Reactor Physics and
Commissioning Tests
Oct 22, 2009
Sweng-Woong Woo
[email protected]
Korea Institute of Nuclear Safety
Contents
I.
II.
III.
IV.
Reactor Physics
Reactivity Calculation Methods
Reactivity Measurement Methods
Physics Tests
2
I. Reactor Phy
Ben Sauerwine
Practice for Qualifying Exams
Electricity and Magnetism
Problem Source: CMU August 2001 Qualifying Exam
(3) A solid glass sphere of mass M and radius R carries on its surface a
uniformly distributed positive charge Q. It is spinning in outer
Ben Sauerwine
Practice for Qualifying Exams
Thanks to Yossef for his presentation on this solution.
Problem Source: CMU August 2001 Qualifying Exam
Pion Photoproduction
Consider the Pion photoreaction + p = p + 0
(a) If the initial proton is at rest in th
Ben Sauerwine
Practice for Qualifying Exams
Thanks to Yossef and Shiang Yong for their input in this problem.
Problem Source: CMU August 2001 Qualifying Exam
Electron in a spherical well
An electron is in a spherical well of radius a and depth V0 , i.e.,
Ben Sauerwine
Practice for Qualifying Exams
Thanks to Ben B. for this solution.
Near absolute temperature T0 , the tension F in a rubber band is given by:
F = aT 2 (L L0 )
where L is the stretched length, L0 is the unstretched length, and a is a constant.
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2002 Qualifying Exam
In a toy model of a nuclear reactor, the conservation law for the number of neutrons
is described by:
v
d
udV = j ndS + V rudV
dt V
S
(1)
where V is the volume of
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 2 (August 2002)
(2) Consider a solid uniform sphere of radius a and mass m which rolls without
slipping inside a fixed cylindrical pipe of radius R. Neglect friction, a
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2002 Qualifying Exam
This problem considers the hyperfine structure of the 1s level of hydrogen. Splitting
of this level is responsible for the famous 21 cm emission line in radio astr
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualifying Exam August 2002
This problem considers electrons confined to a box of length a with a square well
potential
0
V (x ) =
cfw_0 x a
otherwise
In addition to the confining potential,
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2002 Qualifying Exam
Consider N identical but distinguishable very weakly interacting five-state quantum
subsystems with energy levels shown as in figure 1.
Figure 1: Energy level diag
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2003 Qualifying Exam
Consider a supernova explosion occurring at a known distance D from Earth. The
energy spectrum of the photons received on Earth is measured and photons of
energies
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 2 (August 2003)
(7)
A particle of mass m is acted upon by a constant gravitational field with acceleration
v
g. The particle is also acted upon by a force F that is dir
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2003 Qualifying Exam
A three-level quantum system, which might describe a spin-1 particle, for example,
has a Hamiltonian H whose matrix representation in the orthonormal basis
cfw_1 ,
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2003 Qualifying Exam
Consider transitions from excited states of a hydrogen atom (2S and 2P) into the
ground state (1S). The 2S level is slightly higher in energy than the 2P level
(E
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2003 Qualifying Exam
Consider a hollow body at temperature T containing electromagnetic radiation in
equilibrium with its walls. The energy spectrum of this so-called blackbody
radiati
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2004 Qualifying Exam Day 2
An electromagnetic wave with fields
v
E 0 = xE 0 e i (kz t )
v
v
1
B0 = z E 0
c
is incident upon a particle of mass m and charge q at the origin. Assume that
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2004 Qualifying Exam
(a) Solve the energy eigenvalue equation for a particle of mass m in the squarewell potential V (x ) that vanishes for 0 < x < a and equals + elsewhere.
Show that
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualifying Exam August 2004
(1) (a) Write down the canonical partition function Z q for a quantum system
1
( k B is Boltzmanns constant, T is
k BT
the absolute temperature). Next write down t
Ben Sauerwine
Practice for Qualifying Exams
Mathematical Methods
Problem Source: CMU August 2005 Qualifying Exam
Suppose we are interested in studying the motion of an an-harmonic oscillator
whose Lagrangian is given by
L=
1
1
&
mx 2 kx 2 + g (t )x 3
2
2
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 2 (August 2005)
Consider a particle of mass m moving in a one-dimensional potential with infinitely
high walls placed at x = a . The potential vanishes between the wall
Ben Sauerwine
Practice for Qualifying Exams
Thanks to Ryan for his input in this problem.
Problem Source: CMU February 2006 Qualifying Exam
Consider an azimuthally symmetric magnetic field, v
such as might be produced by a
dipole magnet with circular pole
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU February 2006 Qualifying Exam
This problem has to do with diffusion of heat in a slab of material. For the purposes
of this problem we will ignore thermal expansion. As such, we may define th
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 1 (February 2006)
(1) A pendulum of mass m and length b is mounted to a heavy sled of mass m
which is free to slide with negligible friction down an inclined plane of s
Ben Sauerwine
Practice for Qualifying Exams
Solution based on advice from Diana.
Problem Source: CMU February 2006 Qualifying Exam
Consider an ideal gas of N atoms confined to a container of volume V and internal
surface area A. Although you may neglect t
Ben Sauerwine
Qualifying Exam Study Sheet
Mechanics
(In this section, K indicates the kinetic energy of the system in terms of the variables and
V indicates the potential.)
Lagrangian: L = K V
Hamiltonian: H = K + V = qi pi L
i
L
Above, the conjugate mo
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