Expe
rimen
telle
Phy
sik
I W
S 16
/17
Vera
nstal
tung 4
0100
11
https
://cam
pus.s
tudium
.kit.e
du/ev
ent/H
7Ke2
neVD
U6OC
IWVc
uIqYw
PD D
r. And
reas B
. Mey
er (K
IT un
d DES
Y)
20. O
ktobe
r 201
6
1.1 Ph
ysika
lisch
e Grö
ßen,
Maße
inheit
en un
d Dim
ensio
nen
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Orga
nisato
risch
es
�W
ebse
iten:
�W
ebse
ite zu
Vorle
sung
und Ü
bung
en: h
ttp://e
kpww
w.ph
ysik.
uni-k
arlsru
he.de
/~rwo
lf/tea
ching
/ws1
6-17-m
echa
nik.ht
ml
�An
meldu
ng zu
den Ü
bung
en: h
ttp://w
ww.ph
ysik.
kit.ed
u/Tuto
rium/
WS1
617/P
hysik
1/
�Au
ßerde
m: ht
tp://e
kpww
w.ph
ysik.
uni-k
arlsru
he.de
/~ame
yer
�Te
rmin
e:
�Vo
rlesu
ng: 1
8. Ok
tober
2016
- 9. F
ebrua
r 201
7
�Di
ensta
gs
9:4
5 - 11
:15
�Do
nners
tags
9:45
- 11:1
5
�Ins
gesa
mt 29
Vorle
sung
en, d
er 1.1
1. ist
ein F
eierta
g
�Üb
unge
n: 26
. Okto
ber 2
016 -
8. Fe
bruar
2017
�Mi
ttwoc
h 8:00
- 9:30
(5
Grup
pen)
�Mi
ttwoc
h 9:45
- 11:1
5 (8
Grup
pen)
�Mi
ttwoc
h 11:3
0 - 13
:00 (7
Grup
pen)
�1.
Ter
min
: näc
hste
Woc
he M
ittwo
ch: 2
6.10
.201
6
�Kla
usur:
13.02
.2017
15:3
0-17:0
0 Gert
hsen
Hörs
aal u
nd H
örsaa
l Neu
e Che
mie
4
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Bure
au In
terna
tiona
l des
Poid
s et M
esur
es (B
IPM)
http
://www
.bipm
.org/e
n/mea
sure
ment-
units
/
Th
e SI
bas
e un
its a
re a
cho
ice
of s
even
wel
l-def
ined
uni
ts w
hich
by
conv
entio
n ar
e re
gard
ed a
s di
men
sion
ally
inde
pend
ent
�Th
e met
re is
the l
ength
of th
e path
trave
lled b
y ligh
t in va
cuum
durin
g a tim
e inte
rval o
f 1/29
9 792
458 o
f a se
cond
.
�Th
e kilo
gram
is th
e unit
of m
ass;
it is e
qual
to the
mas
s of th
e inte
rnati
onal
proto
type o
f the k
ilogr
am.
�Th
e sec
ond
is the
dura
tion o
f 9 19
2 631
770 p
eriod
s of th
e rad
iation
corre
spon
ding t
o the
trans
ition b
etwee
n the
two
hype
rfine l
evels
of th
e gro
und s
tate o
f the c
aesiu
m 13
3 atom
.
�Th
e am
pere
is th
at co
nstan
t cur
rent
which
, if m
aintai
ned i
n two
stra
ight p
arall
el co
nduc
tors o
f infin
ite le
ngth,
of
negli
gible
circu
lar cr
oss-s
ectio
n, an
d plac
ed 1
m ap
art in
vacu
um, w
ould
prod
uce b
etwee
n the
se co
nduc
tors a
force
eq
ual to
2 x 1
0–7 n
ewton
per m
etre o
f leng
th.
�Th
e kel
vin,
unit o
f ther
mody
nami
c tem
pera
ture,
is the
fracti
on 1/
273.1
6 of th
e the
rmod
ynam
ic tem
pera
ture o
f the t
riple
point
of w
ater.
