Biomedical Engineering Reference
In-Depth Information
Depending on the application, different values of
can be selected, for exam-
ple,
(-d
E
/d
x
)
100 eV
,
(-d
E
/d
x
)
1keV
, and so forth. In the context of restricted stopping
power, the subscript
Q
max
or
∞
is used to designate the usual stopping power:
-
d
E
d
x
-
d
E
d
x
-
d
E
d
x
=
Q
max
=
.
(7.2)
∞
We see from Table 6.1 that restricting single-collision energy losses by electrons
in water to 100 eV or less, for example, limits the range of secondary electrons to
∼ 5×10
-7
cm, or about 50 Å. With
= 1
keV, the maximum range of the secondary
electrons contributing to the restricted stopping power is
5 × 10
-6
cm, or about
500 Å.
Example
A sample of viruses, assumed to be in the shape of spheres of diameter 300 Å, is to
be irradiated by a charged-particle beam in an experiment. Estimate a cutoff value
that would be appropriate for determining a restricted stopping power that would be
indicative of the actual energy
absorbed
in the individual virus
particles
.
Solution
As an approximation, one can specify that the range of the most energetic delta ray
should not exceed 300
Å
=
10
-6
cm. We assume that the virus sample has unit
density. Table 6.1 shows that this distance is approximately the range of a 700-eV
secondary electron. Therefore, we choose
3
×
700 eV and use the restricted stopping
power (-d
E
/d
x
)
700 eV
as a measure of the average energy absorbed in an individual
virus particle from a charged particle traversing it.
=
Restricted mass stopping powers of water for protons are given in Table 7.1.
At energies of 0.05 MeV and below, collisions that transfer more than 100 eV do
not contribute significantly to the total stopping power, and so (-d
E
/
ρ
d
x
)
100 eV
=
d
x
)
∞
. In fact, at 0.05 MeV,
Q
max
=
109 eV. At 0.10 MeV, on the other hand,
(-d
E
/
ρ
220 eV; and so the restricted mass stopping power with
=
1 keV is signifi-
Q
max
=
cantly larger than that with
=
100 eV. At 1 MeV, a negligible number of collisions
result in energy transfers of more than 10 keV; at 10 MeV, about 8% of the stopping
Tab l e 7 . 1
Restricted Mass Stopping Power of Water, (-d
E
/
ρ
d
x
)
in MeV cm
2
g
-1
, for Protons
-
d
E
ρ
d
x
100 eV
-
d
E
ρ
d
x
1keV
-
d
E
ρ
d
x
10 keV
-
d
E
ρ
d
x
Energy (MeV)
∞
0.05
910.
910.
910.
910.
0.10
711.
910.
910.
910.
0.50
249.
424.
428.
428.
1.00
146.
238.
270.
270.
10.0
24.8
33.5
42.2
45.9
100.
3.92
4.94
5.97
7.28
