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


DisciplinaFísico-química I6.504 materiais97.836 seguidores
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r i g i n a l e n e r g y l e v e l o f t h e e l e c t r o n . 
1 - 2 2 . A g r o u n d - s t a t e h y d r o g e n a t o m a b s o r b s a p h o t o n o f l i g h t t h a t h a s a w a v e l e n g t h o f 9 7 . 2 n m . 
I t t h e n g i v e s o f f a p h o t o n t h a t h a s a w a v e l e n g t h o f 4 8 6 n m . W h a t i s t h e f i n a l s t a t e o f t h e 
h y d r o g e n a t o m ? 
1 - 2 3 . S h o w t h a t t h e L y m a n s e r i e s o c c u r s b e t w e e n 9 1 . 2 n m a n d 1 2 1 . 6 n m , t h a t t h e B a l m e r 
s e r i e s o c c u r s b e t w e e n 3 6 4 . 7 n m a n d 6 5 6 . 5 n m , a n d t h a t t h e P a s c h e n s e r i e s o c c u r s b e -
t w e e n 8 2 0 . 6 n m a n d 1 8 7 6 n m . I d e n t i f y t h e s p e c t r a l r e g i o n s t o w h i c h t h e s e w a v e l e n g t h s 
c o r r e s p o n d . 
1 - 2 4 . C a l c u l a t e t h e w a v e l e n g t h a n d t h e e n e r g y o f a p h o t o n a s s o c i a t e d w i t h t h e s e r i e s l i m i t o f 
t h e L y m a n s e r i e s . 
1 - 2 5 . 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 ) a n e l e c t r o n w i t h a k i n e t i c e n e r g y o f 1 0 0 e V , 
( b ) a p r o t o n w i t h a k i n e t i c e n e r g y o f 1 0 0 e V , a n d ( c ) a n e l e c t r o n i n t h e f i r s t B o h r o r b i t o f a 
h y d r o g e n a t o m . 
1 - 2 6 . C a l c u l a t e ( a ) t h e w a v e l e n g t h a n d k i n e t i c e n e r g y o f a n e l e c t r o n i n a b e a m o f e l e c t r o n s 
a c c e l e r a t e d b y a v o l t a g e i n c r e m e n t o f 1 0 0 V a n d ( b ) t h e k i n e t i c e n e r g y o f a n e l e c t r o n t h a t 
h a s a d e B r o g l i e w a v e l e n g t h o f 2 0 0 p m ( 1 p i c o m e t e r = 1 0 -
1 2 
m ) . 
1 - 2 7 . T h r o u g h w h a t p o t e n t i a l m u s t a p r o t o n i n i t i a l l y a t r e s t f a l l s o t h a t i t s d e B r o g l i e w a v e l e n g t h 
i s 1 . 0 X 1 0 - I O m ? 
1 - 2 8 . C a l c u l a t e t h e e n e r g y a n d w a v e l e n g t h a s s o c i a t e d w i t h a n a p a r t i c l e t h a t h a s f a l l e n 
t h r o u g h a p o t e n t i a l d i f f e r e n c e o f 4 . 0 V . T a k e t h e m a s s o f a n a p a r t i c l e t o b e 6 . 6 4 x 
1 0 - 2 7 k g . 
1 - 2 9 . O n e o f t h e m o s t p o w e r f u l m o d e r n t e c h n i q u e s f o r s t u d y i n g s t r u c t u r e i s n e u t r o n d i f f r a c -
t i o n . T h i s t e c h n i q u e i n v o l v e s g e n e r a t i n g a c o l l i m a t e d b e a m o f n e u t r o n s a t a p a r t i c u l a r 
~ 
2 7 
28 Chapter 1 I The Dawn of the Quantum Theory 
temperature from a high-energy neutron source and is accomplished at several accelera-
tor facilities around the world. If the speed of a neutron is given by vn = (3kBT/m) 112 , 
where m is the mass of a neutron, then what temperature is needed so that the neu-
trons have a de Broglie wavelength of 50 pm? Take the mass of a neutron to be 1.67 x 
w-n kg. 
1-30. Show that a small change in the speed of a particle, !<,. v, causes a change in its de Broglie 
wavelength, t<.'A, of 
where v0 and A0 are its initial speed and de Broglie wavelength, respectively. 
1-31. Derive the Bohr formula for v for a nucleus of atomic number Z. 
1-32. The series in the He+ spectrum that corresponds to the set of transitions where the 
electron falls from a higher level into the n = 4 state is called the Pickering series, an 
important series in solar astronomy. Derive the formula for the wavelengths of the ob-
served lines in this series. In what region of the spectrum does it occur? (See Problem 
1-31.) 