�Th
e mol
e is t
he am
ount
of su
bstan
ce of
a sy
stem
which
conta
ins as
man
y elem
entar
y enti
ties a
s the
re ar
e atom
s in
0.012
kilog
ram
of ca
rbon
12. W
hen t
he m
ole is
used
, the e
lemen
tary e
ntitie
s mus
t be s
pecif
ied an
d may
be at
oms,
molec
ules,
ions,
electr
ons,
other
partic
les, o
r spe
cified
grou
ps of
such
partic
les.
�Th
e can
dela
is th
e lum
inous
inten
sity,
in a g
iven d
irecti
on, o
f a so
urce
that
emits
mon
ochr
omati
c rad
iation
of fre
quen
cy
540 x
1012
hertz
and t
hat h
as a
radia
nt int
ensit
y in t
hat d
irecti
on of
1/68
3 watt
per s
terad
ian.
All o
ther
SI u
nits
can
be
deriv
ed fr
om th
ese,
by
mul
tiply
ing
toge
ther
diff
eren
t pow
ers
of th
e ba
se u
nits
. 5
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Seku
nde
�Vo
r 196
0:
�So
nnen
seku
nde:
1/(24
× 60
× 60
) eine
s mittl
eren S
onne
ntage
s (Mi
ttelw
ert üb
er all
e Tag
e)
�19
60-1
967:
�Ep
heme
riden
seku
nde:
1/315
5692
5,974
7 des
tropis
chen
Jahre
s
�Se
it 19
67:
�De
finitio
n: ν(h
fs Cs
) := 91
9263
1770
Hz.
�d.h
. 1 S
ekun
de en
tspric
ht Da
uer v
on 91
9263
1770
Sch
wing
unge
n des
133 C
s Atom
s �
Gena
uigke
it Δt/t
~ 10-14
6
http://hyperphysics.phy-astr.gsu.edu/hbase/acloc.html
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Meter
�17
99 - 1
960:
�Ur
meter
(Par
is)
�Ab
gelei
tet vo
m Um
fang d
er E
rde
(10-7
eine
s Vier
tels d
es E
rdum
fangs
(Mer
idian
))
�Be
stimm
t übe
r Tria
ngula
tion
�Ge
nauig
keit Δ
ℓ/ℓ ~
10-4
�30
Kop
ien (v
ertei
lt an v
ersc
hiede
ne Lä
nder
)
�19
60 - 1
983:
�De
finitio
n übe
r Well
enlän
ge λ
von 86
Kryp
ton
be
im Ü
berg
ang 5
d5 → 2p
10
�1m
= 16
5076
3,73 ×
λ �
Gena
uigke
it Δℓ/ℓ
~ 10
-8
�Se
it 198
3: �
Defin
ition:
Stre
cke,
die Li
cht in
1/29
9792
458 s
zurü
ckleg
t.
