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)

1

Spectral lines and Bohr’s theory

2

3

Spectral Lines

4

5

6

7

8

The Balmer Series

9

10

11

The nuclear atom

12

Rutherford’s apparatus

13

14

15

Bohr’s theory

16

17

18

19

20

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, …

25

Quantum Mechanics

26

27

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?

34

35

36

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

40

41

42

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

43

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)

44

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.

46

Medical Applications of the Laser

Lasers being used to change the shape of the corneaLasers being used to change the shape of the cornea.