Review

The Wave Nature of Light

Interference: Young’s Double Slit Experiment

Constructive Interference: .....2,1,0

;sin

m

md

Destructive Interference:

.....2,1,0

;)2

1(sin

m

md

Line Spacing for Double-Slit Interference

Diffraction by a Single Slit

Diffraction by a Single Slit

Interference by Thin Film

A beam of light reflected by a material whose index of refraction is greater than that of the material in which it is traveling, changes phase by ½ cycle.

Optical Instruments

Focusing The Eye

The Magnifying Glass

The angular of magnification or magnifying power, M, of the lens is defined as the ratio of the angle subtended by an object when using the lens, to the angle subtended using the unaided eye with the object at the near point of the eye.

Telescopes

Magnification of Telescope

M=-fo/fe

Limits of Resolution

The ability of, lens to produce distinct images of two point objects very close together is called the resolution of lens.

Lorentz Factor,

2

21

1

cv

Time Dilation

Clocks moving relative to an observer are measured by that observer to run more slowly.

Length Contraction

220 /1 cvLL

Mass and Energy

2mcE

22 cmmcKE o

Early Quantum Theory and Models of the Atom

Energy distributed among the oscillating electric charges of the molecules is not continuous, but instead consists of a finite number of very small discrete amount, each related to the frequency of oscillation as:

sJh

hfE

34

min

106.6

;

Planck’s Quantum Hypothesis

Planck’s assumption suggests that the energy of any molecular vibration could be only some whole number multiple of hf:

....3,2,1

;min

n

nhfE

Photoelectric Effect

De Broglie Wavelength

mv

h

The Bohr Model

Allowed Angular Momenta

2

hnLn

Allowed Radii

0

22

2

1

1

2

4

1

;4

k

mke

hr

rZ

nrn

Energy Levels of Atom

22

422 12

nh

eZEn

Bohr’s Third Postulate

A single photon is emitted whenever an electron jumps down from one orbit to another.

lowerupper EEhf

Quantum Mechanics of Atoms

The Heisenberg Uncertainty Principle

sJ

hpx

341006.1

2

Quantum Mechanical View of Atoms

Quantum Mechanics of the Hydrogen Atom

n – principal quantum number, positive integer;

l – orbital quantum number, is related to the magnitude of the angular momentum of the electron; at given n can take integer values from 0 to (n-1);

ml – magnetic quantum number, is related to the direction of the electron’s angular momentum, and it can take an integer values from –l to +l.

Complex Atoms and Periodic Table of Elements

Structure and Properties of the Nucleus

Nuclear Radii

3/115 )102.1( Amr

Atomic Mass Unit

227 /5.931106605.11 cMeVkgu

Binding Energy and Nuclear Forces

The total mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons.

Radioactivity

Alpha Decay

Q-Value

The energy released is called the disintegration energy, Q or Q-value:

2)( cMMMQ DP

Beta Decay

Gamma Decay

Half-Life and Rate of Decay

The number of decays N that occur in a very short time interval t is proportional to t and the total number N of radioactive nuclei present:

tNN