�Ge
nauig
keit:
Δℓ/ℓ
~ 10-11
… 10
-13 (
je na
ch M
ethod
e)
7
http://www.leifiphysik.de/mechanik/gleichfoermige-bewegung/geschichte/geschichte-der-laengenmessung
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Kilog
ramm
�Se
it 179
9 �
Kilog
ramm-
Proto
typen
(Pari
s) �
Abge
leitet
von d
er Di
chte
von W
asse
r (4 o C
)
�Se
it 188
9 �
Aktue
ller K
ilogra
mm-P
rototy
p (Pa
ris)
�Pla
tin-Ir
idium
(39,1
7mm
Höhe
und D
urchm
esse
r) �
84 K
opien
, gee
icht a
uf etw
a Δm/
m ~ 5
× 10
-9
�Or
igina
l: Une
rklärt
er Ve
rlust
von M
asse
50
µg /1
00a,
also 5
× 10
-8
�Ge
genw
ärtig
: Vor
bere
itung
en fü
r die
Neu-
Defin
ition
des
Kilo
gram
m au
s Nat
urko
nsta
nten
�
Mehre
re Pr
ojekte
�
Hier:
Avog
adro-
Proje
kt, an
dem
auch
die P
hysik
alisc
h-tec
hnisc
he
Bund
esan
stalt (
PTB)
, Brau
nsch
weig,
betei
ligt is
t
8http://www.bipm.org/en/bipm/mass/ipk/Or
igina
l
Kopie
(fo
tograf
iert 1
915)
https://fr.wikipedia.org/wiki/Kilogramme
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Das A
voga
dro-
Proje
kt�
Besti
mmun
g der
Avog
adro
-Zah
l NA
�Ab
leitun
g des
Kilo
gram
m als
Mas
se ei
ner b
estim
mten
An
zahl
von A
tomen
von 28
Si
9
M =
Mola
re Ma
sse [
kg/m
ol]
N A =
Avog
adro-
Zahl
[1/mo
l] N
= G
esam
tzahl
der T
eilche
n
Quelle: www.ptb.de
Veröf
fentlic
hung
: PRL
106,
0308
01 (2
011)
m=
M NA·N
m=
M NA·n
·V
n =
Teilch
enza
hl / V
olume
n [m-3 ]
V = Vo
lumen
[m3 ]
Kuge
l aus
hoc
hrein
em 28
Si
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
�Pr
oduk
tion z
weier
Kug
eln au
s hoc
hrein
em 28
Si
(g
leich
es S
ample
)
�V
und n
: kom
plexe
inter
ferom
etrisc
he V
erfah
ren
(Bes
timmu
ng vo
n Abs
tände
n)
�M:
Mas
sens
pektr
ometr
ie (B
estim
mung
des A
nteils
von
Veru
nrein
igung
en du
rch 29
Si un
d 30Si
)
�m:
Aus
Ver
gleich
mit K
ilogr
amm-
Proto
typ
�N A
: Ber
echn
ung a
us M
nV/m
�Er
gebn
is (2
015)
�N A
= 6.0
2214
076(
12) ×
1023
mol-1
�Un
siche
rheit
: Δm/
m = 2
× 10
-8
�Er
warte
t: Ne
udef
initi
on im
Jah
r 201
8
10
Das A
voga
dro-
Proje
kt
sphere
volume,andN
iistheconcentrationof
theithpoint
defect
(see
Table
I).
Volum
e.—The
sphere
volumes
weredeterm
ined
from
diam
eter
measurementscarriedoutby
opticalinterferom
-etry.T
wodifferentinterferom
eterswereused,bothrelying
ondifferential
measurements
[10].Eachsphere
isplaced
between
theend
mirrors
(plane,in
oneinterferom
eter,
spherical,in
theother)of
aFizeaucavity
andthedistances
betweenthemirrorsandeach
sphere,as
wellas
thecavity
length,weremeasured.
Since
thesphere
isalmostperfect,
itsvolumeisthatof
amathematicalspherehaving
thesame
meandiam
eter.Hence,anumberof
diam
etersweremea-
suredandaveraged.Figure3show
sthedeviations
from
aconstant
diam
eter
inorthographic
projections.The
mea-
sureddiam
eterswerecorrectedforphaseshifts
inbeam
reflectionsat
thesphere
surface,
aswellforthebeam
retardationthroughthesurfacelayer.The
finalvolumes
aregivenin
Table
III.
Molar
mass.—The
molar
massmeasurementrequires
thattheisotopefractionsof
theenriched
Siaredeterm
ined;
theusualw
aytomeasurethem
isby
gasmassspectrom
etry
ofSiF
4.An
analysis
carried
outat
the
University
ofWarsaw
evidenced
that
the
solutionsused
toconvert
theapproxim
ately45
mgcrystalsamples
into
theSiF
4
gaswerecontam
inated
bymorethan
7!gof
naturalSi.
