[Donald A. McQuarrie, John D. Simon] Physical Chem(BookZZ.org)
1279 pág.

[Donald A. McQuarrie, John D. Simon] Physical Chem(BookZZ.org)


DisciplinaFísico-química I6.502 materiais97.791 seguidores
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F i g u r e 1 . 7 a n d T a b l e 1 . 1 . T h e c o n s t a n t i n E q u a t i o n 1 . 1 0 
i s c a l l e d t h e R y d b e r g c o n s t a n t a n d E q u a t i o n 1 . 1 0 i s c o m m o n l y w r i t t e n a s 
v = R ( 2 _ - 2 _ ) 
H n 2 n 2 
I 2 
( 1 . 1 1 ) 
w h e r e R H i s t h e R y d b e r g c o n s t a n t . T h e m o d e m v a l u e o f t h e R y d b e r g c o n s t a n t i s 
1 0 9 6 7 7 . 5 7 c m -
1
; i t i s o n e o f t h e m o s t a c c u r a t e l y k n o w n p h y s i c a l c o n s t a n t s . 
s 
s 
s 
s 
< = 
< = 
< = 
< = 
0 
r -
. , . , \ 0 
- , 0 
' < ! &quot; \ 0 0 
r -
s 
< = 
s 
< = 
N 
\ 0 
-
\ 0 < r > N 
0 0 
« ) 
\ 0 0 0 
-
-
0 \ 
N 
+ + 
+ 
+ + + 
[ I [ ] 
i 
I \u2022 \u2022 I 
1 - 1 
L y m a n B a l m e r 
P a s c h e n 
I \u2022 \u2022 I 
U l t r a v i o l e t 
V i s i b l e 
I n f r a r e d 
F I G U R E 1 . 7 
A s c h e m a t i c r e p r e s e n t a t i o n o f t h e v a r i o u s s e r i e s i n t h e h y d r o g e n a t o m i c s p e c t r u m . T h e L y m a n 
s e r i e s l i e s i n t h e u l t r a v i o l e t r e g i o n ; t h e B a l m e r l i e s i n t h e v i s i b l e r e g i o n ; a n d t h e P a s c h e n a n d 
B r a c k e t s e r i e s l i e i n t h e i n f r a r e d r e g i o n ( s e e T a b l e 1 . 1 ) . 
1 3 
r 
14 
TABLE 1.1 
The first four series of lines making up the hydrogen atomic spectrum. 
The term &quot;near infrared&quot; denotes the part of the infrared region of the 
spectrum that is near the visible region. 
Series name nl n2 Region of spectrum 
Lyman 1 2, 3, 4, Ultraviolet 
Balmer 2 3, 4, 5, Visible 
Paschen 3 4, 5, 6, Near infrared 
Bracket 4 5, 6, 7, Infrared 
EXAMPLE 1-5 
Calculate the wavelength of the second line in the Paschen series, and show that this 
line lies in the near infrared, that is, in the infrared region near the visible. 
SOLUTION: In the Paschen series, n 1 = 3 and n2 = 4, 5, 6, ... according to 
Table 1.1. Thus, the second line in the Paschen series is given by setting n 1 = 3 and 
n2 = 5 in Equation 1.11: 
v = 109 677.57 ( ; 2 - ; 2 ) cm-1 
= 7.799 x 103 cm-1 
and 
A = 1.282 X 10-4 em = 1282 nm 
which is in the near infrared region. 
The fact that the formula describing the hydrogen spectrum is in a sense controlled 
by two integers is truly amazing. Why should a hydrogen atom care about our integers? 
We will see that integers play a special role in quantum theory. 
The spectra of other atoms were also observed to consist of series of lines, and in 
the 1890s Rydberg found approximate empirical laws for many of them. The empirical 
laws for other atoms were generally more involved than Equation 1.11, but the really 
interesting feature is that all the observed lines could be expressed as the difference 
between terms such as those in Equation 1.11. This feature was known as the Ritz 
combination rule, and we will see that it follows immediately from our modem view 
of atomic structure. At the time, however, it was just an empirical rule waiting for a 
theoretical explanation. 
1 - 6 . L o u i s d e B r o g l i e P o s t u l a t e d T h a t M a t t e r H a s W a v e l i k e P r o p e r t i e s 
A l t h o u g h w e h a v e a n i n t r i g u i n g p a r t i a l i n s i g h t i n t o t h e e l e c t r o n i c s t r u c t u r e o f a t o m s , 
s o m e t h i n g i s m i s s i n g . T o e x p l o r e t h i s f u r t h e r , l e t u s g o b a c k t o a d i s c u s s i o n o f t h e 
n a t u r e o f l i g h t . 
