R e t h in k in g Ma t t e r

I m age is in the public domain.

8 .2 2 5 / S T S .0 4 2 , Ph y s ic s in the 2 0 th C e ntur y Pr of e s s or Da v id K a is e r , 5 O c tobe r 2 0 2 0

“ Ol d Q uan t um T h e o r y ” ( ~ 1900 – 1924*)

t od a y ’ s t op ic

* d ates ar e appr o xi m ate! A s w e w i l l see , ph ysi ci sts d ebated and r ev i si ted eac h of these topi cs o v e r a s p a n o f y e a r s .

A t o m ic St r u c t u re

D m i t r i M en d el eev ’ s o r ig i n a l p er i o d i c t a bl e of t he e l e m e nt s , 1 8 6 9

Image is in the public domain.

By t h e 1 8 8 0 s , m a t t e r s e e m e d t o b e w e l l u nd e r stood : c he m ic a l e le m e nts c onsisting of p h y s i c al at o m s .

C l ou d c ha m be r phot og r a phs , e a r l y 1 9 0 0 s

California Institute of Technology. All rights

reserved. This content is excluded from our Creative Commons license. For more information,

see https://ocw.mit.edu/help/faq-fair- use/

T hi ngs F a l l A pa r t

1896 : r a di oa ct i vi t y

1897 : ca t hod e

L ab o r at o r y ( Cam b r i d g e U n i v e r s i t y ) , c a. 1897

Images are in the public domain.

P i erre an d M ari e C u ri e i n t h ei r P ari s l ab o rat o ry , e arl y 1 9 0 0 s

r a y s

T he new f i ndi ngs sug g est ed t ha t a t om s ca n f a l l apar t, and that the y ha v e i nte r nal st r uct ur e . H e n c e t h e y ar e not r e al l y “ atom s” ! (T he anc i e nt G r e e k w or d “ ato m ” m e an s “ i n d i v i s i b l e . ” )

B y 1 9 0 0 , re s e arc h e rs h ad i d e nti fi e d at l e ast thr e e d i sti nc t t ypes of new r a di a t i ons . T hey h a d d iffe re n t p ro p e r t ie s — s o m e w e re e asi l y d e f l e c te d b y m ag ne ti c f i el ds , ot her s coul d ‘ f og’ phot og r aphi c pl at es — so re s e a rc h e rs a s s ig n e d th e m

d i ffe re n t n am e s :  ,  ,  , . . .

I n te r n a tio n a l s e n s a tio n , th e n a s n ow ...

4

© Working Title F i l ms/Shoebox F ilms. All right s reserved. This c ontent is exclu d e d from our C reative Commons l icense. For m ore information, see https:// o cw.mit.edu/help/faq-fair-use/

R u t h e rf o rd Sc a t t e rin g

E r n est R u t her f o r d g r e w u p i n Ne w Z e a l a nd a nd w on a f e llo w sh ip t o st u d y a t C a m b r id g e U n i v e r sit y . H e st u d ie d u nd e r J . J . T homs on a t t he Ca v e nd i s h l a bor a t or y i n t he 1 8 9 0 s , ju st a s T h o m so n w a s c o n d u c t in g h is c a t h o d e - r ay ex p er i m en ts .

Image is in the public domain.

R u t h e r f o r d b e c a m e f a sc in a t e d b y r a d io a c t i v it y , a n d

R u t he r f or d ’ s d e s c r i pt i on of r a d i oa c t i v e id e n t if ie d  r a y s in t h e d e c a y s o f u r a n iu m . H e a lso “ t r a n s m u ta ti o n ” ( 1 9 0 5 ) : a r a d i u m a t o m e m i t s a n  i nt r od u c e d t he c onc e pt of a “ha l f- l i fe ”: t he t i me d u r i ng p a r t i cl e t o b eco m e a n ew s u b s t a n ce ( n o w i d en t i f i ed a s w h ic h t h e r a d io a c t i v it y o f a sa m p le w o u ld f a ll b y h a lf .

r a d on) ; t he r a d on a t om e m i t s a n p a r t i cl e t o b eco m e

“ R a d i u m A ” ( no w pol oni u m ) , a nd s o on, w i t h c h a r a c te r is tic tim e - s ca l es fo r e a c h t r a n s i t i o n .

R u t h e rf o rd Sc a t t e rin g

R u t h e r fo r d - G e i g e r i oni z a t i on c ha m be r , 1 9 0 8

Image is in the public domain.

