All About Atoms

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Chapter 40 All About Atoms In this chapter we
continue with a primary goal of
physics?discovering and understanding the
properties of atoms. 100 years ago researchers
struggled to find experiments that would prove
the existence of atoms. Today, thanks to
scientific and technological progress, we can
manipulate atoms in amazing ways we can image
individual atoms using scanning tunneling
microscopy we can drag them on surfaces to make
quantum corrals, and even hold an individual atom
indefinitely in a trap in order to study its
properties when isolated.
(40-1)
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40-2 Some Properties of Atoms
Basic Properties Atoms are stable. Essentially
all atoms have remained unchanged for billions of
years. Atoms combine with each other. Atoms
stick together to form molecules and stack up to
form rigid solids. Even though atoms are mostly
empty space, their interactions allow you to
stand on a floor without falling through! These
basic properties can be explained by quantum
mechanics.
(40-2)
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Some Properties of Atoms
Subtler Properties Atoms Are Put Together
Systematically. There are repetitive (periodic)
patterns in the properties of different atoms
that allow them to be organized into a periodic
table.
Six periods with 2, 8, 8, 18, 18, and 32 atoms in
each period, respectively. These numbers are
predicted by quantum mechanics.
Ionization energy vs. atomic number (number of
protons in nucleus)
(40-3)
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Some Properties of Atoms
Subtler Properties, contd Atoms Emit and Absorb
Light Atoms Have Angular Momentum and
Magnetism
Orbit of each electron (more correct to think
in terms of angular momentum of electronic state)
can produce a magnetic moment.
(40-4)
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Some Properties of Atoms
Subtler Properties, contd Einstein-de Haas
Experiment
Angular momentum and magnetic moment of atoms are
coupled. Aligning magnetic moments of iron atoms
using an external magnetic field causes the iron
cylinder to rotate in a direction opposite to the
now-aligned angular momenta of the iron atoms
(conservation of angular momentum).
(40-5)
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40-3 Electron Spin
Trapped or free, electrons have intrinsic spin
angular momentum S (spin). This is a basic
characteristic like the electrons mass or
charge. This leads to two additional quantum
numbers that are required to fully specify the
electronic state s (magnitude of the spin, which
is always ½ for electrons) and ms (the component
of spin along the z-axis).
States with same n form a shell. States with
same value for n and l form a subshell.
(40-6)
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40-4 Angular Momenta and Magnetic Dipole Moments
Orbital Angular Momentum and Magnetism
Orbital Angular Momentum
Orbital Magnetic Dipole Moment
(40-7)
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Orbital Angular Momentum and Magnetic Dipole
Moments
Bohr magneton
(40-8)
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Spin Angular Momentum and Spin Magnetic Dipole
Moment
S, the magnitude of the spin angular momentum,
has a single value for any electron, whether free
or trapped
where s (½) is spin quantum number of the
electron. The spin magnetic dipole moment ms is
related to S and is given by
(40-9)
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Orbital and Spin Angular Momentum Combined
(40-10)
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40-5 Stern-Gerlach Experiment
Magnetic Deflecting Force on Silver Atom
Stronger B
z
Weaker B
(40-11)
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Stern-Gerlach Experiment, contd
Experimental surprise
Meaning of Experiment
Silver atoms
(40-12)
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40-6 Magnetic Resonance
(40-13)
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Magnetic Resonance, contd
The net magnetic field that a proton experiences
consists of the vector sum of the externally
applied magnetic field Bext and internal fields
Bint
magnetic dipole moments of atoms and nuclei near
the proton? Bint
For fixed radio frequency light, when Bext
hf/2mz - Bint? absorption occurs. Bint is
different for protons in different molecules, so
the resonance Bext will be different for protons
in different molecules (local environment). Resona
nces provide a fingerprint of what (and where in
the case of Magnetic Resonance imaging) different
proton-containing molecules are present in the
material studied.
(40-14)
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40-7 Pauli Exclusion Principle
40-8 Multiple Electrons in Rectangular Traps
1. One-dimensional trap. Two quantum numbers n1,
2, 3 (wavefunction state along L) and ms ½ or
-½. 2. Rectangular corral. Three quantum numbers
nx 1, 2, 3 (wavefunction state along Lx) , ny
1, 2, 3 (wavefunction state along Ly), and ms
½ or -½. 3. Rectangular box. Four quantum
numbers nx 1, 2, 3 (wavefunction state along
Lx) , ny 1, 2, 3 (wavefunction state along
Ly), nz 1, 2, 3 (wavefunction state along Lz),
and ms ½ or -½.
(40-15)
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Finding the Total Energy
Adding electrons to a rectangular trap Use
energy level diagram. Start at lowest energy
level and move up as lower levels become filled.
Empty (unoccupied) level
Partially filled level
Filled levels
(40-16)
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40-9 Building the Periodic Table
Four quantum numbers n, l, ml, and ms identify
the quantum states of individual electrons in a
multi-electron atom. Subshells are labeled by
letters l 0 1 2 3 4 5 . . . s p d f g h . .
. Example n 3, l 2? 3d subshell
(40-17)
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Building the Periodic Table, contd
For smaller atoms such as these, one can assume
that the energy only depends on n.
(40-18)
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Building the Periodic Table , contd
Iron Z 26?26 electrons For atoms with a larger
number of electrons, the interactions among the
electrons causes shells with the same n but
different l to have different energies
(degeneracy lifted). 1s2 2s2 2p6 3s2 3p6 3d6
4s2 Due to interactions, it takes less energy to
start filling the 4s subshell before completing
the filling of the 3d subshell, which can
accommodate 10 electrons.
(40-19)
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40-10 X Rays and Ordering of Elements
X rays are short-wavelength (10-10 m),
high-energy (keV ) photons. Photons in the
visible range 10-6 m eV. Useful for probing
atoms
Independent of target material
(40-20)
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Characteristic X-Ray Spectrum

