32
Phy
sics
2D
Lec
ture
Slid
esO
ct 1
5
Viv
ek S
harm
aU
CSD
Phy
sics
()
0
20
0
0
2 0
0
Pow
er in
cide
n
t on
an a
rea
A
:1
Larg
er
Poy
Ener
gy ntin
g V
ecto
r =
(
)
1.
()
1
Flow
in E
M W
Inte
nsity
of R
adia
tion
=
t
aves
S
2
I
EB
SA
AEBSin
cE
kxt
µ
ωµ µ
×
==
−
he a
mpl
itude
of O
scill
atio
nM
ore
inte
nse
is th
e ra
diat
ion
Pro
perti
es o
f EM
Wav
es: M
axw
ell’s
Equ
atio
ns
Dis
aste
rs in
Cla
ssic
al P
hysi
cs (1
899-
1922
) •
Dis
aste
r Ex
perim
enta
l ob
serv
atio
n th
at c
ould
not
be
expl
aine
d by
Cla
ssic
al th
eory
(Phy
s 2A
, 2B
, 2C
)
–D
isas
ter #
1 :
Nat
ure
of B
lack
body
Rad
iatio
n fro
m y
our B
BQ
gril
l
–D
isas
ter #
2: P
hoto
Ele
ctric
Effe
ct
–D
isas
ter #
3: S
catte
ring
light
off
elec
trons
(Com
pton
Effe
ct)
•R
esol
utio
n of
Exp
erim
enta
l Obs
erva
tion
will
requ
ire
radi
cal c
hang
es in
how
we
thin
k ab
out n
atur
e
–Q
UA
NTU
M M
EC
HA
NIC
S
•The
Art
of C
onve
rsat
ion
with
Sub
atom
ic P
artic
les
Bla
ckbo
dy R
adia
tor:
An
Idea
lizat
ion
T
Bla
ckbo
dy A
bsor
bs e
very
thin
g R
efle
cts
noth
ing
All
light
ent
erin
g op
enin
g ge
ts a
bsor
bed
(ulti
mat
ely)
by
the
cavi
ty w
all
Cav
ity in
equ
ilibr
ium
Tw
.r.t.
surr
ound
ing.
So
it ra
diat
es e
very
thin
g It
abso
rbs
Emer
ging
radi
atio
n is
a s
ampl
eof
radi
atio
n in
side
box
at t
emp
T
Pred
ict n
atur
e of
radi
atio
n in
side
Box
?
Cla
ssic
al A
naly
sis:
•Box
is fi
lled
with
EM
sta
ndin
g w
aves
•Rad
iatio
n re
flect
ed b
ack-
and-
fort
h be
twee
n w
alls
•Rad
iatio
n in
ther
mal
equ
ilibr
ium
with
wal
ls o
f Box
•How
may
wav
es o
f wav
elen
gth λ
can
fit in
side
the
box
?
less
mor
eEv
en m
ore
Sta
ndin
g W
aves
34
#
of st
andi
ng w
aves
betw
een
Wav
eleng
8V
N()d
Clas
sical
Calcu
lati
= ;
V =
ths
and
+d a
Volu
me o
f box
re
Each
stan
ding
w
on
ave
t
=
c
L
on
dπ
λ
λ
λλ
λ
λ
λ
• 44
ribut
es en
ergy
to
radi
ation
in B
oxEn
ergy
den
sity
= [#
of s
tandi
ng w
aves
/vol
ume]
Ene
rgy/
Stan
ding
Wav
e
u(
)8
8
E
kT
=
=
kT
=
k
R
T
ad
V1 V
λπ
πλ
λ×
×
×
44
cc8
2ian
cy R
() =
u(
) =
kT
k
T 4
4
Radi
ancy
is R
adiat
ion
inten
sity p
er u
nit
inter
val:
Lets
plot
it
cπ
πλ
λλ
λλ=
The
Beg
inni
ng o
f The
End
! H
ow B
BQ
Bro
ke P
hysi
cs
Pred
ictio
n : a
s λ
0 (h
igh
freq
uenc
y) ⇒
R(λ
) In
finity
! O
ops
!
Ultr
a V
iole
t (Fr
eque
ncy)
Cat
astro
phe
Expe
rimen
tal
Dat
a
Cla
ssic
al T
heor
y
RadiancyR(λ)
Dis
aste
r # 1
OO
PS !
