Lecture 8' Overview Ch' 13

1
Lecture 8. Overview Ch. 1-3

• Relativistic Kinematics
• Relativistic Dynamics
• Photons Photoelectric and Compton effects
• de Broglie waves
• Uncertainty Principle (both momentum-position
  and energy-lifetime)

2
Problem (Doppler)
A spaceship approaches an asteroid and sends out
a radio signal with proper frequency 6.5x109 Hz.
The signal bounces off the asteroids surface and
returns shifted by 5x104 Hz. What is the relative
speed of the spaceship and the asteroid?
In this situation, there Doppler shift occurs
twice firstly, the original frequency is
received by an asteroid as
secondly, the spaceship receives the reflected
signal with the frequency
3
Problem (Relativistic Dynamics)
The nuclear reaction pd?3He? can occur even
when the initial particles have zero kinetic
energy. If the gamma photon has energy 5.5MeV
when the reaction occur with the initial
particles at rest, what is the mass of the 3He
nucleus? mp1.6724x10-27kg, md3.3432x10-27kg
4
Problem (Relativistic Dynamics)
Beiser 38. A moving electron collides with a
stationary electron and an electron-positron pair
comes into being as a result. When all four
particles have the same velocity fter the
collision, the kinetic energy required for this
process is a minimum. Use a relativistic
calculation to show that Kmin6mc2, where m is
the electron mass.
energy conservation
after
before
momentum conservation
In the center-of-mass RF
relative speed
before
after
5
Problem (Relativistic Dynamics)
Find the minimum energy a proton must have to
initiate the reaction
(production of anti-protons (Berkeley Bevatron
1954) the energy and, thus, the cost of the
accelerator, must be minimized)
The minimum energy when the products of
reaction are at rest in the center of mass
reference frame all the incoming energy is
transformed into the rest energy.
The invariant has the same value in all RFs!
Lets use the lab RF
For colliding beam accelerators (e.g., LHC),
the center-of-mass frame and the lab frame are
the same (each proton should have E2mc2)
6
Problem (de Broglie waves, relativity)

• Can we consider an electron as a relativistic
  particle if
• its momentum is comparable to the momentum of a
  visible-light photon with hf2eV
• its de Broglie wavelength is comparable to the
  size of a hydrogen atom (0.1nm)
• its kinetic energy is of an order of 1MeV.
• Calculate and explain!

(a)
non-relativistic (vltltc)
(b)
still non-relativistic
K is twice the rest energy of course,
relativistic!
(c)
7
Problem (Photoelectric Effect)
When iron is illuminated with ultraviolet
light with a wavelength of 250nm, the maximum
voltage developed between the plates in the
experiment shown in Figure is 0.46V. Find the
voltage difference between the plates if the
ultraviolet light wavelength is changed to 220nm.
Also find W for iron.
anode
- - - - - - - -
light
V

cathode
8
Problem (Compton)
In a Compton scattering experiment with
electrons, a detector is set at an angle of 570.
What must the frequency of the incoming X rays be
in order to produce a final X ray with a
frequency 1 less than the initial frequency?.
9
Problem (Compton)
A beam of monochromatic X-rays is directed at
electrons at rest. After a collision between an
X-ray photon and an electron, it was observed
that the electron had a kinetic energy of 400keV
while the scattered photon had a wavelength
exactly twice its wavelength before the
collision. (a) (10) Calculate the wavelength and
the energy of the photon before the collision
(use conservation of energy). (b) (5) Calculate
the angle by which the photon was deviated from
its original direction. (c) (5) Calculate the
total energy E and the momentum p of the electron
after the collision. (d) (5) Find the angle
between the directions of the recoil electron and
the incident photon (use conservation of
momentum).
(a)
(b)
(c)
(d)
10
Problem (de Broglie waves)
Find the de Broglie wavelength of an electron
with kinetic energy of 10MeV.
Because the kinetic energy is much greater than
the rest energy, we use the relativistic approach
to estimate p.
For what kinetic energy will a particles de
Broglie wavelength equal its Compton wavelength?
11
Problem (Uncertainty Principle)
An electron microscope is designed to resolve
objects as small as 0.1nm. What energy electrons
must be used in this instrument? Express your
answer in eV.
for comparison
thus, we can use non-relativistic approach
12
Problem (Uncertainty Principle, de Broglie waves)
Calculate the de Broglie wavelength of a
5.4MeV ? particle (the nucleus of 4He 2
protons2 neutrons) emitted from an 241Am
nucleus. Could this particle exist inside the
241Am nucleus (diameter 1.6?10-15 m)?
- the energy is much smaller than the rest energy
of the ? particle, thus we can apply the
non-relativistic approach.
- the nucleus is too small for such a low-energy
? particle