Thiscontam
inationrequired
acorrection
ofabout0:6!
10"6M.The
isotopefractionsweremeasuredalso
atthe
Instituteof
MineralResources
oftheChinese
Academyof
Science
stillby
gasmassspectrom
etry,butusingadiffer-
entpreparationof
theSiF
4gasbasedon
fluorination
by
BrF
5.Alsoin
this
case
thecontam
inationby
naturalSi
proved
tobe
aproblem.Furthermore,
theextrem
elyhigh
isotopic
enrichmentproved
tobe
abig
challenge;
ion
currentratios
morethan
5orders
ofmagnitude
larger
than
theunityhadto
bemeasured.
Toovercomethesedifficulties,anew
concepthasbeen
developed[11,12
].It
isbasedon
isotopedilution
mass
spectrom
etry
(IDMS)combinedwithmulticollectorinduc-
tively
coupledplasmamassspectrom
etry—withsamples
beingdissolvedin
aqueousNaO
H.T
henoveltyisthatonly
the29Siþ
and
30Siþ
currentsweremeasured;
torecoverthe
missed28Sifraction,thesamples
wereblendedwithaspike
highly
enriched
with
30Si.The
30Siþ
and
29Siþ
currents
weremeasuredforthesample,spike,andblend;
the
28Siþ
currentwas
measuredonly
forthespike.The
28Sifraction
ofthesamplewas
obtained
bydata
analysis.Calibration
was
carriedoutonline
bymixturesof
naturalSiandtwo
crystalsenriched
withthe29Siand
30Siisotopes.NaturalSi
contam
ination,
mem
oryeffects,
andoffsetsweremoni-
toredandcorrectedonline
byhaving
theNaO
Hsolutions
remeasuredbefore
each
sample,
spike,
blend,
ormixture.
The
isotopic
composition
ofthe
28Sicrystalwas
deter-
mined
also
attheInstituteforPhysics
ofMicrostructures
oftheRussian
Academyof
Sciencesby
asecondaryion
massspectrom
eter
(SIM
S)using
atime-of-flight
mass
analyzer.
Figure4
show
sthemeasured
29Siand
30Siam
ount
fractions.
The
highest
enrichments
are
observed
byID
MS
andSIM
S.Continuouslyadding
naturalSito
amaterialhaving
theisotopic
composition
determ
ined
byID
MS,the
29Siand
30Sifractionswillmovealongthe
blackline
andalso
pass
quitenear
totheothermeasure-
mentresults.Under
thisassumptiontheisotopiccomposi-
tionsdeterm
ined
byID
MSandgasmassspectrom
etry
are
consistent
witheach
other.The
IDMSdata
arethemost
accurateandhave
been
considered
only;the
relevantmolar
massvalues
aregivenin
Table
III.
NAdeterm
ination.—The
measuredvalues
ofthequanti-
ties
necessarytodeterm
ineN
Aaresummarized
inTableIII.
The
NAdeterm
inations
basedon
twospheresdifferonlyby
3ð3Þ
!10
"8N
A,thus
confi
rmingthecrystalhomogeneity.
Byaveragingthesevalues,weobtain
FIG
.3(color).
Diameter
topo
graphies
ofthesiliconspheres.
The
rainbow
colors
rang
efrom
"63
nm(blue)
to37
nm(red).
Peak-to-valleydistancesare97
nm(AVO28
-S5,
left)and89
nm(AVO28
-S8,
righ
t).
FIG
.2(color).
Top
ograph
icmapsof
thesurfacelayerthick-
ness.LeftAVO28
-S5;
righ
tAVO28
-S8.
The
rainbow
colors
rang
efrom
2.0nm
(blue)
to4.5nm
(yellow).
TABLEIII.
NAdeterm
ination.
Lattice
parameter,vo
lume,and
densityaremeasuredat
20:0
& Cand0Pa.