A c h a m b e r is fille d w ith a n i n e r t g a s . W h e n r a d ia tio n e n te r s , it w ill io n iz e a to m s w ith in th e tu b e . G i v e n th e a ppl i e d v ol t a g e , t he i ons w i l l f l o w t o w a r d t he a nod e , c o m p le tin g th e c ir c u it. D is tin c t “ p u ls e s ” o r c o u n ts c a n t he n be i d e nt i f i e d .

© Svjo-2 on Wikimedia Commons. All rights reserved.

This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/

E r n est R u t her f o r d g r e w u p i n Ne w Z e a l a nd a nd w on a f e llo w sh ip t o st u d y a t C a m b r id g e U n i v e r sit y . H e st u d ie d u nd e r J . J . T homs on a t t he Ca v e nd i s h l a bor a t or y i n t he 1 8 9 0 s , ju st a s T h o m so n w a s c o n d u c t in g h is c a t h o d e - r ay ex p er i m en ts .

R u t h e r f o r d b e c a m e f a sc in a t e d b y r a d io a c t i v it y , a n d id e n t if ie d  r a y s in t h e d e c a y s o f u r a n iu m . H e a lso i nt r od u c e d t he c onc e pt of a “ha l f- l i fe ”: t he t i me d u r i ng w h ic h t h e r a d io a c t i v it y o f a sa m p le w o u ld f a ll b y h a lf .

Us i ng a ne w i oni z a t i on c ha mbe r ( d e v e l ope d w i t h H a n s G e ig e r , no w k no w n a s a “Ge i g e r c ou nt e r ”) , R u t he r for d d e t e r m in e d in 1 9 0 8 t h a t  p a r ti cl es ca r r y tw i ce th e el ectr i c c ha r g e ( a nd ha v e t he oppos i t e s i gn) c ompa r e d t o T homs on ’ s

 p a r t ic le s .

R u t h e rf o rd Sc a t t e rin g R u t he r for d a nd hi s g r ou p a t Ma nc he s t e r Uni v e r s i t y

( U K ) q u ic k ly t u r n e d  p a r t ic le s in t o a t ool t o in v e st ig a t e a t o m ic st r u c t u r e . B e g in n in g in 1 9 0 9 , t h e y d ir e c t e d  p a r t ic le s f r o m a r a d o n so u r c e t o w a r d a t h in g o ld f o il.

T h e y su r r o u n d e d t h e f o il w it h a f lu o r e sc e n t sc r e e n , w h ic h w o u ld f la sh w h e n st r u c k b y a n  p a r t ic le . ( R e se a r c h e r s n e e d e d t o sit in a d a r k e n e d r o o m a n d le t t h e ir e y e s a d ju st , so t h e y c o u ld c o u n t f la sh e s . )

S c h e m at i c o f 1909 - 1911 R u t h e r f o r d - G e i g e r s c a t t e r i n g e x p e r i m en t s .

B u t o n r a r e o c c a sio n s — a b o u t 1 o u t

M o st o f t h e t im e , t h e  p a r t ic le s p a sse d t h r o u g h o f ev er y 1 0 5 ev en ts — th e  p a r t ic le w it h n o d e f le c t io n o r o n ly a sm a ll d e f le c t io n  . w o u ld sc a t t e r b y a lar g e a ngl e  .



Au

g o ld a to m s



p a r t ic le

Au Au

w i t hi n t he f oi l



Au

R u t h e rf o rd Sc a t t e rin g R u t he r for d a nd hi s g r ou p a t Ma nc he s t e r Uni v e r s i t y

( U K ) q u ic k ly t u r n e d  p a r t ic le s in t o a t ool t o in v e st ig a t e a t o m ic st r u c t u r e . B e g in n in g in 1 9 0 9 , t h e y d ir e c t e d  p a r t ic le s f r o m a r a d o n so u r c e t o w a r d a t h in g o ld f o il.

T h e y su r r o u n d e d t h e f o il w it h a f lu o r e sc e n t sc r e e n , w h ic h w o u ld f la sh w h e n st r u c k b y a n  p a r t ic le . ( R e se a r c h e r s n e e d e d t o sit in a d a r k e n e d r o o m a n d le t t h e ir e y e s a d ju st , so t h e y c o u ld c o u n t f la sh e s . )

S c h e m at i c o f 1909 - 1911 R u t h e r f o r d - G e i g e r s c a t t e r i n g e x p e r i m en t s .

