Medical Physics 501 2015
Midterm Exam
I. (20%) Briefly define the following – include a labeled diagram and/or an equation with
each:
a. (5%) restricted stopping power
b. (5%) triplet production
c. (5%) Chilton’s fluence
d. (5%) effective attenuation coefficient
II. (20%) Given the following quantities that we have discussed, and that are related to
attenuation: aσ, NA, ρ, A, Φ, and a distance, l:
a. (6%) What are the units for each of these quantities?
b. (7%) Write the attenuation coefficient, µ, in terms of some of these quantities.
c. (7%) Write a first-order linear differential equation to describe the loss of
particles per distance into some material from a primary beam.
III. (18%) What is the energy transferred, εtr, and net energy transferred, εtrnet, and the
energy imparted, ε, to the semi-infinite material below the horizontal line (infinite
below the line) in each of the following numerically labeled interactions for each of ‘a’
and ‘b’ of primary photons of energy hν. Wavy lines are photons, and discontinuous or
straight lines are charged particles. (3% each)
a
b
hν=10MeV
To = 5MeV
1
hν’=5MeV
hν‘’=0.5MeV
IV. (25%) How many charged particles, on average, are released in lead (z=82) by a single
8.0 MeV photon? {hint: not in general an integer, and Auger and Fluorescence are
mutually exclusive}.
V. (17%): Ionized helium is accelerated to 14.3 MeV, and your job as a physicist requires
that you get the mass stopping power for ionized helium (z=2) in water. Find this
quantity using the tables provided for the cases below:
a. (10%) The helium nucleus is fully ionized.
b. (7%) The helium nucleus is singly ionized.
Equations that may be useful or maybe not !
2

 β2 
 dT 
 z  Z  
 − β 2 − ln I 

 = (0.3071)  2  13.84 + ln
2 
 A  β  
 ρdx  c
1− β 

 dT 
N

 = σ 0 A z 2 (T + mc 2 ) Br
A
 ρdx  r
(γ − 1) = T / Mc 2
ε = Rin |u − Rout |u + Rin |c − Rout |c + ∑ Q
β2
T ' max ≈ 2m0 c
with T<<Mc2
2
1− β
2
σ (γ , p )
µtr τ tr σ tr κ tr
=
+
+
+
+ ...
ρ
ρ ρ
ρ
ρ
τ  hν − PK YK (hν ) K − (1 − PK ) PLYL (hν ) L 
= 
+
hν
ρ

σ  Te
ρ  hν
−

+


κ  hν − 2m0 c 2 

 +
hν
ρ 

σ (γ , p )  T p

ρ  hν

 + other photonuclear terms possible ...


BE 

(hν ) min = − BE 1 −
2 
 2 Mc 
hν ' =
hν
1 + α 0 (1 − cos ϕ )
γ = 1/ 1 − β 2
T0
RCSDA
con’t:
α0 ≡
hν
m0 c 2
−1
 dT 
≡ ∫ 
 dT
ρdx 
0
Tmax = hν
2α 0
1 + 2α 0
From Attix, Tables that may be useful or maybe not !