Absorption / Emission of Photons and Conservation of Energy
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Transcript of Absorption / Emission of Photons and Conservation of Energy
Absorption / Emission of Photonsand Conservation of Energy
Ef - Ei = hv Ei - Ef = hv
hv
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
Prism
Photographic Film
Slit
White Light Source
Emission Spectra of Hydrogen
Prism
Photographic Film
Film
Slit
Low DensityGlowing
Hydrogen Gas
Discrete Emission Spectrum
Portion of the Absorption Spectrum of Hydrogen
Discrete Absorption Spectrum
Prism
Photographic Film
Film
Slit
White Light Source
Discrete Emission Spectrum
Hot Hydrogen Gas
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
Portion of the Emission Spectrum
Absorption Spectrum
Hot Gas
Cold Gas
Absorption spectrum of
Sun
Emission spectra of various
elements
Usually the Emission spectrum has more “features” of the absorption spectrum
Atom excitation,Absorption linesfrom the ground
state (n=1)
Atom de-excitation,Emission lines
from the excited states
Schrodinger equation for one electron atoms
Coulomb potential
€
V (r) = −Ze2
(4πε0)r
€
−h2
2m∇ 2 −
Ze2
(4πε0)r
⎢
⎣ ⎢
⎥
⎦ ⎥ψ (
r r ) = Eψ (
r r )
€
ψ(r r )=ψ(r,θ,ϕ)=ψE,l,m(r,θ,ϕ)=RE,l(r)Υl,m(θ,ϕ)
€
E = En = −Z 2e2
4πε0a0
1
2n2
€
l = 0,1,...,n −1
m = −l.− l +1,..., l −1, l
€
ψ(r r )=ψn,l,m(r,θ,ϕ)=Rn,l(r)Υl,m(θ,ϕ)
Radial and angular part
BORN POSTULATEThe probability of finding an electron in a certain region of space is proportional to ψ2, the square of the value of the wavefunction at that region.
ψ can be positive or negative. ψ2 is always positive
ψ2 is called the “electron density”
What is the physical meaning of the wave function?
E.g., the hydrogen ground state
1 1 3/2
ψ 1s = e -r/ao (ao: first Bohr radius=0.529 Å)
ao
1 1 3ψ2
1s = e -2r/ao
ao
ψ21s
r
Radial electron densitiesThe probability of finding an electron at a distance r from the
nucleus, regardless of direction
The radial electron density is proportional to r2ψ2
Surface = 4r2
r
Volume of shell = 4r2 r