N B u t o n r a r e o c c a sio n s — a b o u t 1 o u t

o f ev er y 1 0 5 ev en ts — th e  p a r t ic le w o u ld sc a t t e r b y a lar g e a ngl e  .



Au

R u t h e rf o rd Sc a t t e rin g R u t he r for d a nd hi s g r ou p a t Ma nc he s t e r Uni v e r s i t y

( U K ) q u ic k ly t u r n e d  p a r t ic le s in t o a t ool t o in v e st ig a t e a t o m ic st r u c t u r e . B e g in n in g in 1 9 0 9 , t h e y d ir e c t e d  p a r t ic le s f r o m a r a d o n so u r c e t o w a r d a t h in g o ld f o il.

T h e y su r r o u n d e d t h e f o il w it h a f lu o r e sc e n t sc r e e n , w h ic h w o u ld f la sh w h e n st r u c k b y a n  p a r t ic le . ( R e se a r c h e r s n e e d e d t o sit in a d a r k e n e d r o o m a n d le t t h e ir e y e s a d ju st , so t h e y c o u ld c o u n t f la sh e s . )

S c h e m at i c o f 1909 - 1911 R u t h e r f o r d - G e i g e r s c a t t e r i n g e x p e r i m en t s .

N

10 5

B u t o n r a r e o c c a sio n s — a b o u t 1 o u t

o f ev er y 1 0 5 ev en ts — th e  p a r t ic le w o u ld sc a t t e r b y a lar g e a ngl e  .

10 4

10 3

10 2

10 1

N u m be r of  p a r t i cl es s ca t t er ed b y



Au

d ef l ect i o n a n g l e  .

45 ! 90 ! 135 ! 180 !

9

R u t h e r f o r d ( 1 9 1 1 ) a r g u e d t h a t t h is sc a t t e r in g p a t t e r n

N o n l y m a d e s en s e i f mo s t o f t h e a t o m ’ s ma s s w e r e co n cen tr a ted i n a d en s e “ n ucl eus ” i n th e cen ter : th e a t o m w a s mo s t l y e mp t y s p a c e .

T h e n u c le u s ( lik e t h e  p a r t ic le s) m u st h a v e p o s it i v e c ha r g e , w h ile t h e lig h t w e ig h t “ e le c t r o n s , ” w it h ne g a t i v e c ha r g e ( id e n t if ie d a s T h o m so n ’ s  p a r t ic le s) , c ir c le d a r o u n d t h e n u c le u s .

N u m be r of  p a r t i cl es s ca t t er ed b y d ef l ect i o n a n g l e  .

R u t he r f or d m od e l of t he a t om : m a s s i v e n u c l eu s i n t h e c e n t e r w i t h p o s i t i v e c h a r g e; l i g h t w ei g h t el ect r o n s u r r ou nd i ng i t , w i t h ne g a t i v e c ha r g

R u t he r f or d m od e l of t he a t om : m a s s i v e n u cl eu s i n t h e cen t er w i t h p o s i t i v e c h a r g e; l i g ht w e i g ht e l e c t r ons s u r r ou nd i ng i t , w i t h n eg a t i v e c h a r g e .

B y 1 9 1 1 , R u t h e r f o r d h ad i n t r o d u c e d a ‘ so la r sy st e m ’ m o d e l o f a t o m ic st r u c t u r e . B u t t h is le d t o n e w q u e st io n s:

E le c t r o n s w o u ld b e c o n st a n t ly a c c e l e ra t e d a s th ey m o v ed a r o un d th e n ucl eus . Acco r d i n g t o M a x w e ll ’ s e le c t r o m a g n e t ic w o r k , a ccel er a ted c h a r g es s h o ul d r adi at e . W h e r e is al l t h at l i g h t ?

E v e n mor e i mpor t a nt : t he e l e c t r ons sh o u ld l o s e e ne r g y a s th ey r a d i a ted . So w h y d id n ’ t e le c t r o n s q u ic k ly c r a sh in t o t h e n u c le u s? W h y i s m at t e r s t a bl e at al l ?

Q u e s tion s ?

N ie l s Bo h r w a s a y o u n g D a n ish p h y sic ist , w h o w a s a pos t d oc i n R u t he r for d ’ s g r ou p be t w e e n 1 9 1 1 - 1 9 1 3 .

H e w a s fa s c i na t e d b y t he ne w R u t he r for d mod e l of a t o m ic st r u c t u r e , b u t a lso p u zzle d b y t h e q u e st io n o f t h e st a b ilit y o f m a t t e r .

