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ZEEMAN EFFECT

THEORY

The spl i t t i ng of t he spect r al l i nes of a l i ght sour ce by an appl i ed

magnet i c f i el d i s cal l ed Zeeman ef f ect . I n t hi s exper i ment , t he spect r al

l i nes of a cadmi um l i ght sour ce ar e exami ned. The emi ssi on of t he r ed l i ne

( = 643. 8 nm) , of t he cadmi um at om i s mai nl y pr oduced by t he

11

21

P5D5 t r ans i t i on.

The r ed l i ne of cadmi um i s spl i t i n t he magnet i c f i el d i nt o t wo outer

- component s and one - component . Thi s appl i es t o t r ansver se vi ewi ng, t hat

i s, obser vat i on per pendi cul ar t o t he di r ecti on of t he magnet i c f i el d. Al l

t hr ee vi si bl e l i nes of t hi s Lor ent z- t r i pl et are l i near l y pol ar i zed. The

cent r al l i ne, whi ch cor r esponds t o t he spect r al l i ne of t he l i ght sour ce

( i n t he absence of an appl i ed magnet i c f i el d) , i s pol ar i zed i n di r ect i on of

t he magnet i c f i el d, whi l e t he t wo out er l i nes ar e pol ar i zed per pendi cul ar

t o t he di r ect i on of t he magnet i c f i el d. However , when vi ewi ng i n t he

l ongi t udi nal di r ecti on, i . e. , i n t he di r ecti on of t he ext er nal magnet i c

f i el d, a doubl et i s obser ved. No cent r al l i ne i s vi si bl e her e. The t wospl i t l i nes ar e ci r cul ar l y pol ar i zed agai nst each ot her .

The spl i t t i ng ment i oned above i s a consequence of t he addi t i onal energy

shi f t r esul t i ng f r om t he i nt er act i on of t he el ect r oni c magneti c moment wi t h

t he magnet i c f i el d. The corr espondi ng f r equency shi f t can be expr essed as:

1 eB

4 m =

wher e i s t he Lar mor f r equency.

To obser ve t he spl i t t i ng of spect r al l i nes i n magnet i c f i el d, a

spect r oscope of hi gh resol vi ng power i s r equi r ed. I n the exper i ment al

assembl y a Lummer- Gehr cke pl ate, wi t h a r esol vi ng power of approxi matel y

500000, i s used.

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From t he vi si bl e di spl acement of t he spect r al l i nes a measur abl e change of

t he wavel engt h or f r equency i s obt ai ned. The two - component s ar e shi f t ed,

f or exampl e, t o a f r equency + or - , wher e

Bme

41

=

wher e

B = magnet i c f l ux densi t y ( t esl as)

= f r equency shi f t

i s t o be deri ved f r om t he r esol ut i on of t he Lummer - Gehr cke pl ate and

f r om t he wavel engt h di spl acement det er mi ned at a cer t ai n B.

Usi ng t he vel oci t y of l i ght ,c = 2/c = .

The di f f er ences of wavel engt h obser ved at a Lummer - Gehrcke pl at e ar e

)1n(d2

1n

s

ds

2

22

=

ds = di st ance of one of t he spl i t l i nes f r om t he or i gi nal posi t i on of t he

i nt er f er ence l i nes ( wi t hout magnet i c f i el d)

s = di st ance bet ween t wo adj acent i nt erf erence l i nes wi t hout magnet i c

f i el d

= wavel ength of t he r ed l i ne of cadmi um= 643. 8 nm

n = r ef r act i ve i ndex of t he Lummer- Gehr cke quar t z gl ass = 1. 4567

d = t he t hi ckness of t he Lummer - Gehr cke pl at e = 4. 04 mm

The e/ m r at i o can t hen be cal cul at ed by usi ng t he f ol l owi ng f or mul a:

)1n(d2

1n

s

ds

B

c4

m

e

2

2

=

( See Ref erence pr ovi ded by Lab)

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EXPERI MENT

Caut i on: Before turning on the magnet current, make sure that the pole

shoes of the magnet are firmly screwed on. When the field is

turned on, do not bring any magnetic objects near the spectral

lamp.

