I Relativity
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1.Principle of relativity: All the laws of Physics
are the same in all inertial frames
2.The constancy of the speed of light: The
speed of light in a vacuum has the same value,
c=2.99792458 x108 m/s, in all inertial reference
frames, regardless of the velocity of the observer
or the velocity of the source emitting the light
In relativistic mechanics, there is no such thing
as absolute length of absolute time. Events at
different locations that are observed to occur
simultaneously in one frame are not observed to
be simultaneous in another frame moving
uniformly past the first
Two events that are simultaneous in one
reference frame are in general not simultaneous
in a second frame moving relative to the first.
Simultaneity depends on the state of motion to
the observer, and is there not an absolute
concept
 Time Dilatation
Δt=Δtp/ √(1- v2/c2) = γ Δtp
Where γ=1/ √(1- v2/c2)
 The time interval Δt between two events
measured by an observer moving with respect to
a clock is longer that the time interval Δtp
between the same two events measured by an
observer at rest with respect to the clock.
Δtp- proper time
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A clock moving past an observer at speed v runs
more slowly than an identical clock at rest with
respect to the observer by a factor γ-1
Proper time- the time interval between two
events as measured by an observer who sees
the events occur at the same position
Length Contraction
Proper length Lp of an object is the length of the
object as measured by an observer at rest
relative to the object
L=Lp / γ =Lp√(1- v2/c2)
Length contraction takes place only along the
direction of motion
Relativistic energy
 KE=γ mc2-mc2
 Er=mc2 –rest energy
Total Energy =Kinetic Energy +Rest Energy
 E =KE+mc2 =γmc2
 E=mc2 / √(1- v2/c2)
 A stationary particle with ZERO kinetic
energy has a energy proportional to its
mass
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Einstein’:s postulates of general
relativity
 1.All the laws of nature have the same
form for observers in any frame of
reference, accelerated or not
 2. In the vicinity of any given point, a
gravitational field is equivalent to an
accelerated frame of reference without a
gravitational field
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General relativity also predicts extreme states of matter created by
gravitational collapse. If the concentration of mass become very
great, when a large star exhausts its nuclear fuel and collapses to a
very small volume, a BLACK HOLE may form
II Quantum Physics
Electromagnetic radiation is emitted and
absorbed by matter as though it existed in
individual bundles called QUANTA
 A quantum of electromagnetic energy is
knows as a photons
 Light behaves like a stream of photons,
and this is illustrated by the photoelectric
effect
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When a piece of metal is
illuminated by electromagnetic
radiation (visible light,
ultraviolet, or x-rays), the
energy absorbed by electrons
near the surface of the metal
can liberate them from their
bound state, and these
electrons can fly off
The released electrons are
knows as photoelectrons
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Wave-only theory of light would predict three
results:
A) There would be a significant time delay
between the moment of illumination and the
ejection of photoelectrons, as the electrons
absorbed incident energy until their KE was
sufficient to release them from the atom’s grip
B) Increasing the intensity of light would cause
the electrons to leave the metal surface with
greater KE
C) Photoelectrons would be emitted regardless
of the frequency of the incident energy, as long
as the intensity was high enough
None of these prediction was observed!
 A) photoelectrons were ejected within few
billionths of the second after illumination
 B) Increasing the intensity of light did not
cause photoelectrons to leave the metal
surface with greater KE. More e- were
ejected as the intensity was increased
 C) If light of frequency lower than fo
(threshold frequency) were used to
illuminate the metal surface, no
photoelectrons were ejected
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Einstein postulated these observations
by postulating that the energy of the
incident electromagnetic wave was
absorbed in individuals bundles
(photons)
 Energy of a photon is proportional to
the frequency of a wave
E=hf
 h=6.63x10-34 J s– Planck constant
 A certain amount of energy had to be
imparted to the metal surface in order to
liberate it – Φ – metal work function
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Increasing the intensity of and the incident
energy means bombardment with more
photons and results in the ejection of more
photoelectrons:
KEmax=hf- Φ
 E =hf –energy of each incident photon
 Threshold frequency fo= Φ/h
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The dual nature of light and matter:
 Light has a dual nature, exhibiting both
wave and particle characteristics
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Because photons have wave and
particle characteristic, perhaps all
forms of matter have both properties
 E=hf =hc/λ
p=E/c =hc/cλ =h/λ – momentum of a photon
 λ=h/p =h/mv – de Broglie wavelength of
a particle
