Boh
r’s E
xpla
natio
n of
Hyd
roge
n lik
e at
oms
•B
ohr’
s Sem
icla
ssic
alth
eory
exp
lain
ed so
me
spec
trosc
opic
da
ta
Nob
el P
rize
: 192
2•
The
“hot
ch-p
otch
” of
cla
sica
l& q
uant
um a
ttrib
utes
left
man
y (E
inst
ein)
unc
onvi
nced
–“a
ppea
red
to m
e to
be
a m
iracl
e –
and
appe
ars
to m
e to
be
a m
iracl
e to
day
......
One
oug
ht to
be
asha
med
of t
he s
ucce
sses
of t
he th
eory
”
•Pr
oble
ms w
ith B
ohr’
s the
ory:
–Fa
iled
to p
redi
ct IN
TEN
SIT
Y o
f spe
ctra
l lin
es
–Li
mite
d su
cces
s in
pre
dict
ing
spec
tra o
f Mul
ti-el
ectro
n at
oms
(He)
–Fa
iled
to p
rovi
de “
time
evol
utio
n ” o
f sys
tem
from
som
e in
itial
stat
e–
Ove
rem
phas
ized
Par
ticle
nat
ure
of m
atte
r-cou
ld n
ot e
xpla
in th
e w
ave-
parti
cle
dual
ity o
f lig
ht
–N
o ge
nera
l sch
eme
appl
icab
le to
non
-per
iodi
c m
otio
n in
sub
atom
ic
syst
ems
•“C
onde
mne
d” a
s a o
ne tr
ick
pony
! W
ithou
t fun
dam
enta
l in
sigh
t …ra
ised
the
ques
tion
: Why
was
Boh
r suc
cess
ful?
Ato
mic
Exc
itatio
n by
Ele
ctro
ns: F
ranc
k-H
ertz
Exp
tO
ther
way
s of E
nerg
y ex
chan
ge a
re a
lso
quan
tized
! Ex
ampl
e:
•Tr
ansf
er e
nerg
y to
ato
m b
y co
llidi
ng e
lect
rons
on
it•
Acc
eler
ate
elec
trons
, col
lide
with
Hg
atom
s, m
easu
re e
nerg
y tra
nsfe
r in
inel
astic
col
lisio
n (r
etar
ding
vol
tage
)
Ato
mic
Exc
itatio
n by
Ele
ctro
ns: F
ranc
k-H
ertz
Exp
tPl
ot #
of e
lect
rons
/tim
e (c
urre
nt) o
verc
omin
g th
e re
tard
ing
pote
ntia
l (V
)
Equa
lly sp
aced
Max
ima
and
min
ima
in I-
V c
urve
Ato
ms a
ccep
t onl
y di
scre
te a
mou
nt o
f Ene
rgy,
no
mat
ter t
he fa
shio
n in
whi
ch e
nerg
y is
tran
sffe
red
∆E
∆E
Prin
ce L
ouis
e de
Bro
glie
•K
ey to
Boh
r ato
m w
as A
ngul
ar m
omen
tum
qua
ntiz
atio
n•
Why
Qua
ntiz
atio
n m
vr=
|L|
= nh
/2π
?•
Invo
king
sym
met
ry in
nat
ure
the
Prin
ce d
eBro
glie
post
ulat
ed
–B
ecau
se p
hoto
ns h
ave
wav
e an
d pa
rtic
le li
ke n
atur
e pa
rtic
les
mus
t hav
e w
ave
like
prop
ertie
s –
Elec
tron
s ha
ve a
ccom
pany
ing
“pilo
t” w
ave
(not
EM
) whi
ch g
uide
pa
rtic
les
thru
spa
cetim
e.