1. Energetic electron strikes atom in target, knocks
   out deep-lying (low n value). If deep-lying
   electron in n 1 (K-shell), it leaves a vacancy
   (hole) behind.
2. Another electron from a higher energy shell in
   the atom jumps down to the K-shell to fill this
   hole, emitting an x-ray photon in the process.

If the electron that jumps into the hole starts
from the n 2 (L-shell), the emitted radiation
is the Ka line. If it jumps from the n 3
(M-shell), the emitted radiation is the Kb line.
The hole left in the n 2 or n 3 shells is
filled by still higher lying electrons, which
relax by emitting lower energy photons (higher
lying energy levels are more closely spaced).
(40-21)
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Ordering Elements
Moseley (1913) bombarded different elements with
x rays. Nuclear charge, not mass, is the critical
parameter for ordering elements.
(40-22)
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Ordering Elements, contd
Accounting for the Moseley Plot
Energy levels in hydrogen
Approximate effective energy levels in
multi-electron atom with Z protons (replace e2 x
e2 with e2 x (e(Z - 1))2
Ka energy
Ka frequency
(40-23)
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40-11 Lasers and Laser Light

1. Laser light is highly monochromatic Its spread
   in wavelength is as small as 1 part in 1015.

1. Laser light is highly coherent Single
   uninterrupted wave train up to 100 km long. Can
   interfere one part of beam, with another part
   that is very far away.

1. Laser light is highly directional Beam spreads
   very little. Beam from Earth to Moon only spreads
   a few meters after traveling 4 x 108 m.

1. Laser light can be sharply focused Can be
   focused into very small spot so that all the
   power is concentrated into a tiny area. Can reach
   intensities of 1017 W/cm2, compared to 103 W/cm2
   for oxyacetylene torch.

Lasers have many uses Small voice/data
transmission over optic fibers, CDs, DVDs,
scanners Medium medical, cutting (from cloth to
steel), welding Large nuclear fusion research,
astronomical measurements, military applications
(40-24)
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40-12 How Lasers Work
Thermal distribution (Boltzmann)
To get more stimulated emission than absorption,
Nx gt N0 ? population inversion ? not in thermal
equilibrium
(40-25)
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Helium-Neon Gas Laser
Population Inversion
Thermal Equilibrium
(40-26)