Download H-atom, emission spectra

PH 103
Dr. Cecilia Vogel
Lecture 20
Review
uncertainty
atoms and nuclei
The quantum model of the atom
Outline
Quantum numbers
H-atom
spectra
Current Model of Atom
Electron “cloud” is wavefunction
describes the probability of electron being
at various points around the nucleus.
Electron wave behavior based on
Schroedinger equation.
The electron states are quantized
4 different quantities are quantized
4 different quantum numbers
n, ℓ, mℓ, ms.
http://www.falstad.com/qmatom/directions.html
Four Quantum Numbers
Quantum
number
n
ℓ
mℓ
ms
Physical
quantity
Possible
values
Positive
Energy
Size of orbital integers
Orbital angular Non-negative
momentum
integers
(Energy)
Orb. ang. mom.
integers
z-component
Spin
z-component
+ ½ or - ½
Additional
restrictions
n>ℓ
ℓ<n
ℓ > |mℓ|
|mℓ| < ℓ
none
Principle Quantum
Number
Principle quantum number, n,
n = 1, 2, 3, 4, 5, ....
Determines what “shell” the electron is in.
n=1 is called the K-shell,
n=2 is the L-shell, etc
tells a lot about the electron’s energy
for hydrogen atom, it determines the
electron’s energy

13
.
6
eV
for hydrogen atom: E 
n
n
2
Hydrogen Ground State
Consider the electron in hydrogen
the ground state is the lowest energy
state
lowest E, lowest n, n = 1
Since n =1, then  = 0
Since  = 0, then m = 0
ms = ½ (2 possibilities)
Ground state has a degeneracy of two
because there are two states with the same E
Transition Up
Electron absorbs energy
perhaps from a photon
goes to a higher energy level
ee
photon
Transition Up
Some ways to add energy to the atom
i.e. ways to excite electron:
HEAT
like blackbody radiation
ZAP
electric discharge through a gas
SLAM
hit atom with high-energy particle
for example, nuclear radiation
SHINE
hit atom with light (photons)
Transition Down – H-atom
Electron loses energy to a photon - gives off light
 Electron goes to a lower energy
level
13.6eV 13.6eV
losing energy | E | nf 2  ni 2
ee-
photon
Transition Down – H-atom
Electron loses energy to a photon - gives off light
Light created has the energy that
the electron lost
so
13.6eV 13.6eV
Ephoton 

2
2
nf
ni
hc
13.6eV 13.6eV


2
2

nf
ni
Hydrogen spectrum
Visible lines
in H-spectrum
come from
transitions to
nf=2.
Ex: with ni=3
hc
13.6eV 13.6eV


2

nf
ni 2
1240eVnm

13.6eV 13.6eV


4
9
  656 nm
H and Multi-electron Atoms
Recall for Hydrogen
electron Energy depends on n only
Other atoms
electron energy depends on n and ℓ
So…
L-shell (n=2) for hydrogen atom
is just one energy level
L-shell for other atoms
-- two different energy levels
2s and 2p
and M-shell splits into 3s, 3p, 3d subshells, etc
Single-electron
atoms
(like Hydrogen)
Other
atoms
Compare Hydrogen
to Multi-electron Atoms
Hydrogen has
few e- energy levels
few e- transitions
few photon energies, few wavelengths
Other atoms
many e- energy levels
many e- transitions
many photon energies, many wavelengths
generally have more complicated spectrum