FORMULARIO Y CONSTANTES FÍSICAS

F ORMULARIO
Y CONSTANTES FÍSICAS Formulario
p̂ =
~ d
i dx
ˆlz (φ) =
Em =
m2 ~2
;
2M R2
2
En =
m = 0, ±1, . . .
2
ke Z
En = − 2a
2 = −13.6
o n
Z2
n2
Ĥ(θ, φ) =
eV
; n = 1, 2, ...
ψm (φ) = √12π eimφ
1
1 ∂
∂
∂2
2
2
L̂ (θ, φ) = −~ sen2 θ ∂φ2 + senθ ∂θ senθ ∂θ
L̂2 (θ,φ)
2mR2
∂U
∂T V
dS ≥
o
d ln KP
dT
∆Go = −RT ln KPo
=
CP =
dQ
T
Kf =
∆H o
RT 2
dP
dT
n!
R∞
R (Tf∗ )2 P mA
t
=
∆S
∆V
cos(α ± β) = cos α cos β ∓ sen α sen β
∗
∆H̄fus,A
z n e−bz dz =
µ(P, T ) = µ∗ (P, T ) + RT ln xi
sen2 α = 12 (1 − cos 2α)
bn+1
∂H
∂T P
µ(T ) = µo (T ) + RT ln PPo
Pi = xi,l Pi∗
+ cte
∆Tf = −Kf mB
0
H = U + PV
CP = CV + n R
rn e−br dr =
nπx
l
sen
∆U = Q + W
Cv =
sen(2α) = 2 sen α cos α
=
2
l
L̂2 ψl,ml = l(l + 1)~2 ψl,ml ; l = 0, 1, . . .
G = H − TS
R∞
L̂2 (θ,φ)
2I
q
dV = r2 sen θ dr dθ dφ
ao
< r >n,l = 2Z
[3n2 − l(l + 1)]
2
P + a Vn 2 (V − nb) = nRT
1
T
ψn (x) =
ˆlz (φ)ψm (φ) = m~ ψm (φ)
~ ∂
i ∂φ
v
ln P = − ∆H
R
h2 n2
8ml2
n!
bn+1
sen(α ± β) = sen α cos β ± cos α sen β
e−bt 1 + bt +
(bt)2
2!
+
(bt)3
3!
+ ... +
Constantes físicas
R = 8.31 J mol−1 K−1
R = 1.98 cal mol−1 K−1
R = 0.082 atm l mol−1 K−1
h = 6.62608 · 10−34 J s
me = 9.10939 · 10−31 kg
0 = 8.854 · 10−12 F m−1
e = 1.602 · 10−19 C
1 atm = 1.013 · 105 Pa
1 bar = 105 Pa
a0 = 5.292 · 10−11 m
(bt)n n!
Factores radiales de los orbitales atómicos
3/2
e−Zr/ao
R1s = 2 aZo
3/2 Zr
R2s = √12 aZo
1 − 2a
e−Zr/2ao
o
5/2
1
√
re−Zr/2ao
R2p = 2 6 aZo
3/2 2Z 2 r2
1 − 2Zr
+
e−Zr/3ao
R3s = 3√2 3 aZo
3ao
27a2o
3/2 8√
Z
Zr
Z 2 r2
R3p = 27 6 ao
− 6a2 e−Zr/3ao
ao
o
Armónicos esféricos. Yl,m (θ, φ) = √12π Sl,m (θ)eimφ
Rπ
|Sl,m |2 sen θdθ = 1
0
√
l=0:
S0,0 = 12 2
√
l=1:
S1,0 = 12 6 cos θ
√
S1,±1 = 12 3 sen θ
√
l=2:
S2,0 = 14 10(3 cos2 θ − 1)
√
S2,±1 = 12 15 sen θ cos θ
√
S2,±2 = 14 15 sen2 θ
√
l=3:
S3,0 = 34 14( 35 cos3 θ − cos θ)
√
S3,±1 = 18 42 sen θ(5 cos2 θ − 1)
√
S3,±2 = 14 105 sen2 θ cos θ
√
S3,±3 = 18 70 sen3 θ