S c i e n t i s t s h a v e a l w a y s h a d t r o u b l e d e s c r i b i n g t h e n a t u r e o f l i g h t . I n m a n y e x p e r -
i m e n t s l i g h t s h o w s a d e f i n i t e w a v e l i k e c h a r a c t e r , b u t i n m a n y o t h e r s l i g h t s e e m s t o 
b e h a v e a s a s t r e a m o f p h o t o n s . T h e d i s p e r s i o n o f w h i t e l i g h t i n t o i t s s p e c t r u m b y a 
p r i s m i s a n e x a m p l e o f t h e f i r s t t y p e o f e x p e r i m e n t , a n d t h e p h o t o e l e c t r i c e f f e c t i s a n 
e x a m p l e o f t h e s e c o n d . B e c a u s e l i g h t a p p e a r s w a v e l i k e i n s o m e i n s t a n c e s a n d p a r t i c l e -
l i k e i n o t h e r s , t h i s d i s p a r i t y i s r e f e r r e d t o a s t h e w a v e - p a r t i c l e d u a l i t y o f l i g h t . I n 1 9 2 4 , 
a y o u n g F r e n c h s c i e n t i s t n a m e d L o u i s d e B r o g l i e r e a s o n e d t h a t i f l i g h t c a n d i s p l a y 
t h i s w a v e - p a r t i c l e d u a l i t y , t h e n m a t t e r , w h i c h c e r t a i n l y a p p e a r s p a r t i c l e l i k e , m i g h t a l s o 
d i s p l a y w a v e l i k e p r o p e r t i e s u n d e r c e r t a i n c o n d i t i o n s . T h i s p r o p o s a l i s r a t h e r s t r a n g e a t 
f i r s t , b u t i t d o e s s u g g e s t a n i c e s y m m e t r y i n n a t u r e . C e r t a i n l y i f l i g h t c a n b e p a r t i c l e l i k e 
a t t i m e s , w h y s h o u l d m a t t e r n o t b e w a v e l i k e a t t i m e s ? 
d e B r o g l i e w a s a b l e t o p u t h i s i d e a i n t o a q u a n t i t a t i v e s c h e m e . E i n s t e i n h a d s h o w n 
f r o m r e l a t i v i t y t h e o r y t h a t t h e w a v e l e n g t h , A , a n d t h e m o m e n t u m , p , o f a p h o t o n a r e 
r e l a t e d b y 
h 
A = -
p 
( 1 . 1 2 ) 
d e B r o g l i e a r g u e d t h a t b o t h l i g h t a n d m a t t e r o b e y t h i s e q u a t i o n . B e c a u s e t h e m o m e n t u m 
o f a p a r t i c l e i s g i v e n b y m v , t h i s e q u a t i o n p r e d i c t s t h a t a p a r t i c l e o f m a s s m m o v i n g 
w i t h a v e l o c i t y v w i l l h a v e a d e B r o g l i e w a v e l e n g t h g i v e n b y A = h j m v . 
E X A M P L E 1 - 6 
C a l c u l a t e t h e d e B r o g l i e w a v e l e n g t h f o r a b a s e b a l l ( 5 . 0 o z ) t r a v e l i n g a t 9 0 m p h . 
S 0 L U T I 0 N : F i v e o u n c e s c o r r e s p o n d s t o 
( 
l i b ) ( 0 . 4 5 4 k g ) 
m = ( 5 . 0 o z ) -
6
- = 0 . 1 4 k g 
1 o z l i b 
a n d 9 0 m p h c o r r e s p o n d s t o 
v = ( 9 0 m i ) ( 1 6 1 0 m ) (~) = 
4 0 
m · s _
1 
1 h r 1 m i 3 6 0 0 s 
T h e m o m e n t u m o f t h e b a s e b a l l i s 
p = m v = ( 0 . 1 4 k g ) ( 4 0 m - s -
1
) = 5 . 6 k g · m · s -
1 
1 5 
16 Chapter 1 I The Dawn of the Quantum Theory 
The de Broglie wavelength is 
h 6.626 x 10-34 J. s -34 
A= - = 1 = 1.2 x 10 m p 5.6 kg·m·s-
a ridiculously small wavelength. 
We see from Example 1.6 that the de Broglie wavelength of the baseball is so small 
as to be completely undetectable and of no practical consequence. The reason is the 
large value of m. What if we calculate the de Broglie wavelength of an electron instead 
of a baseball? 
EXAMPLE 1-7 
Calculate the de Broglie wavelength of an electron traveling at 1.00% of the speed of 
light. 
SOL U Tl 0 N: The mass of an electron is 9.109 x 10-31 kg. One percent of the speed 
of light is 
v = (0.0100)(2.998 x 108 m-s- 1) = 2.998 x 106 m-s- 1 
The momentum of the electron is given by 
p = m
0
V = (9.109 X 10-3! kg)(2.998 X 106 m-s-1) 
= 2.73 X 10-24 kg·m·S-l 
The de Broglie wavelength of this electron is