Dis
aste
r # 2
: P
hoto
-Ele
ctric
Effe
ct
Can
tune
I, f,
λ
iLigh
t of i
nten
sity
I, w
avel
engt
h λ
and
freq
uenc
y ν
inci
dent
on
a ph
oto-
cath
ode
Mea
sure
cha
ract
eris
tics
of c
urre
nt in
the
circ
uit a
s a
fn o
f I, f
, λ
Pho
to E
lect
ric E
ffect
: Mea
sura
ble
Pro
perti
es•
Rat
e of
ele
ctro
n em
issi
on fr
om c
atho
de–
From
cur
rent
i se
en in
am
met
er
•M
axim
um k
inet
ic e
nerg
y of
em
itted
ele
ctro
n –
By
appl
ying
reta
rdin
g po
tent
ial o
n e
lect
ron
mov
ing
tow
ards
Col
lect
or
plat
e
»KM
AX
= eV
S(V
S=
Stop
ping
vol
tage
) »S
topp
ing
volta
ge
no c
urre
nt fl
ows
•Ef
fect
of d
iffer
ent t
ypes
of p
hoto
-cat
hode
met
al
•Ti
me
betw
een
shin
ing
light
and
firs
t sig
n of
pho
to-
curr
ent i
n th
e ci
rcui
t
Obs
erva
tions
: C
urre
nt V
s Fr
eque
ncy
of In
cide
nt L
ight
-VS
I 3=
3I1
I 2=
2I1
I 1=
inte
nsity
f
Sto
ppin
g V
olta
ge V
sV
sIn
cide
nt L
ight
Fre
quen
cy
f
eVS
Stop
ping
V
olta
ge
Diff
eren
t M
etal
Ph
otoc
atho
desu
rfac
es
eVS
Ret
ardi
ng P
oten
tial V
s Li
ght F
requ
ency
Shin
ing
Ligh
t With
Con
stan
t Int
ensi
tyB
ut d
iffer
ent f
requ
enci
esf 1
> f 2
>f 3
Tim
e E
laps
ed b
etw
een
Shi
ning
Lig
ht &
Cur
rent
•Ti
me
betw
een
–
Ligh
t shi
ning
on
phot
o-ca
thod
e–
And
firs
t pho
to-e
lect
ons
ejec
ted
curr
ent i
n ci
rcui
t
–D
epen
ds o
n di
stan
ce b
etw
een
light
sou
rce
& c
atho
de s
urfa
ce
–S
eem
s in
stan
tane
ous
( < 1
0-9S
econ
ds b
y th
e ex
perim
ente
r’s w
atch
)
Con
clus
ions
from
the
Exp
erim
enta
l Obs
erva
tion
•M
ax K
inet
ic e
nerg
y K
MA
Xin
depe
nden
tof I
nten
sity
I fo
r lig
ht o
f sam
e fr
eque
ncy
•N
oph
otoe
lect
ric e
ffec
t occ
urs i
f lig
ht fr
eque
ncy
f is
belo
w a
thre
shol
d no
mat
ter h
ow h
igh
the
inte
nsity
of
light
•Fo
r a p
artic
ular
met
al, l
ight
with
f >
f 0 ca
uses
ph
otoe
lect
ric e
ffec
t IR
RES
PEC
TIV
E of
ligh
t int
ensi
ty.
–f 0
is c
hara
cter
istic
of t
hat m
etal
•Ph
otoe
lect
ric e
ffec
t is i
nsta
ntan
eous
!...n
ot ti
me
dela
y
Can
one
Exp
lain
all
this
Cla
ssic
ally
!
•A
s lig
ht In
tens
ity in
crea
sed ⇒
field
am
plitu
de la
rger
–E
fiel
d an
d el
ectri
cal f
orce
see
n by
the
“cha
rged
sub
atom
ic o
scill
ator
s”La
rger
• •M
ore
forc
e ac
ting
on th
e su
bato
mic
cha
rged
osc
illat
or•⇒
Mor
e en
ergy
tran
sfer
red
to it
•⇒
Cha
rged
par
ticle
“ho
oked
to th
e at
om”
shou
ld le
ave
the
surf
ace
with
m
ore
Kin
etic
Ene
rgy
KE
!! T
he in
tens
ity o
f lig
ht sh
inin
g ru
les !