•M
atte
r Wav
e :
–“P
ilot w
ave”
of
Wav
elen
gth λ=
h /
p =
h / (γm
v)–
freq
uenc
y
f = E
/ h
•If
mat
ter
has w
ave
like
prop
ertie
s the
n th
ere
wou
ld b
e in
terf
eren
ce (d
estr
uctiv
e &
con
stru
ctiv
e)•
Use
ana
logy
of s
tand
ing
wav
es o
n a
pluc
ked
stri
ng to
ex
plai
n th
e qu
antiz
atio
n co
nditi
on o
f Boh
r or
bits
Mat
ter W
aves
: H
ow b
ig, h
ow s
mal
l
3434
1.W
avel
engt
h of
bas
ebal
l, m
=140
g, v
=27m
/sh
6.63
10.
=
p(.1
4)(
27/
)
size
of n
ucle
us
Bas
ebal
l "lo
oks"
2. W
avel
engt
h of
ele
ctr
like
a pa
rticl
e
1.75
10
baseball
hJs
mv
kgms
m
λ
λ−
−×
=
<<<
=
⇒
×=
⇒
1
2
-31
19
-24
3
20
4
4
on K
=120
eV (a
ssum
e N
R)
pK
=2
2m
=
2(9.
1110
)(120
)(1.6
10)
=5.
91 1
0.
/6.
6310 Siz
e
.5.
9110
./
of
at
1
o
1.12
0e
e
pmK
eV
Kgms
Js
kgms
hm
p
λ
λ
−
−
−−
⇒=
××
×
×=
=×
⇒
=×
m !!
Mod
els
of V
ibra
tions
on
a Lo
op: M
odel
of e
in a
tom
Mod
es o
f vib
ratio
n w
hen
a in
tegr
al
# of
λfit
into
lo
op( S
tand
ing
wav
es)
vibr
atio
ns c
ontin
ue
Inde
finite
ly
Frac
tiona
l # o
f wav
es in
a
loop
can
not
per
sist
due
to
dest
ruct
ive
inte
rfer
ence
De
Bro
glie
’sE
xpla
natio
n of
Boh
r’s Q
uant
izat
ion
Stan
ding
wav
es in
H a
tom
:
sCon
stru
ctiv
e in
terf
eren
ce w
hen
n =
2r
Ang
ular
mom
entu
m
Qua
ntiz
atio
n co
ndit
ince
h=
p
....
..
io!
()
2
n
h mNR
nhr
m nmvr
v
v
λπ λ
π⇒ ⇒
=
==n
= 3
This
is to
o in
tens
e ! M
ust v
erify
such
“lo
ony
tune
s” w
ith e
xper
imen
t
Rem
inde
r: Li
ght a
s a
Wav
e : B
ragg
Sca
tterin
g E
xpt
Inte
rfer
ence
Pa
th d
iff=2
dsinϑ
= nλ
Ran
ge o
f X-r
ay w
avel
engt
hs sc
atte
rO
ff a
cry
stal
sam
ple
X-r
ays c
onst
ruct
ivel
y in
terf
ere
from
C
erta
in p
lane
s pro
duci
ng b
right
spot
Ver
ifica
tion
of M
atte
r Wav
es: D
avis
son
& G
erm
erE
xpt
If e
lect
rons
hav
e as
soci
ated
wav
e lik
e pr
oper
ties
expe
ct in
terf
eren
ce
patte
rn w
hen
inci
dent
on
a la
yer o
f ato
ms (
refle
ctio
n di
ffra
ctio
n gr
atin
g) w
ith in
ter-
atom
ic se
para
tion
d su
ch th
at
path
diff
AB
= ds
inϑ
= nλ
Laye
r of N
icke
l ato
ms
Ato
mic
latti
ce a
s diff
ract
ion
grat
ing
Ele
ctro
ns D
iffra
ct in
Cry
stal
, jus
t lik
e X
-ray
s
Diff
ract
ion
patte
rn
prod
uced
by
600
eVel
ectro
ns in
cide
nt o
n a
Al f
oil t
arge
t
Not
ice
the
wax
ing
and
wan
ing
of
scat
tere
d e
lect
ron
Inte
nsity
.
