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/