Absorption / Emission of Photons
and Conservation of Energy
hv
hv
Ef - Ei = hv
Ei - Ef = hv
Energy Levels of Hydrogen
Electron jumping to
a higher energy level
E = 12.08 eV
Spectrum of Hydrogen, Emission lines
Bohr’s formula:
Hydrogen is therefore a fussy
absorber / emitter of light
It only absorbs or emits photons with precisely the
right energies dictated by energy conservation
Electron in a Hydrogen Atom
• The three quantum numbers:
– n = 1, 2, 3, …
– l = 0, 1, …, n-1
– m = -l, -l+1, …, l-1, l
• For historical reasons, l = 0, 1, 2, 3 is also known
as s, p, d, f
1s Orbital
Density of the cloud gives
probability of where the electron
is located
2s and 2p Orbitals
Another diagram of 2p orbitals
Note that there are three different configurations
corresponding to m = -1, 0, 1
3d Orbitals
Now there are five different configurations
corresponding to m = -2, -1, 0, 1, 2
4f Orbitals
There are seven different configurations
corresponding to m = -3, -2, -1, 0, 1, 2, 3
• The excited atom usually de-excites in about 100
millionth of a second.
• The subsequent emitted radiation has an energy
that matches that of the orbital change in the atom.
• This emitted radiation gives the characteristic
colors of the element involved.
Emission Spectra
Continuous Emission Spectrum
Slit
White Light
Source
Prism
Photographic Film
Emission Spectra of Hydrogen
Discrete Emission Spectrum
Slit
Film
Low Density
Glowing
Hydrogen Gas
Prism
Photographic Film
Portion of the Absorption
Spectrum of Hydrogen
Discrete Emission Spectrum
Discrete Absorption Spectrum
Slit
Hot
Hydrogen Gas
White Light
Source
Film
Prism
Photographic Film
Absorption Spectra
• Frequencies of light that represent the correct energy
jumps in the atom will be absorbed.
• When the atom de-excites, it may emit the same kinds of
frequencies it absorbed.
• However, this emission can be in any direction.
Emission and Absorption
Continous Spectrum
Hot Gas
Portion of the Emission Spectrum
Cold Gas
Absorption Spectrum
Absorption
spectrum of
Sun
Emission
spectra of
various
elements
Usually the Emission spectrum has more
“features” of the absorption spectrum
Atom excitation,
Absorption lines
from the ground
state (n=1)
Atom de-excitation,
Emission lines
from the excited states
Schrodinger equation for one electron atoms
Ze 2
V (r)  
(40 )r
Coulomb potential

 2 2
Ze 2 
 

 (r )  E (r )
(4 0 )r 
 2m
(r )   (r,, )  E,l,m (r,, )  RE,l (r)l,m (, )

2 2
Z e
1
E  En  
4 0 a0 2n 2
l  0,1,...,n 1
m  l. l  1,...,l 1,l
(r )  n,l,m (r,,)  Rn,l (r)l,m (,)

Radial and angular part
What is the physical meaning of the wave function?
BORN POSTULATE
The probability of finding an electron in a certain
region of space is proportional to 2, the square of
the value of the wavefunction at that region.
 can be positive or negative. 2 is always positive
2 is called the “electron density”
E.g., the hydrogen ground state

1s
=
21s =
1
1
3/2
ao

1

1
3
ao
e
-r/ao
e
(ao: first Bohr radius=0.529 Å)
-2r/ao
21s
r
Radial electron densities
The probability of finding an electron at a distance r from the
nucleus, regardless of direction
The radial electron density is proportional to r22
Dr
Surface = 4r2
Volume of shell =
4r2 Dr