•A
s lon
g as
ligh
t is i
nten
se e
noug
h, l
ight
of A
NY
freq
uenc
y f s
houl
d ca
use
phot
oele
ctric
eff
ect
•B
ecau
se th
e En
ergy
in a
Wav
e is
uni
form
ly d
istri
bute
d ov
er th
e Sp
heric
al w
avef
ront
inci
dent
on
cath
ode,
thou
ldbe
a n
otic
eabl
e tim
e la
g ∆T
betw
een
time
is in
cide
nt &
the
time
a ph
oto-
elec
tron
is
ejec
ted
: Ene
rgy
abso
rptio
n tim
e –
How
muc
h tim
e ?
Lets
cal
cula
te it
cla
ssic
ally
.
Cla
ssic
al E
xpla
natio
n of
Pho
to E
lect
ric E
ffect
E
FeE
=
Cla
ssic
al P
hysi
cs: T
ime
Lag
in P
hoto
-Ele
ctric
Effe
ct
•El
ectro
n ab
sorb
s ene
rgy
inci
dent
on
a su
rfac
e ar
ea w
here
the
elec
tron
is c
onfin
ed ≅
size
of a
tom
in c
atho
de m
etal
•El
ectro
n is
“bo
und”
by a
ttrac
tive
Cou
lom
b fo
rce
in th
e at
om, s
o it
mus
t abs
orb
a m
inim
um a
mou
nt o
f rad
iatio
n be
fore
its s
tripp
ed o
ff
•Ex
ampl
e : L
aser
ligh
t Int
ensi
ty I
= 12
0W/m
2 on
Na
met
al–
Bin
ding
ene
rgy
= 2.
3 eV
= “W
ork
Func
tion”
–E
lect
ron
conf
ined
in N
a at
om, s
ize
≅0.
1nm
..ho
w lo
ng b
efor
e ej
ectio
n ?
–Av
erag
e P
ower
Del
iver
ed P
AV
= I
. A
, A
= πr
2 ≅
3.1
x 10
-20
m2
–If
all e
nerg
y ab
sorb
ed th
en ∆
E =
PA
V. ∆
T ⇒
∆T =
∆E
/ P
AV
–C
lass
ical
Phy
sics
pre
dict
s M
easu
rabl
e de
lay
even
by
the
prim
itive
clo
cks
of 1
900
–B
ut in
exp
erim
ent,
the
effe
ct w
as o
bser
ved
to b
e in
stan
tane
ous
!!
–C
lass
ical
Phy
sics
fails
in e
xpla
inin
g al
l res
ults
& g
oes
to
DO
GH
OU
SE
!
19
220
2
(2.3
)(1.6
10/
)0.
10
(1
20/
)(3.
110
)eV
JeV
TS
Wm
m
−
−
×∆
==
×
Max
Pla
nck
& B
irth
of Q
uant
um P
hysi
cs
Plan
ck n
oted
the
Ultr
aVio
letC
atas
troph
e a
t hig
h fr
eque
ncy
“Coo
ked”
cal
cula
tion
with
new
“id
eas”
so a
s brin
g:R
(λ)
0 as
λ0
f ∞
Bac
k to
Bla
ckbo
dy R
adia
tion
Dis
crep
ancy
•C
avity
radi
atio
n as
equ
ilibr
ium
exc
hang
e of
ene
rgy
betw
een
EM
radi
atio
n &
“at
omic
” os
cilla
tors
pre
sent
on
wal
ls o
f cav
ity•
Osc
illat
ors c
an h
ave
any
freq
uenc
y f
•B
ut th
e En
ergy
exc
hang
e be
twee
n ra
diat
ion
and
osci
llato
r NO
T co
ntin
uous
and
arb
itara
ry…
it is
dis
cret
e …
in p
acke
ts o
f sam
e am
ount
•E
= n
hf, w
ith n
= 1
,2 3
…. ∞
h =
cons
tant
he
inve
nted
, a v
ery
smal
l num
ber h
e m
ade
up
Pla
nck,
Qua
ntiz
atio
n of
Ene
rgy
& B
B R
adia
tion
•K
eep
the
rule
of c
ount
ing
how
man
y w
aves
fit i
n a
BB
Vol
ume
•R
adia
tion
Ener
gy i
n ca
vity
is q
uant
ized
•
EM st
andi
ng w
aves
of f
requ
ency
f ha
ve e
nerg
y •E
= n
hf(
n =
1,2
,3 …
10 …
.100
0…)
•Pr
obab
ility
Dis
tribu
tion:
At a
n eq
uilib
rium
tem
p T,
po
ssib
le E
nerg
y of
wav
e is
dis
tribu
ted
over
a
spec
trum
of s
tate
s: P
(E) =
e(-
E/kT
)
•M
odes
of O
scill
atio
n w
ith :
•Les
s ene
rgy
E=hf
= fa
vore
d •M
ore
ener
gy E
=hf
= di
sfav
ored
hf
P(E)
E
e(-E/
kT)
By
this
stat
istic
s, la
rge
ener
gy, h
igh
f mod
es o
f EM
dis
favo
red
Pla
nck’
s C
alcu
latio
n
2x
2
4
3
8(
)4
O
dd l
ooki
ng f
orm hc
Whe
n
larg
e
sm
all
kT
1
1
11
(...
