化学原理Chemistry课件post3atomicstructure

( Ephoton = DE = RH
1 n2i
1 n2f
)
Ephoton = 2.18 x 10-18 J x (1/25 - 1/9)
Ephoton = DE = 1.55 x 10-19 J
Ephoton = h c/ l
l = h c / Ephoton
l = 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J
Nobel Prize in 1929
What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?
l = 6.63 x 10-34 / (2.5 x 10-3 x 15.6)
1. Application of Schrödinger to Hydrogen Atom
z
(x,y,z)
Ĥ = E Ĥ 2 2 e2
2m
r
r
y
2 2m
2
e2 r
(x,y,z)
= E (x,y,z)
After transferred into sphere coordinate
x x r sin cos y r sin sin z r cos
Ĥ2 2m2V2: Laplacian Operator
2 2 2
2 x2 y2 z2
Uncertainty principle (1927, W K Heisenberg): DX Dp h/4
It is impossible to determine precisely both the position and momentum of a particle at the same time.
l = 1.7 x 10-32 m = 1.7 x 10-23 nm
& 7. 3 Quantum Mechanical Description of Electrons in Atoms Schrödinger Wave Equation
Basis:
1) Bohr’s theory, good to explain the H emission spectrum, but failed for the spectrum of other elements.
hn = KE + BE
Here BE is the binding energy of the metal lattice electron
KE = hn - BE
7.2 Dual Nature of Electron
1. Hydrogen Emission line spectrum: Bohr’s Planetary model
r)
E1s=-13.6 eV
2s 2 pz
N2(2
N2
(
Z a0
Z
z
r) • exp( r)
a0 r) • exp(
z
2a0
r ) c os
2a0
2 px
Z N2 ( a0
r) • exp(
z 2a0
r ) sin
cos
E** = -3.4 eV
2py
Z N2 ( a0
r) • exp(
Wave (Huygens, 1690): an elastic vibrator, emitted from light source, that move in space in three dimensional direction.
Different waves have different color, and different wavelength.
n;
n, l, m (r,,) l
Rn,l (r) • l,ml ( ) • ml ()
Spacial part
Angular part
n=1 l =0 n=2 l =0 n=2 l =1 n=2 l =1 n=2 l =1
ml=0 ml=0 ml=0 ml=-1 ml=+1
1s
N1
• exp(
z a0
2) Dual nature of electron (m and l).
In 1926, Schrodinger wrote an equation for electron in the atom.
Ĥ = E
Total energy of the system
E = V + KE
Potential energy
Einstein Photon Theory (1905)
Light are both wave and particle:
1. Wave nature (l): E = hv
2. Particle nature(m): momentum p = mc
3. Energy E = mc2 hv =pc
nf = 2
nnff ==11
Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state.
8 v2kT
at low v, but very bad at high v. E(v)dv C3 dv
Planck’s Quantum Hypothesis (1901):
Energy is emitted or absorbed in discrete units (quantum).
For a single quantum, the smallest quantity of energy :
l = 1280 nm
2. Dual nature of the Electron: Matter as waves De Broglie (1924) reasoned that e- is both particle and wave. 2r = nl l = h/mu u = velocity of e- m = mass of e-
7.1 Light and Classic Quantum Theory
Maxwell (1893) wrote an equation for light as a wave
Light is an electromagnetic wave that spread in space.
Wavelength l is the distance
3. The Particle Nature of Light:
Photoelectric Effect:
hn
current
V0
voltage
Experimental evidence:
(1) minimum frequency of light (v0) (2) v0 is dependent of metal. (3) The current light intensity.
7.1 Light and Classic Quantum Theory
1. Classic theory of Light
Particles (Newton, 1680): an array of particles, emitted from light source, that move in space in one dimensional direction.
kinetic energy
(psi): wave function, or atomic orbital
that describes the movement of electron in
the atom in three dimensional space.
Ĥ: Hamiltonian Operator
z 2a0
r)sin sin
1s
N1
•
exp(
z a0
r)
2
Electron density
90 % of electron density found
r distance from the nucleus But the probability to find e in space (DV)
Bohr’s Model of H Atom (1913)
1. e- only has a specific energy values (quantized)
2. light is emitted as e- moves
from one energy level to a
lower energy level
speed u dx dt
force f m du dt
Kinetic energy KE 1 mu2 2
Acceleration speed
g
du dt
d2x dt 2
One can determine the exact position and speed at the same time.
I ua02
8
Energy changes continuously !
2. Classic quantum theory of Light (Plank, 1900)
Black body radiation: curve E vs v E T 4 ( constant)
Classical theory explains it well
En
= -RH (
1 n2
)
n (principal quantum number)
= 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J = 13.6 eV
3. Ephoton = DE = Ef - Ei
DE
=
RH(
1 n2i
1 n2f
)
ni = 3 ni = 3 ni = 2
E=hv
Planck constant h = 6.63 x 10-34 J•s
E(v)dv
8 v2kT
C3
dv
ehv
/
kT
1
Explains all results well.
Energy change is only by hv, 2hv, 3 hv, 4 hv ...
but never by 1.5 hv or 3.06 hv… Then in 1918, he won Nobel Prize in physics.
between two successive waves.
Frequency n is the number
of waves that pass in 1 s.
Speed u is the distance of
waves that pass in 1 s.
u l ·n
For a light in vacuum, u = c = 3.00 x 108 m/s
p h
l
Particle Wave nature nature
It explains well the evidence: (1) minimum frequency of light (v0) (2) v0 is dependent of metal. (3) The current light intensity.
r x2 y2 z2
1 r
r
r
2
r
1
r 2 sin
1
r 2 sin 2
2 2
8 2m
h2
E
e2 r
0
here (r, ,)
General solution for Hydrogen Atom
En
13.6
Z2 n2
(e V )
(Z is atomic number, and for H, Z=1) Same as Bohr’s result, ie. Only dependent of
about 1.28 s from moon to Earth
a( x, t )
a0
cos[2
(x
l
ut)]
a0 amplitude
At a certain position (x),
the wave change with t.
At a certain time (t), the wave change with x.
Electromagnetic radiation is the emission and transmission
of energy in the form of electromagnetic waves.
The energy intensity
Energy passed through a unit area per unit time