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Relativity
1- Two inertial frames of reference S (at rest) and S' are moving with relative
velocity (v = 0.70c). Use Lorenz transformation equation to find the x" and t' in
the S' frame, if x = 100m, t = 50 s.
(Assume y = z = y' =z' =0)
2- The length of a spaceship traveling with velocity (v = 0.80c) relative to an
observer at rest is measured by its commander to be 100 m. What would be the
length measured by the observer at rest.
3- An observer at rest measures the time of flight of an electron to 400μs.
If the velocity of the electron is 0.95c then calculate the time of flight measured
by another observer traveling at the same velocity as the electron.
4- The relativistic momentum of a particle is three times its rest mass energy
per c. Calculate, the particles velocity.
5- The total energy of a moving proton is 1938 MeV. If the rest mass of a
proton is equal to 1.67x10-27 kg and the speed of light is 3x108 m/s, calculate
the proton's kinetic energy.
Duality of waves and particles
1- In photoelectric effect, the incident photon energy is 3.6 eV. If the work
function of the material is 1.56 eV, Calculate the electron stopping potential.
2- If the work function for a given material is 2.56 eV, calculate the threshold
frequency and the threshold wavelength.
3- The minimum wavelength of an x-ray photon is 1.5x10-10 m. If the
accelerating potential used to create this photon is 8260 Volts, calculate the
ratio h/e.
4- for a photon of frequency equal to 1018 Hz, calculate its:
a) Energy
b) Mass
c) Momentum
5- In Compton scattering calculate the Compton wave-length.
6- In a Compton scattering experiment, the scattered photon is collected at an
angle of 40o. If the incident photon energy is 80 keV, calculate the produced
wavelength difference Δλ.
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7- The wave property of particle is proven by performing diffraction
experiment using particles such as electron and neutrons. Why can't we
measure waves associated with the motion of our bodies.
8- Calculate the de Broglie wavelength for and electron moving at 2000 m/s
9- Calculate the de Broglie wavelength for and electron moving at 2x108 m/s
10- In an electron diffraction experiment, what would be the accelerating
potential to be used to produce an electron de Broglie wave length equal to10-11
m
Introductory quantum mechanics
1- The total energy of an electron is 2 keV. If its velocity is 3000 m/s, calculate
the phase velocity of the wave associated with it.
2- What is the relation between the probability of finding a particle between x
and (x+dx) and its wave-function.
3- Use Heisenberg uncertainty principle to calculate the minimum energy of an
electron inside an atom (radius = 10-10 m).
 n
 L
4- The wave function of a particle is  ( x)  A sin 

x  Where, 0  x  L

And A is the amplitude of the wave. Using the normalization condition, find A
in terms of L.
5- Derive the electron energy levels in an infinite square potential well (take
the potential inside the well as zero and the width of the well as a) .
6- Calculate the first energy state (ground state) for an electron trapped in an
infinite square well potential (V0 = zero and a = 10-11 m).
7- Calculate the first excited energy state for an electron trapped in an infinite
square well potential (V0 = zero and a = 10-11 m).
8- For an electron in a simple harmonic potential, calculate the first energy
state (ground state) if the force constant is 10 N/m. Give your answer in units
of eV.
9- Use the diagram to calculate the ratios R and T
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