hf.

or

hc

i

Remaining

energy

of

emitted

Photon

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.

2,

Wave

_-

Particle Duality

Matter

exhibiting its wave or particulate nature in different situation is known as wave-particle duality.

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.

Particle behave as wave Wave behave as

particle

Experiment demonstrating wave-particle

duality

Electron Diffraction Experiment Electrons passingthrough diffraction

grating _{Bive rise} to a diffraction pattern _{similar to that of} a

light

diffraction pattern.

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,

3.

Energy tevels in Atoms

A typical _{energy level diagram in} a single atom looks like this:

Et E1

n=3

n=2

hf

_=LE-8:,

Ez Er E3

.

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

is said

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_

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

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

Une Spectra

The existence of line spectra demonstrates the existence of discrete energv levels

within

_atems.

Emission Spectrum

Description

Source

Explanation

of

spectra

Lines of certain colours on a dark

background-Hot _Bas.

lncreasing frequency

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.

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

lncaeasing wavelength questions

_to

_Try

Absorption Spectrum

Dark lines across a continuous band of colours.

White light passed

through

a coolgas.

YJCi

t1 :. ,:::. 28,29!.30

_'

l:

P2

lr.:ri

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

P''

P2 P1

:,.-:8.

''r'

cJc

P1 27,28,29,30 P2

MJc

P1

F

6lPase