.]
Rec
all e
1
11
....
2!
2
=
3!
hc kT
hc kT
hc
e
hchc
ekT
kTh
x
c
c
x
R
x
λ
λ
π
λ
λ
λ
λ
λλ
λ
λ
+
⎛⎞⎛
⎞=⎜
⎟⎜⎟
⎝⎠⎝
⎡⎤
⎛⎞
⎢⎥
⎜⎟
⎢⎥
⎜⎟
−⎝
⎠⎣
⎦
⎛⎞
−=
⎠
→⇒
→
=+
+
++
+−
⇒
+ ⎜⎟
⎝⎠
4
8
plu
ggin
g th
is in
R(
) eq
:
)
(
4cR
kThc kT
λ
λ
λπ λ
⎛⎞⎛
⎞=⎜
⎟⎜⎟
⎝⎠⎝
⎠
Gra
ph &
Com
pare
With
BB
Q d
ata
Pla
nck’
s Fo
rmul
a an
d S
mal
l λ
4
Wh
en
is
smal
l (l
arg
e f)
11
1S
ub
stit
uti
ng
in
R(
) eq
n:
Just
as
seen
in
th
e ex
per
imen
t
As
0,
8(
)4
()
0al
dat
0
a
hc kT
h
hc
hc
kTkT
c k
c kT
T
hc
Re
R
e
e
ee
λλ
λλ
λ
πλ
λ
λ
λ
λλ
−−
−
⎛⎞⎛
⎞=⎜
⎟⎜
⎟⎝
⎠⎝
⎠
→
→→
≅=
−
⇒
Pla
nck’
s E
xpla
natio
n of
BB
Rad
iatio
n
Fit f
orm
ula
to E
xpta
ldat
ah
= 6.
56 x
10-3
4J.S
= ve
ry v
ery
smal
l
Con
sequ
ence
of P
lanc
k’s
Form
ula
Ein
stei
n’s
Exp
lana
tion
of P
hoto
elec
tric
Effe
ct
•En
ergy
ass
ocia
ted
with
EM
wav
es in
not
uni
form
ly
dist
ribut
ed o
ver w
ave-
fron
t, ra
ther
is c
onta
ined
in p
acke
ts
of “
stuf
f”⇒
PHO
TON
•E=
hf
= h
c/λ
[ but
is it
the
sam
e h
as in
Pla
nck’
s th.
?]•
Ligh
t shi
ning
on
met
al e
mitt
er/c
atho
de is
a st
ream
of
phot
onso
f ene
rgy
whi
ch d
epen
ds o
n fr
eque
ncy
f•
Phot
ons k
nock
off
ele
ctro
n fr
om m
etal
inst
anta
neou
sly
–Tr
ansf
er a
ll en
ergy
to e
lect
ron
–E
nerg
y ge
ts u
sed
up to
pay
for W
ork
Func
tion Φ
(Bin
ding
Ene
rgy)
•
Res
t of t
he e
nerg
y sh
ows u
p as
KE
of e
lect
ron
KE
= hf
-Φ•
Cut
off F
requ
ency
hf 0
= Φ
(pop
s an
elec
tron,
KE
= 0)
•La
rger
inte
nsity
I m
ore
phot
ons i
ncid
ent
•Lo
w fr
eque
ncy
light
fno
t ene
rget
ic e
noug
h to
ov
erco
me
wor
k fu
nctio
n of
ele
ctro
n in
ato
m
Ein
stei
n’s
Exp
lana
tion
of P
hoto
Ele
ctric
Effe
ct
Pho
to E
lect
ric &
Ein
stei
n (N
obel
Priz
e 19
15)
-VS
I 3=
3I1
I 2=
2I1
I 1=
inte
nsity
Ligh
t shi
ning
on
met
al c
atho
de is
mad
e of
pho
tons
Each
of t
he sa
me
ener
gy E
, dep
ends
on
freq
uenc
y f
E =
hf=
h (c
/λ)
This
QU
AN
TA u
sed
to k
nock
off
ele
ctro
n &
giv
e K
EE
= h
f=
KE
+ ϕ
⇒K
E =
hf-ϕ
Pho
to E
lect
ric &
Ein
stei
n (N
obel
Priz
e 19
15)
Ligh
t shi
ning
on
met
al c
atho
de is
mad
e of
pho
tons
Qua
ntum
of E
nerg
y E
= h
f=
KE
+ ϕ
⇒K
E =
hf-ϕ
Shin
ing
Ligh
t With
Con
stan
t Int
ensi
ty
f 1 >
f 2 >
f 3
Is “h
” sam
e in
Pho
toel
ectri
c E
ffect
as
BB
Rad
iatio
n?