Quantity
Unit
AVO28
-S5
AVO28
-S8
apm
543.09
962
40(19)
543.09
961
85(20
)m
g10
00.087
560(15
)10
00.064
543(15
)V
cm3
431.05
905
9(13
)43
1.04
911
0(10
)"
kg=m
323
20.070
855(76
)23
20.071
007(63
)M
g=mol
27.976
97026
(22)
27.976
97029
(23)
NA
1023
mol
"1
6.02
214
091
(21)
6.02
214
071
(18)
PRL106,
030801
(2011)
PHYSICAL
REVIEW
LETTERS
weekending
21JA
NUARY
2011
030801-3
M =
Mola
re Ma
sse [
kg/m
ol]
V =
Volum
en [m
3 ] n
= Te
ilchen
zahl
/ Volu
men [
m-3 ] N A
= Av
ogad
ro-Za
hl [1/
mol]
Beisp
iel
Volum
enme
ssun
g:
Veröf
fentlic
hung
en u.
a.: PR
L 106
, 030
801 (
2011
), Me
trolog
ia 52
, 360
(201
5)
m=
M NA·n
·V
Andre
as B.
Mey
er
1.1. G
rößen
, Einh
eiten
und D
imen
sione
n
Exp.
Phys
ik I, 2
0. Ok
tober
2016
Ausz
ug au
s CGP
M Pr
otoko
llTh
e Ge
nera
l Con
fere
nce
on W
eigh
ts a
nd M
easu
res
(CGP
M),
at it
s 24
th m
eetin
g ta
kes
note
of
th
e in
tent
ion
of th
e In
tern
atio
nal C
omm
ittee
for W
eigh
ts a
nd M
easu
res
to p
ropo
se a
revi
sion
of t
he S
I
as fo
llows
:
�th
e In
tern
atio
nal S
yste
m o
f Uni
ts, t
he S
I, will
be th
e sy
stem
of u
nits
in w
hich
:
�the
grou
nd st
ate hy
perfin
e spli
tting f
reque
ncy o
f the C
aesiu
m 13
3 atom
Δν(13
3 Cs) h
fs is e
xactl
y 9 19
2 631
770 H
z, �
the sp
eed o
f ligh
t in va
cuum
c is
exac
tly 29
9 792
458 m
etre p
er se
cond
, �
the P
lanck
cons
tant h
is ex
actly
6.62
6 06X
×10-34
joule
seco
nd,
�the
elem
entar
y cha
rge e
is ex
actly
1.60
2 17X
×10-19
coulo
mb,
�the
Bolt
zman
n con
stant
k is e
xactl
y 1.38
0 6X
×10-23
joule
per k
elvin,
�
the Av
ogad
ro co
nstan
t NA i
s exa
ctly 6
.022 1
4X ×1
023 re
ciproc
al mo
le,
�the
lumi
nous
effic
acy K
cd of
mon
ochro
matic
radia
tion o
f freq
uenc
y 540
×101
2 Hz i
s exa
ctly 6
83 lu
men p
er wa
tt,
�Th
e ki
logr
am w
ill co
ntin
ue to
be
the
unit
of m
ass,
but
its
mag
nitu
de w
ill be
set
by
fixin
g th
e nu
mer
ical
val
ue o
f the
Pla
nck
cons
tant
to b
e eq
ual t
o ex
actly
6.6
26 0
6X ×1
0-34 w
hen
it is
exp
ress
ed in
th
e SI
uni
t m2 k
g s-1
, whi
ch is
equ
al to
Js
�…
�th
e de
finiti
on o
f the
kilo
gram
in fo
rce
sinc
e 18
89 b
ased
upo
n th
e m
ass
of th
e in
tern
atio
nal p
roto
type
of
the
kilo
gram
(1st
mee
ting
of th
e CG
PM, 1
889,
3rd
mee
ting
of th
e CG
PM, 1
901)
will
be a
brog
ated
11
http:/
/www
.bipm
.org/e
n/CGP
M/db
/24/1/