 Frequency of matter waves:
 f= E/h (Einstein relationship for photons)
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III Atomic Physics
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The Bohr Model Of The Atom
The light from a glowing gas, passed through a
prism to disperse the beam into its components
wavelengths, produces patterns of sharp lines
called atomic spectra
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the atomic spectra of all the elements:
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The visible wavelength that appear in the
emission spectrum of Hydrogen has been
summarized by the Balmer Formula:
1/λn=R(1/22-1/n2)
R-Ryderberg ct. = 1.1 x107 m-1
Bohr’s postulated that the electron would orbit
the nucleus only at certain discrete radii (when
the e- is in one of these special orbits it does not
radiate away energy)
If the e- absorbs a certain amount of energy, it is
exited to a higher orbit, one with a greater
radius
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After a short time in this excited state, it returns
to a lower orbit, emitting a photon in the process
Each allowed orbit-energy level, has a specific
radius
(corresponding energy), the photons emitted
have only specific wavelengths
Bohr found that the energy of each state was a
particular fraction of energy of the ground state
The energy of the n-th energy level:
En=(1/n2)E1
E1- ground state energy= -13.6 eV
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State energy is known as the ionization energy
– the minimum energy that must be supplied to
release the atom’s electron
En=(Z2/n2)(-13.6eV)
Z- nr of protons in the atom’s nucleus
When an exited electron drops from energy level
n=j to a lower one n=I, the transition causes a
photon of energy to be emitted, and the energy
of the photon is the difference between the two
energy levels:
E emitted photon =‫׀‬ΔE‫ = ׀‬Ej –Ei
Wavelength of this photon:
λ=c/f =c/(Ephoton/h)=hc/ (Ej –Ei )
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1/λn=R(1/nf2-1/ni2)
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Wave-Particle Duality
Electromagnetic radiation propagates like a wave but
exchanges energy like a particle
A particle of mass m and speed v with linear momentum
p=mv has an associated wavelength: de Broglie
wavelength
λ=h/p
Bohr postulated that the electron’s orbital angular
momentum, mevnrn, had to be an integral multiple of
h=ħ/2π
mevnrn =nħ (ħ=h/2π), n=1,2,3
2 πrn=nh/ (mevn); 2rn=n (h/pe); 2πrn = n λe
The circumference of the e- ‘s orbit must equal to a
whole number of wavelengths in order for it to be
stable
IV Nuclear Physics
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The nucleus of the atom of particles called
protons and neutrons, which collectively called
nucleons
Atomic nr. - Z –nr of protons
Neutron nr. (nr. of neutrons) - N
Mass nr. (nucleon nr.) – A =Z+N
Nuclei that contain the same nr. of protons but
different nr. of neutrons are called izotopes
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Strong nuclear force- binds neutrons and
protons together
mp=1.6726x10-27kg= 1.00728 u
mn=1.6749x10-27kg= 1.00867 u
Atomic mass unit u defined as 1/12 the mass
of 12C atom
1u=1.6605x10-27kg
If we consider the deutron, the nucleus of
deutrium an isotope of hydrogen that contains 1
proton and 1 neutron
mdeutron=2.01356 u
The difference between the mass of any bound
nucleus and the sum of the masses, is called
mass defect
Δm= (mp + mn)-md = 0.00239 u
The missing mass wasd converted to
energy when the deutron was formed, is
the enery needed to break the deutron into
a separtate protonand neutron, and is
called – the binding energy of the
nucleus
 Binding energy per nucleon (for
deutron)
 2.23MeV/2 nucleons =1.12 MeV/nucleon
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Nuclear Reactions
 Ex:- Natural Radioactive decay is the process by which
an atomic nucleus of an unstable atom loses energy by
emitting ionizing particles (ionizing radiation). The
emission is spontaneous, in that the atom decays
without any interaction with another particle from outside
the atom .
-Nuclear fission is a nuclear reaction in which the nucleus
of an atom splits into smaller parts (lighter nuclei), often
producing free neutrons and photons (in the form of
gamma rays). Fission of heavy elements is an
exothermic reaction which can release large amounts of
energy both as electromagnetic radiation and as kinetic
energy of the fragments
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- Nuclear fusion is the process by which
two or more atomic nuclei join together, or
"fuse", to form a single heavier nucleus.
This is usually accompanied by the
release or absorption of large quantities of
energy. Large-scale thermonuclear fusion
processes, involving many nuclei fusing at
once, must occur in matter at very high
densities and temperatures.
 We write 11p ,11H, 10n, 00γ
 Ex: 10n+19880 Hg→19779Au + ??X
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Disintegration energy
 Nuclear reaction must conserve total energy
ΔE=(Δm)c2
 A general nuclear reaction:
A+B→C+D+Q
 Q- disintegration energy
 Q<0- reaction is endothermic (endoergic) Q>reaction is exothermic (exoergic)
 Q=[(mA+mB)-(mC+mD)]c2 =Δmc2
 Most of energy is revealed as KE of the least
massive product nuclei
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