8/3/2019 Review Exam 1 2011

1/4

Chemistry 341

Physical Chemistry IFall 2011

EXAM 1 REVIEW SHEET[Exam 1: Friday September30, 11:10 AM12:00 PM, Packard Lab Aud. 101]

Quantum Mechanics

1. Wave theory of light

constructive interference destructive interference

2. Planck quantum theory

blackbody radiation

( )

=

8

1

2

3c

h

eh

kT

average energy of an oscillator

=

h

e

h

kT 1

3. Photoelectric effect

k e m v he

. . = = 12

2

4. de Broglie relation =h

p

5. Wave behavior in 1-D

wavelength ( ) wavenumber ( ~

=1

)

period ( ) frequency (

=1

)

6. Differential equation for the spatial dependence of a standing wave

d

dxD D

2

2

22

=

7. Schrdinger equation in 1-D

+ =h

2 2

22m

d

dxV E

8/3/2019 Review Exam 1 2011

2/4

8. Eigenvalue problem$ =

is an eigenfunction of the operator $ with eigenvalue

9. Heisenberg uncertainty principle

x p h

2

10. Three postulates concerning quantum theory

11. Average value theorem

=

* $

*

dv

dv

12. Quantum mechanical operators

$x x $p

i xi

xx =

hh

13. Particle in a 1-D box

condition for a standing wave in a 1-D box of length aa n=

2with n=1, 2, 3,

E h nman

=2 2

28

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

n a

n x

a=

2 1 2/sin with n=1, 2, 3,

probability of finding a particle between x1 and x2nx x

xdx

2

1

2

=

electronic spectra of polyenes CNHN+2 prediction of lowest energy p-electrontransition

14. Quantum mechanical tunneling through barrier of height Vo and width a light massparticles can tunnel into regions where E

8/3/2019 Review Exam 1 2011

3/4

15. Schrdinger equation in 2-D

Particle in 2-D box of dimensions a x b E

h

m

n

a

n

bn nx y

x y,= +

2 2

2

2

28

with nx = 1, 2, and ny = 1, 2,

Particle in 2-D square box of sides a idea of degenerate levels

{ }E hma

n nn n x yx y,

= +2

2

2 2

8with nx = 1, 2, and ny = 1, 2,

16. Schrdinger equation in 3-D

Particle in 3-D box of dimensions a x b x c E

h

m

n

a

n

b

n

cn n nx y z

x y z, ,= + +

2 2

2

2

2

2

28

with nx = 1, 2, , ny = 1, 2, and nz = 1, 2,

Particle in 3-D cubic box of sides a idea of degenerate levels{ }E h

man n nn n n x y z x y z, , = + +

2

2

2 2 2

8with nx = 1, 2, , ny = 1, 2, and nz = 1, 2,

17. Harmonic oscillator

( )V x k x= 12

2

E v hv o= + 12 with v =0, 1, 2, with

o

k=

1

2

1 2/

v the number of nodes ( ) as the energy Ev goes ( )18. Particle of mass m on a circle on a circle of radiusR [also rigid rotor in 2-D where

m = ]

E h mm R

nl=

2 2

2 28

with ml = 0, 1, 2,

m

i m

l

le=

1

2

1 2/

with ml > 0 counterclockwise rotation looking down on circle (clockwise rotationlooking along positive-z axis)

and ml

< 0 clockwise rotation looking down on circle (counterclockwise rotation

looking along positive z-axis)

benzene and porphine group as examples

8/3/2019 Review Exam 1 2011

4/4

19. Rigid rotor in 3D Diatomic molecule I R= 2 ( ) ( ) E J J

IB h c J J

J= + = +1

21

2h

with ( J = 0, 1, 2, ...)

where Bh

c I= 8 2

( )$ L Y l l Y l

m

l

ml l2 21= + h with ( l = 0, 1, 2 ...)

$ L Y m Y z l m l l ml l= h with ( ml = 0, 1, 2, )