Slop
e h
= 6
.626
x 1
0-34 JS
Eins
tein
N
obel
Priz
e!
No
mat
ter w
here
you
trav
el
in th
e ga
laxy
and
bey
ond…
..no
mat
ter w
hat e
xper
imen
tY
ou d
o
h : P
lanc
k’s c
onst
ant i
s sam
e
NO
BEL
PR
IZE
FOR
PLA
NC
K
Wor
k Fu
nctio
n (B
indi
ng E
nerg
y) In
Met
als
22
Lig
ht o
f Int
ensi
ty I
= 1.
0 W
/cm
inc
A
Pho
toel
ectr
ic E
ffec
t on
An
Iron
Sur
fa
ssum
e Fe
refl
ects
96%
of l
igh
ce:
furt
her o
n
iden
t on
ly 3
% o
f
1.0
cm s
urfa
inci
dent
li
ce o
f
ght i
i
Ft
e
s V
µ
2(a
) Int
ensi
ty a
vaila
ble
for P
h. E
l eff
I =3
olet
regi
on (
= 25
0nm
) b
arel
y ab
ove
thre
sec
t
(b) h
ow m
hold
freq
uenc
y fo
r Ph
any
phot
o-el
ectr
ons
e
. El e
ffec
mitt
ed p
er
t
#
s%
4%(1
.0
W/c
econ
d ?
m)
of
λ
µ×
×
8
9
34
2 9
Pow
er
= h
fhc
(250
10)(1
.210
/)
=
(6.6
10)(
3.0
1
p3%
4
0/
)
hoto
%(1
.0
W/c
elec
tro
mn
)
s
mJs
Js
ms
µλ
−−
−
=
××
××
××
i
10
-15
9
151
-19
0
9
=
(c
) Cur
rent
in A
mm
eter
: i =
(1.6
10)(1
.510
)(d
) Wor
k Fu
nctio
n =
()(
)
2.4
10h
4.14
1
1.5
10
f1.
110
0
=
4.5
eV
CA
seV
s
−
−
××
=
Φ=
×
×
××
i
Pho
ton
& R
elat
ivity
: Wav
e or
a P
artic
le ?
•Ph
oton
ass
ocia
ted
with
EM
wav
es, t
rave
l with
spee
d =c
•
For l
ight
(m =
0) :
Rel
ativ
ity sa
ys E
2 =
(pc)
2 +
(mc2 )
2
•⇒
E =
pc•
But
Pla
nck
tells
us :
E =
hf=
h (c
/λ)
•Pu
t the
m to
geth
er :
hc/λ
= pc
–
⇒p
= h/λ
–M
omen
tum
of t
he p
hoto
n (li
ght)
is in
vers
ely
prop
ortio
nal t
o λ
•B
ut w
e as
soci
ate λ
with
wav
es &
p w
ith
parti
cles
….w
hat i
s goi
ng o
n??
–A
new
par
adig
m o
f con
vers
atio
n w
ith th
e su
bato
mic
par
ticle
s : Q
uant
um P
hysi
cs
Pho
to E
lect
ric &
Ein
stei
n (N
obel
Priz
e 19
15)
Ligh
t shi
ning
on
met
al c
atho
de is
mad
e of
pho
tons
Qua
ntum
of E
nerg
y E
= h
f=
KE
+ ϕ
⇒K
E =
hf-ϕ
Stop
ping
V
olta
ge
Diff
eren
t M
etal
Ph
otoc
atho
desu
rfac
es
