PH 202 7B Summer 2007PH 202-7B Summer 2007
Particles & Waves, Nature of Atom (selected topics)(selected topics)
Lectures 14-15Chapters 29, 30
(Cutnell & Johnson, Physics 7th edition)
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Spectral lines and Bohr’s theory
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Spectral Lines
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The Balmer Series
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The nuclear atom
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Rutherford’s apparatus
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Bohr’s theory
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The Bohr Model of the Hydrogen Atom
…,3,2,1 22
2
2
422
=⎟⎟⎠
⎞⎜⎜⎝
⎛−= n
nZ
hemkEn
π
⎠⎝
B h l l
( ) …,3,2,1J1018.2 2
218 =×−= − nZE
Bohr energy levels
( ) …,3,2,1 J1018.2 2× nn
En
( ) …,3,2,1eV6.132
=−= nZE ( ) …,3,2,1 eV 6.13 2 nn
En
The Bohr Model of the Hydrogen Atom
ENERGY LEVEL DIAGRAMS
The Bohr Model of the Hydrogen Atom
Example 3 The Ionization Energy of Li2+
Li2+ is a lithium atom (Z=3) with only one electron. Obtain the ionizationenergy of Li2+.
322Z( ) ( ) eV 12213eV 6.13eV 6.13 22 −=−=−=
nZEn
V122I i ti + eV122energy Ionization +=
( )emk ⎟⎞
⎜⎛ 11Z21 2
422π ( )if nnch ⎟⎟⎠
⎜⎜⎝
−= Z 222
3λ
24fifi nnnn >= ,3,2,1, …
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Quantum Mechanics
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The de Broglie Wavelength and the Wave Nature of Matter
The wavelength of a particle is given by the same relation that applies to aby the same relation that applies to a photon:
ph=λ
de Broglie wavelength
The de Broglie Wavelength and the Wave Nature of Matter
E l 5 Th d B li W l th f El t d B b llExample 5 The de Broglie Wavelength of an Electron and a Baseball
Determine the de Broglie wavelength of (a) an electron moving at a speed of 6 0x106 m/s and (b) a baseball (mass = 0 15 kg) moving at a speedof 6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speedof 13 m/s.
( )( )( ) m102.1
sm100.6kg101.9sJ1063.6 10
631
34−
−
−
×=××
×== phλ
( ) 1033sJ1063.6 3434
−−×hλ ( )
( )( ) m103.3sm13kg 15.0
34−×=== phλ
The de Broglie Wavelength and the Wave Nature of Matter
Particles are waves of probability.
The Heisenberg Uncertainty Principle
THE HEISENBERG UNCERTAINTY PRINCIPLETHE HEISENBERG UNCERTAINTY PRINCIPLE
Momentum and position
( )( ) hyp ≥ΔΔ( )( )π4
ypy ≥ΔΔ
Uncertainty in y componentof the particle’s momentum
Uncertainty in particle’sposition along the y direction
The Heisenberg Uncertainty Principle
THE HEISENBERG UNCERTAINTY PRINCIPLETHE HEISENBERG UNCERTAINTY PRINCIPLE
Energy and time
( )( ) htE ≥ΔΔ( )( )π4
tE ≥ΔΔ
Uncertainty in the energyof a particle when the particleis in a certain state
time interval during which the particle is in that state
is in a certain state
The Heisenberg Uncertainty Principle
Conceptual Example 7 What if Planck’s Constant Were Large?
A bullet leaving the barrel of a gun is analogous to an electron passingthrough the single slit. With this analogy in mind, what would hunting b lik if Pl k’ t t h l ti l l l ?be like if Planck’s constant has a relatively large value?
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X-Rays
Electrons are emitted from a heated filament and acceleratedthrough a large voltage.
When they strike the target, X-raysare emitted.
X-Rays
The sharp peaks are called characteristic X-rays because they arecharacteristic of the target material.characteristic of the target material.
X-Rays
Spontaneous and stimulated transitions
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LasingLASER - Light Amplification by StimulatedExcited state LASER - Light Amplification by Stimulated
Emission of Radiation
Stimulated emission - Stimulated emission occurs when a traveling photon interacts with
an exited atom. During the interaction, the atom will become de-excited and release a
photon of the same frequency and direction of
Ground state
photon of the same frequency and direction of the incident photon.
Lasers have 3 parts:100% Mirror 75 % Mirror
Lasers have 3 parts:
1. Gain medium – a place for stimulated emmision to occur (crystal, gas, etc.)
2 P iti f db k f ill ti
Gain medium
2. Positive feedback – means for oscillation (mirrors, diffraction grating, etc.)
3. Source of energy – an incoming energy so rce hich keeps more atoms in the
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source which keeps more atoms in the excited state than in the ground state.
First Solid State Ruby Laser (1961)First Solid State Ruby Laser (1961)
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He-Ne Laser
Laser ApplicationsTh h t i ti f l li ht k l l bl t l i• The characteristics of laser light make lasers a valuable tool in many areas, such as communications, industry, medicine, military and scientific research.
• Communications: Lasers working in the infrared area are right now revolutionizing the communications industry. A laser transmits voice or g ydata via fiber optic cables at much improved speed and capacity. These lasers are part of the broadband revolution we hear about daily. Other everyday, low power applications for lasers are CD and DVD players.
• Industry: Lasers are used to cut, drill, weld, guide and measure with high accuracy. For some of these applications very powerful lasers (10,000accuracy. For some of these applications very powerful lasers (10,000 Watts) are used, and the laser light is focused in a very small area (0.0025 mm), which produces an extreme heat (10,000 F) that can cut through and melt extremely hard materials.
• Medicine: Surgeons use lasers to remove deceased body tissue, with little damage to surrounding area In addition lasers seal off blood vesselsdamage to surrounding area. In addition lasers seal off blood vessels severed during the surgery, thus reducing the amount of bleeding. Laser eye surgery is becoming common for correcting near sightedness as well as for reattaching retinas.
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Medical Applications of the Laser
Lasers being used to change the shape of the corneaLasers being used to change the shape of the cornea.
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