B ohr a i me d t o a c c ou nt for a t omi c s t r u c t u r e fr om f ir st p r in c ip le s , w it h a g o a l o f a c c o u n t in g f o r a ll t h e

B ohr ’ s not e s ( 1 9 1 3 ) on a t om i c a nd m ol e c u l a r s t r u c t u r e e le m e n t s o f t h e p e r io d ic t a b le .

H e b e g a n b y c o n sid e r in g e le c t r o st a t ic r e p u lsio n a nd ma gne t i c e ffe c t s a mong e l e c t r ons i n mul t i - e l e c t r o n a t o ms a nd mo l e c ul e s , se e k in g e q u ilib r iu m c o n f ig u r a t io n s . P e r ha ps s u c h ba l a nc e d c onfi gu r a t i ons c ou l d a c c ou nt f o r w h y m a t t e r w a s st a b le .

W he n t ha t pr o v e d c u mbe r s ome , he t u r ne d t o t he s i mpl e s t c a s e of a h y d r o g e n a t o m , w it h a sin g le e le c t r o n . A g a in f o r sim p lic it y , h e c o n sid e r e d a c ir c u la r o r b it . B y b a la n c in g t h e f o r c e s , h e c o u ld so lv e f o r t h e e le c t r o n ’ s v e lo c it y . I n t h e se e x p r e ssio n s , b o t h v a n d r w e r e c o nt inuo us v a r ia b le s .

n = 1, 2, 3, ... ,

N ex t h e i m p o sed a n e w “ q u a n t u m c o n d it io n , ” t h a t t h e e le c t r o n ’ s o r b it a l a n g u la r m o m e n t u m c o u ld o n ly t a k e sp e c if ic v a lu e s . H e w a s in sp ir e d b y Pla n c k a n d ( e sp e c ia lly ) E in st e in , w h o h a d e m p h a size d d is c r e t e ne s s a t a sc a le se t b y Pla n c k ’ s c o n st a n t h .

No w B ohr ha d t w o e x pr e s s i ons for v ; e q u a t in g t h e m , h e c o u ld so lv e f o r r . T h e a llo w a b le r a d ii f o r el ectr o n o r b i ts w er e n o w d is c r e t e :

“B ohr r a d i u s ”:

a 0 4 a

+ 9 a 0

D i s c r e t e o r b it s

a 0 4 a 0

+ 9 a 0

N ow Bo h r g o t ex ci ted ! Ba l me r s p e c t r um fr om e x c i t e d h y d r og e n a t oms :

B ohr pr opos e d : l i ght w ou l d be e mit t e d w h en ev er a n el ectr o n j um p ed fr om a n “e x c i t e d ” or bi t t o a l o w e r - en er g y o r b i t:  E = h  , or :

R : “ R y d be r g c ons t a nt ”

J oha nn B a l m e r,

1 8 8 5

B o h r w a s r e lu c t a n t t o p u b lish h is n e w id e a s , b e c a u se h e h a d o n ly t r e a t e d h y d r og e n a t oms ; hi s g oa l ha d be e n t o a c c ou nt for t he st a b ilit y a n d st r u c t u r e o f all t h e a t o m s o f t h e p e r io d ic t a b le !

H a ppi l y , R u t he r for d c on v i nc e d B ohr t o pu bl i s h a ny w a y ( 1 9 1 3 ) .

Ce nt r a l t o B ohr ’ s e x pl a na t i on w a s t he ne w “q u a nt u m c ond i t i on” ( J = n h ) , w h ic h r e st r ic t e d e le c t r o n s t o d is c r e t e o r b it s ( r = n 2 a 0 ) ; o n ly for t hos e c hoi c e s of r w ou l d t he a t om r e ma i n s t a bl e . B ohr ha d ne i t he r d e r i v e d nor e x pl a i ne d t he or i gi n of hi s pr opos e d “q u a nt u m c ond i t i on, ” bu t b y u s i ng i t he ha d be e n a bl e t o r e pr od u c e t he B a l me r s pe c t r u m for h y d r og e n.

T h e q u e st io n st ill r e m a in e d : w h y d id n ’ t t h is d isc r e t e n e ss a p p e a r i n or d i na r y e x pe r i e nc e ? B ohr w or k e d ou t t he “ c o r r e s p o nd e nc e p rinc ip l e ” : in t h e lim it o f la r g e q u a n t u m n u m b e r s , n > > 1 , q u a n t u m sy st e m s sh o u ld r e p r o d u c e c la ssic a l b e h a v io r .