The Hydrogen atom

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The Hydrogen atom
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Space quantization

• radial function quantized (bound potential)
• angular functions Ylm(?,?) are quantized for any
  potential
• spherical waves

• 2 angular coordinates ?, ?
• 2 quantum numbers l, ml
• direction of L unknown Heisenberg uncertainty
  principle

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Wave function components
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Radial wave function and probability
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Hydrogen atom orbitals
One Radial Lobe
Two Radial Lobes
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Atomic magnetic moments
S
N S
N
? -e/2m gyromagnetic ratio
Bohr magneton quantum magnetic moment
ml magnetic quantum number
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Magnetic moment and precession
MRI - magnetic resonance imaging
The precession of nuclear spin about a magnetic
field is detected. The density of H atoms
(protons) or other nuclei in the body can be
mapped to form an MRI image.
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Normal Zeeman effect
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Force on magnetic moment
Stern-Gerlach experiment first direct
measurement of space quantization ml -1,
-0, 1
Gradient B-field
Dipole moment

• the net force is in the direction of the dipole
  moment

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Spin intrinsic angular momentum
Its all about spin!

• spin always has the same magnitude
• integer or half-integer
• the electron has nothing to spin(it is a point
  particle)

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Pauli exclusion principle
electron orbitals
No two electrons can exist in the same quantum
state
3d
3p
multi-particle wave function
3s
indistinguishable particles
2p
2s
1s
wave function symmetry
Fermions - spin 1/2, 3/2, 5/2 Pauli exclusion
principle
Bosons - spin 0, 1, 2, bosons flock together
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Sum of angular momenta
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Coupling of angular momentum
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Spin-orbit interaction fine structure
2p3/2
2s1/2
2p1/2
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Periodic Table
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10
5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6
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X-ray spectra (part II)
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X-ray spectra (part II)
Re (Z75)
Hydrogenic ions
Hf (Z72)
Pm (Z61)
Tc (Z43)

• Z2 200 (Si) 6000 (Au) X-rays

Moseley formula (K?)

• first direct measurement of Z
• gaps at Z43, 61, 72, 75,