1) Positioning of the cadmium lamp between the pole shoes of the magnet.Ti ghten t he t wo capst an- head scr ews on t he spect r al l amp hol der and on

t he pol e shoes. Tur n t he l amp so t hat i t poi nt s t owar ds t he si de of t he

el ectr i cal connecti ons and di agonal l y t o t he di r ecti on of t he f i el d.

2) Turn on t he power suppl y t o t he cadmi um l amp. Al l ow 5 mi nutes f or t her ed cadmi um l i ne t o be suf f i ci ent l y i nt ense.

3) Pre-adjustment with eyepiece removed.a) Shi f t t he opt i cal system i n a r i ght - l ef t di rect i on unt i l a f i ne

st r ai ght pat t ern can be seen on the Lummer- Gehr cke pl ate.

b) Adj ust t he hei ght of t he Lummer - Gehr cke pl at e unt i l i t i s l evel wi t ht he cadmi um l amp ( t he scr ew t o do t hi s i s at t he base of t he col umn

of t he opt i cal syst em) .

Repeat ( a) and ( b) unt i l a br i ght and cl ear l i ne pat t er n can be seen

above and underneath t he Lummer- Gehr cke pl ate. Repl ace t he eyepi ece. By

movi ng t he t ube of t he eyepi ece, br i ng t he spect r al l i ne i nt o f ocus.

Focus t he gr at i cul e by t ur ni ng t he eyepi ece.

Caution: Dur i ng f ocusi ng, t he eyepi ece can come of f easi l y, so handl e

t he eyepi ece wi t h car e.

4) Put t he mi cr ometer gauge, wi t h t he probe t i p f aci ng downwards, i nto thehol der , l ocat ed to the l ef t of t he Lummer - Gehr cke pl at e.

5) Calibration of the magnetic field as a function of the magnet current.Turn of f t he cadmi um l amp and pul l i t out of i t s hol der . Cal i brat e t he

t angent i al f i el d pr obe.

Connect t he el ect r omagnet t o t he st abi l i zed power suppl y uni t as shown

i n Fi g. 1.

Turn on t he power suppl y uni t .

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Wi t h t he t angent i al f i el d pr obe i n t he posi t i on of t he cadmi um l amp,

measur e pai r s of cur r ent I and magnet i c f l ux densi t y B f or I up t o

20 A. Pl ot a di agr amof B ver sus I . Comment on your pl ot .

Fig. 1: Connection of the electromagnet

6) Measurement of the separation (s) of the line pattern at B = 0 tesla.Turn of f t he coi l cur r ent . Put t he cadmi um l amp back i n i t s hol der and

t ur n i t on. Al l ow 5 mi nut es f or t he l amp t o war m up.

Make the cr osshai r i n the eyepi ece and t he l i ne whi ch needs t o be

measured coi nci de and set t he mi cr ometer cl ockwi se t o zero. By t ur ni ng

t he scr ew at t he bot t om of t he cl ockwor k, make t he cr osshai r i n t he

eyepi ece coi nci de wi t h t he next l i ne and t hen r ead t he separ at i on s

bet ween adj acent l i nes on t he mi cr ometer cl ockwork.

7) Measurement of the Zeeman splitting ds (distance between twoneighbouring lines of a triplet).

Turn on magnet i c f i el d ( I = 20 A) , wat ch t he spl i t t i ng of t he l i ne i nto

t hr ee component s. Rot at e t he pol ar i zat i on f i l t er t o f i l t er out t he

mi ddl e l i ne whose posi t i on i s i ndependent of magnet i c f i el d.

Make the cr oss i n t he eyepi ece coi nci de wi t h the l owest component of

t he t r i pl et . Set t he mi cr omet er cl ockwork t o zer o and measure t hespl i t t i ng 2( ds) whi ch i s dependent on magnet i c f i el d.

Note: Because t he syst em of l i nes gener ated by t he Lummer- Gehr cke

pl at e i s not equi di st ant , ds and s must be measur ed on t he

same t r i pl et .

8) Sl owl y r educe the cur r ent and observe t he dependence of t he spl i t t i ngon t he magnet i c f i el d. Descr i be your obser vat i ons.

9) Cal cul at e e/ m. I ncl ude an er r or anal ysi s. Comment on your r esul t s.Revised 2005