SU20Ex1 Constants Eqs.pdf - Summer 2020 CHEM 452 Useful...

Summer 2020 CHEM 452
Useful equations and constants for Exam I
Useful Constants:
h = 6.626 x 10 –34 Js ħ = h/2 p c = 2.998 x 10 8 m/s
1 amu = 1.6605·10 –27 kg m
e
= 9.109 x 10 –31 kg eV = 1.602 x10 –19 J
!
!
= 8.8542 × 10
"#$
,
$
-
"#
.
"#
R
H
= 109677 cm –1
Useful Equations:
/ = (1 +
#
$
)ℏ5
! = #
ℏ
!
"#
$
$/&
! = ± $√ 2' + 1 * +
, sin
2
) (
2 / 1
÷
ø
ö
ç
è
æ
÷
ø
ö
ç
è
æ
= Y
L
x n
L
x
n
p
2
2 2
8 mL
h n
E
n
=
D
h
p
l =
2 ( ) p mv m E V = = - ( ) ikx ikx
k
x Ae Be - Y = +
2 2
2
k
k
E
m
=
!
ˆ
x x =
ˆ
( )
x
V V x =
ˆ
x
d
p i
dx
= - !
2 ˆ
ˆ
2
x
x
p
T
m
=
ˆ
* d y y t W = W
ò
j j
j
c y f =
å ˆ
j j j
f w f W =
2
j j
j
c w W =
å
ˆ ˆ ˆ ˆ ˆ ˆ
, A B AB BA
é ù
= -
ë û
1
ax ax
e dx e C
a
= +
ò
1
0
!
n ax
n
n
x e dx
a
¥
-
+
=
ò
2
0
1
2
ax xe dx
a
¥
- =
ò
( )
ar ar
d
dr
e ae =
( )
2 2
2 ax ax
d
dx
e axe =
( )
2
1
sin 1 cos(2 )
2
x x = -
2
2
sin(2 ) cos(2 )
2
4 4
8
sin ( )
x ax ax
x
a
a
x ax dx = - -
ò
( )
3 2
3 2
cos(2 ) 2 2
1
6 4
8 4
sin ( ) sin(2 ) x ax
x x
a
a a
x ax dx ax = - - -
ò
( )
sin cos
d
dx
ax a ax =
( )
cos sin
d
dx
ax a ax = -
2
1
2
V kx =
k
m
w =
y x a =
( )
2 ( )exp /2
v v v
N H y y y = -

Harmonic Oscillator Wavefunctions
%
'
= &
'
'
'
())+
(
*
!
+
,
&
'
= #
$
,√. +
"
'!
$
$/+
, ) =
0
,
, ! = #
ℏ
!
"#
$
$/&
, . = 0,1,2, …

PERIODIC TABLE of the ELEMENTS
MAIN GROUPS MAIN GROUPS
1A
1
7A
17
8A
18
1
H
1.008
2A
2
3A
13
4A
14
5A
15
6A
16
1
H
1.008
2
He
4.003
3
Li
6.941
4
Be
9.012
TRANSITION METALS
5
B
10.811
6
C
12.011
7
N
14.007
8
O
15.999
9
F
18.998
10
Ne
20.180
11
Na
22.990
12
Mg
24.305
3B
3
4B
4
5B
5
6B
6
7B
7
8B
8
8B
9
8B
10
1B
11
2B
12
13
Al
26.982
14
Si
28.086
15
P
30.974
16
S
32.066
17
Cl
35.453
18
Ar
39.948
19
K
39.098
20
Ca
40.078
21
Sc
44.956
22
Ti
47.867
23
V
50.942
24
Cr
51.996
25
Mn
54.938
26
Fe
55.845
27
Co
58.933
28
Ni
58.693
29
Cu
63.546
30
Zn
65.39
31
Ga
69.723
32
Ge
72.61
33
As
74.992
34
Se
78.96
35
Br
79.904
36
Kr
83.80
37
Rb
85.468
38
Sr
87.62
39
Y
88.906
40
Zr
91.224
41
Nb
92.906