Wha
t to
expe
ct if
el
ectro
n ha
d no
wav
e lik
e at
tribu
te
Dav
isso
n-G
erm
erE
xper
imen
t: 54
eV
elec
tron
Bea
m
Scattered Intensity
Pola
r Plo
tC
arte
sian
plo
t
max
Max
scat
ter a
ngle
Pola
r gra
phs o
f DG
exp
twith
diff
eren
t ele
ctro
n ac
cele
ratin
g po
tent
ial
whe
n in
cide
nt o
n sa
me
crys
tal (
d =
cons
t)
Peak
at Φ
=50o
whe
n V
acc
= 54
V
Ana
lyzi
ng D
avis
son-
Ger
mer
Exp
twith
de
Bro
glie
idea
10ac
c
acc
22
de B
rogl
ie
for e
lect
ron
acce
lera
ted
thru
V=5
4V
12
; 2
2If
you
belie
ve d
e B
rogl
ie
h=
2
(de
Br
2
V =
54
Vol
ts1.
6og
p2
Flie
)Ex
ptal
d7
10
or
predict
peV
mv
KeV
vm
m
hh
mv
eVm
m
eVpmvm
m
h meV
m
λ
λλ
λ−
•=
==
⇒=
==
=
=
×
=
=
⇒=
nick
elm
-10
ax
ata
from
Dav
isso
n-G
erm
er O
bser
vatio
n:
Diff
ract
ion
Rul
e : d
sin
=
=2.1
510
(fro
m B
ragg
Sca
tterin
g)
(obs
erva
tion
from
scat
terin
g in
tens
ity p
n
d=2
.15
A
50lo
o
)
F
t
rP
odiff
m
θ
φλ
=
⇒
×
pred
oic
t
obse
rv
1.67
rinci
pal M
axim
a (n
=1);
=
agr
eem
ent
(2.1
5 A
)(si
n =
150
).6
5 meas
AExcellent
Aλ
λλ
=
Elec
tron
Mic
rogr
aph
Show
ing
Bac
terio
phag
eV
iruse
s in
E. C
oli b
acte
rium
The
bact
eriu
m is
≅1µ
size
Ele
ctro
n M
icro
scop
e : E
xcel
lent
Res
olvi
ng P
ower
Just
WH
AT
is W
avin
g in
Mat
ter W
aves
?•
For w
aves
in a
n oc
ean,
it’s
the
wat
er th
at “
wav
es”
•Fo
r sou
nd w
aves
, it’s
the
mol
ecul
es in
med
ium
•
For l
ight
it’s
the
E&
Bve
ctor
s •
Wha
t’s w
avin
g fo
r mat
ter
wav
es ?
–It’
s th
e PR
OB
AB
LILI
TY O
F FI
ND
ING
TH
E PA
RTI
CLE
that
w
aves
!–
Part
icle
can
be
repr
esen
ted
by
a w
ave
pack
et in
•
Spac
e •
Tim
e •
Mad
e by
supe
rpos
ition
of
man
y si
nuso
idal
wav
es o
f di
ffer
ent λ
•It
’s a
“pu
lse”
of p
roba
bilit
y
Imag
ine
Wav
e pu
lse
mov
ing
alon
g a
strin
g: it
s loc
aliz
ed in
tim
e an
d sp
ace
(unl
ike
a pu
re h
arm
onic
wav
e)
Wav
e pa
cket
repr
esen
ts p
artic
le p
rob
loca
lized
Mak
ing
Wav
e pa
cket
s w
ith S
inus
oida
l Wav
es: M
odel
11
12
12
12
ff
f-f
Wa
Ex:
Phe
nom
enon
of "
Bea
ting"
A
dd tw
o w
aves
of s
light
ly d
iffer
ent
, f
Star
t with
two
wav
es
y(
),
in S
ve w
ith :
f =
, Am
p
ound
litud
e A
2
:
y
2
ACoskxwt
ACos
λ+
⎛⎞
⎛⎞
⇒∝
⎜⎟
⎜⎟
⎝
=−
=
⎠⎝
⎠
22
2(
):,
2kxwtk
wf
ππ
λ−
==