1-33. Using the Bohr theory, calculate the ionization energy (in electron volts and in kJ -mol- 1) 
of singly ionized helium. 
1-34. Show that the speed of an electron in the nth Bohr orbit is v = e2 /2e0nh. Calculate the 
values of v for the first few Bohr orbits. 
1-35. If we locate an electron to within 20 pm, then what is the uncertainty in its speed? 
1-36. What is the uncertainty of the momentum of an electron if we know its position is 
somewhere in a 10 pm interval? How does the value compare to momentum of an electron 
in the first Bohr orbit? 
1-37. There is also an uncertainty principle for energy and time: 
t<.Et<.t ~ h 
Show that both sides of this expression have the same units. 
1-38. The relationship introduced in Problem 1-37 has been interpreted to mean that a particle 
of mass m (E = mc2 ) can materialize from nothing provided that it returns to nothing 
within a time t<.t :::: h / mc2 \u2022 Particles that last for time t<.t or more are called real particles; 
particles that last less than time t<.t are called virtual particles. The mass of the charged 
pion, a subatomic particle, is 2.5 X w-zs kg. What is the minimum lifetime if the pion is 
to be considered a real particle? 
1-39. Another application of the relationship given in Problem l-37 has to do with the 
excited state energies and lifetimes of atoms and molecules. If we know that the life-
time of an excited state is 10-9 s, then what is the uncertainty in the energy of this 
state? 
P r o b l e m s 
1 - 4 0 . W h e n a n e x c i t e d n u c l e u s d e c a y s , i t e m i t s a y - r a y . T h e l i f e t i m e o f a n e x c i t e d s t a t e o f 
a n u c l e u s i s o f t h e o r d e r o f 1 0 -
1 2 
s . W h a t i s t h e u n c e r t a i n t y i n t h e e n e r g y o f t h e y - r a y 
p r o d u c e d ? ( S e e P r o b l e m l - 3 7 . ) 
1 - 4 1 . I n t h i s p r o b l e m , w e w i l l p r o v e t h a t t h e i n w a r d f o r c e r e q u i r e d t o k e e p a m a s s r e v o l v i n g 
a r o u n d a f i x e d c e n t e r i s f = m v
2 
I r . T o p r o v e t h i s , l e t u s l o o k a t t h e v e l o c i t y a n d t h e 
a c c e l e r a t i o n o f a r e v o l v i n g m a s s . R e f e r r i n g t o F i g u r e 1 . 1 2 , w e s e e t h a t 
I L ' . r l R ; L ' . s = r t . e 
( 1 . 2 7 ) 
i f 1 ' . 8 i s s m a l l e n o u g h t h a t t h e a r c ~ength L ' . s a n d t h e v e c t o r d i f f e r e n c e I L ' > r l = l r
1 
- r
2
1 a r e 
e s s e n t i a l l y t h e s a m e . I n t h i s c a s e , t h e n 
. t . s . t . e 
v = h m - = r h m - = r w 
L ' > t - - > 0 L ' . t L ' > t - - > 0 L ' . t 
( 1 . 2 8 ) 
w h e r e w = d 8 1 d t = v i r . 
r i r > l . . : i r l &quot; &quot; L i s &quot; &quot; r < i 8 
v r 2 
F I G U R E 1 . 1 2 
D i a g r a m f o r d e f i n i n g a n g u l a r s p e e d . 
I f w a n d r a r e c o n s t a n t , t h e n v = r w i s c o n s t a n t , a n d b e c a u s e a c c e l e r a t i o n i s 
l i m , _ _ .
0
( L ' . v I L ' . t ) , w e m i g h t w o n d e r i f t h e r e i s a n y a c c e l e r a t i o n . T h e a n s w e r i s m o s t d e f i n i t e l y 
y e s b e c a u s e v e l o c i t y i s a v e c t o r q u a n t i t y a n d t h e d i r e c t i o n o f v , w h i c h i s t h e s a m e a s L ' . r , i s 
c o n s t a n t l y c h a n g i n g e v e n t h o u g h i t s m a g n i t u d e i s n o t . T o c a l c u l a t e t h i s a c c e l e r a t i o n , d r a w 
a f i g u r e l i k e F i g u r e 1 . 1 2 b u t e x p r e s s e d i n t e r m s o f v i n s t e a d o f r . F r o m y o u r f i g u r e , s h o w 
t h a t 
t . v = I L ' > v l = v t . e 
( 1 . 2 9 ) 
i s i n d i r e c t a n