%*************  PHY 5846  Fall 1998  -- Homework  ***************8
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\begin{document}
\centerline {\bf PHY5846C: INTRODUCTION TO EXPERIMENTAL TECHNIQUES}
\medskip
\centerline {PARTICLE DETECTION}
\bigskip
%\centerline {\bf ***** Homework due 5 November 1998 *****}

\begin{enumerate}
\item  Consider an $\alpha $ particle of 5 MeV kinetic energy moving in
silicon;
\begin{itemize}
\item[(a)] what is its range (i.e. the distance travelled before it stops)?
\item[(b)] make a rough estimate of the time required for it to slow down and
stop. (Hint: use the Bethe-Bloch formula; relate energy loss to change in
velocity; make appropriate approximations).
\end{itemize}
\item Estimate the energy loss of a 10 MeV proton when passing through 100
$\mu$m of silicon.
\item Calculate the energy of a 1 MeV $\gamma $ ray after Compton scattering at
$180^{\circ}$.
\item Give a rough estimate of the ratio of the probability per atom for
photoelectric absorption in silicon to that in germanium.
\item What is the mean free path of a photon of 1 MeV in NaI?
\item Calculate the rate of temperature rise in a sample of liquid water
adiabatically exposed to radiation that results in an absorbed dose rate of 10
mrad.
\item Indicate which of the three major photon interaction processes
(photoelectric absorption, Compton scattering, pair production) is dominant in
the following situations:
\begin{itemize}
\item[(a)] 1 MeV $\gamma $ rays in Al
\item[(b)] 100 keV $\gamma $ rays in H
\item[(c)] 100 keV $\gamma $ rays in Fe
\item[(d)] 10 MeV $\gamma $ rays in Co
\item[(e)] 10 MeV $\gamma $ rays in Pb
\end{itemize}
\item In which way are semiconductor detectors superior to scintillation
detectors?
\item Calculate the mean value and variance in the number of electron-hole pairs
created by the loss of 100 keV particle energy in silicon. 

\item In a germanium detector which is deep enough to contain a 50 keV photon,
what is the expected intrinsic resolution of the energy measurement in the
photopeak?

\item The probability that an electron-hole pair is thermally created is given
by
$$ p(T) = C T^{3\over 2} exp(-{E_g\over {2kT}}),$$
where $T$ = absolute temperature, $E_g$ = band gap energy, $k$ = Boltzmann
constant, and $C$ = proportionality factor characteristic of the material.\\
By what factor is the rate of thermal generation of electron-hole pairs in
germanium reduced by cooling it from room temperature ($20^{\circ}$) to 
liquid nitrogen temperature (77K)?

\item How do the following properties of a p-n junction depend on the applied
reverse bias voltage?
\begin{itemize}
\item[(a)] depletion width
\item[(b)] capacitance
\item[(c)] maximum electric field.
\end{itemize}

\item Find the ratio of the number of charge carriers created in silicon by a 1
MeV proton to the number generated {\sl by the same energy deposition} in air.

\item A 10 MBq source of $\alpha$ particles is located 10 cm in front of a
silicon surface barrier detector. After which length of exposure time is
radiation damage to the detector likely to be significant?

\item Find the maximum energy that can be deposited  by a 1 MeV gamma-ray photon
if it undergoes two successive Compton scattering events and then 
escapes the detector.



\end{enumerate}
\bigskip
References
\begin{enumerate}
\item    Particle Data Group: Review of particle properties, 
European Physical Journal {\bf C 3} (1998) 1 - 794.\\
\tab  (a) p. 69 for physical constants,\\
\tab  (b) p. 76 for properties of materials used in detectors,\\
\tab (c) p. 144 for passage of particles through matter,\\
\tab (d) p. 154 for overview of particle detectors,\\
\tab (e) p. 163 for radioactivity.
\item  R.D. Evans: The Atomic Nucleus; McGraw Hill 1955.
\item G.F. Knoll: Radiation detection and measurement; John Wiley 1989.
\item W. Leo: Techniques for nuclear and particle physics; Springer 1994.
\item D.J. Skyrme, Nucl. Instr. Meth. {\bf 138}(1976) 331.
\end{enumerate}
\end{document}
