Download General Physics I - University of Rochester

Lasers and effects of magnetic
field
Physics 123
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Lecture XXI
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Light emission: classical case
• Light bulb: current heats up atoms, they collide
with each other and emit EM waves – light
• Incoherent source of light – a continuous
spectrum, isotropic in direction, no correlation in
phase
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Light emission: quantum
transitions
Energy transition  light emission  fixed photon energy
(frequency and wave length)
Atoms are usually in the ground state (no emission)
When excited (e.g. from temperature collisions) they go back
to the ground state through spontaneous incoherent light
emission (frequency=color).
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Fluorescence, phosphorescence
• Three level system, middle state is metastable (DL(E2-E0)=2)
• Transition between energy levels  frequency of emitted light is
the same
• Phase and direction are still uncorrelated
E’3
Ne
E’2
Electrons from
current collide
with atoms and
excite them
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Two photons
emitted
E’0
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How lasers work
Metastable level
Electrons sit there
Until emission is
stimulated
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How lasers work
The laser in its non-lasing state
The flash tube fires and injects light
into the ruby rod. The light
excites atoms in the ruby.
Some of these atoms emit photons.
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How lasers work
Some of these photons run in a direction parallel to the ruby's axis, so
they bounce back and forth off the mirrors. As they pass through the
crystal, they stimulate emission in other atoms. Photons are bosons
 they want to be emitted with the same
•
Energy (monochromatic),
•
Phase (single-phase),
•
Direction (collimated)
Light leaves the ruby through the half-silvered mirror -- laser light!
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He-Ne laser
• Lasing material is gas: 15% He +85%Ne
• He is excited to second highest energy level (E1) by electric
discharge
• Ne atoms get excited by collisions with He atoms to E3
• Ne goes down to E2 state which is metastable (DL(E2-E0)=2)
E1
He
E’3
Ne
1.96eV
20.61eV
E’2
20.66eV
18.70eV
E’0
E0
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Lasers
• Angular spread is very small, determined by diffraction
on end mirror:
 Q~l/D
D
Main advantage of lasers – energy is concentrated in one spot  precision.
Applications
– laser surgery;
- optical alignment;
- drilling precision holes
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Electron quantum state
• Orbital quantum number is a
vector length l
• Orbital angular momentum:
L  l (l  1)h
• Its projection on z axis is Lz =mlh
another q.n. – magnetic quantum
number ml
• ml can be only integer
ml  l;(l  1);(l  2),...  2,1,0
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l  2; ml  2
l  2; ml  1
l  2; ml  0
l  2; ml  1
l  2; ml  2
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Atom in magnetic field
• Magnetic dipole moment associated with orbital angular

momentum    1 e L
2m
• Since ml is quantized, z-projection of magnetic dipole moment
eh
is quantized as well
z  
• Bohr’s magneton
2m
ml    B ml
eh
B 
 9.27 10  24 J / T
2m
• Potential energy of the magnetic dipole in magnetic field (in zdirection
 
U    B   z B  B ml B
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Zeeman effect
• Potential energy of the magnetic
dipole in magnetic field splits into
several levels
U ml   B ml B
• Transitions between these levels –
Zeeman effect
• Zeeman effect is due to interaction of
external magnetic field with orbital
angular momentum of electrons in
atoms
• Electrons also have internal “angular
momentum” - spin
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Spin
•
•
•
•
All electrons have spin=1/2
It is a vector
Its projection on z axis is another q.n. – spin ms
ms can be only
1
ms  
2
• Similar to orbital angular momentum we expect
eh
z  
ms    B ms
2m
• But experimentally measured value turned out to
be different
z
1
1
s  ; ms 
2
2
1
1
s  ; ms  
2
2
 z   g B ms
g  2.0023
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Gyromagnetic ratio, g-factor
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G-2 experiment in BNL
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G-2 experiment in BNL
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Fine structure
• In the absence of magnetic field some small splitting of
levels in atoms was still observed – interaction of
magnetic field created by orbital angular momentum
(current loop=nucleus around electron) with electron’s
spin


DU  s Bn  s L
• Constant of fine structure (spin-orbit interaction)
e2
1


2 0 hc 137
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Spins in magnetic field
• Imagine free spin (electron or
nucleus) placed inside magnetic
field directed along z-axis
• Energy levels split by
DE  2 z B
1
ms 
2
• This system can absorb photons
of the corresponding frequency
f  2 z B / h
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z
Lecture XXI
E0
DE
1
ms  
2
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Nuclear magnetic resonance
• Transition between the two states
– photons of only a certain energy
(frequency) will be absorbed –
resonance absorption (NMR)
– For H f=42.58MHz for B=1.0T
– This frequency varies slightly for
bound (trapped in molecules) H
atoms
– By mapping f, we can map chemical
composition of human body
– Precision of NMR – 0.5 – 1.0 mm
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