**Part
2: Mathematical Problem Solving
**

1. A vial
contains 100 mCi of an unidentified radionuclide, at 10 a.m. Thursday. At 10
a.m. Friday, the activity has decayed to 25 mCi. What is the half-life
of the unidentified radionuclide?

a)
24 hours

b)
12 hours

c)
4 hours

d)
100 hours

2. A vial contains a
mixture of 20 mCi of ^{124}I (half life 4 days) and 6 mCi of ^{131}I
(half life 8 days). What will be the activity in the vial 8 days from now?

a)
5 mCi

b)
3 mCi

c)
8 mCi

d)
13 mCi

3. For a T_{phys} = 1 year and the T_{biol }= 10 years,
what is the T_{eff}

a)
1.10 years

b)
0.909 year

c)
9.0 years

d)
none of the above

4. A collimated
beam with 3 half‑value layers of lead in front of it gives a reading of
10 mR/hr. If 1 half-value layer is removed, what would be the intensity
reading?

a)
5 mR/hr

b)
20 mR/hr

c)
3/2 x 10 mR/hr

d)
none of the above

5. A collimated
beam has initial intensity I_{1}=10 mR/hr. What would be the intensity
I_{2} if 3 half-value layers of lead (density 13.6 g/cc) were placed
between source and detector?

a)
3.33 mR/hr

b)
1.25 mR/hr

c)
10 x 3 mR/hr

d)
none of the above

6. Refer to the
diagram below and assume an uncollimated point source at point A. Calculate
value for I_{2}

a)
9 IU

b)
1 IU

c)
27 IU

d)
243 IU

7. Refer to the diagram above and calculate value for d_{2}.

a)
16 cm

b)
18 cm

c)
22.5 cm

d)
324 cm

8. At some point
in time a source has an activity of 1,000 mCi. At a later point in time the
activity is 62.5 mCi. The half‑life is unknown. How many half-lives
have elapsed?

a)
three

b)
four

c)
five

d)
can't be determined from the data provided

9. A Tc-99m
source has an activity of 100 mCi at 9 a.m. today. What will be the activity
at 5:46 p.m.?

a)
not enough information to solve problem

b)
40.0 mCi

c)
36.3 mCi

d)
37.63 mCi

e)
none of the above

10.
For a T_{phys} = 46 d and a T_{eff}
= 14 d what is T_{biol} ?

a)
32 d

b)
60 d

c)
15.94 d

d)
20.12 d

e)
<14 d

11.
The t_{phys} of Ga-67 is 3 days.
If t_{eff} = 1.5 days, what is t _{biol}?

a) 1.5 days

b)
4.5 days

c)
0.67 day

d)
none of the above

12.
At 1 cm from a point source, the intensity is 1000 R/hr. At what
distance
from the source would the intensity be reduced to 1000 mR/hr?

a)
100 cm

b)
1000 cm

c)
31.62 cm

d)
31.72 cm

13.
For Tc-99m, what fraction remains after 19 hours?

a)
6/19

b)
(6/19)^{2}

c)
(0.5)^{6/19}

d)
(0.5)^{19/6}

14.
The first half-value layer (HVL) for a polychromatic beam is 3mm.
of Al. The second HVL is _______________ the first.

a)
Less than

b)
Equal to

c)
Greater than

d)
1.44 x first HVL

15
A narrow beam of monoenergetic photons is directed upon a 20 cm water
phantom from a source 50 cm above the surface. The HVL is 10 cm of water. The
photon flux at the bottom of the phantom relative to that at the surface is
about _________ %

a)
6.2

b)
12.5

c)
25

d)
50

16.
The gamma ray dose rate constant G for a particular isotope is
__1.65 R x cm ^{2}__.

hr X mCi

If
a 6 mCi source is held at a distance of 8 cm for 10 hours, what would be the
absorbed dose in Rads?

a.
12.375

b.
1.547

c.
0.22

d.
1.76

17.
A source has an intensity of 4 mR/hr. A barrier 4 cm thick is placed
between the source and the detector and the reading drops to 0.4 mR/hr. What is
the half-value layer of the absorber?

a.
0.4 cm

b.
1.2 cm

c.
4 cm

d.
20 cm

18. Using the same
information in problem 17, calculate the tenth value layer.

a. 0.4 cm

b.
1.2 cm

c.
4 cm

d.
20 cm

19. If a certain ^{131}I
compound has a t_{biol} of 24 days, what is the mean effective
half-life.?

a. 8 days

b.
6 days

c.
8.7 days

d.
24 days

20. If the decay constant
of a commonly used isotope is 0.05210 hr^{-1}, what is the isotope?

a. Cr-51

b. I-123

c. Tc-99m

d. Kr-81m

21. A
sample has a count rate of 3.7 x 10^{8} c/sec in a detector. The
detector efficiency is 42%. How many mCi are present?

a.
1.55

b.
10

c.
4.2

d.
23.8

22. If
a 1 cm thick lead absorber is placed between a point source and a detector, the
intensity of the beam is reduced to 42% of its initial value. What is the
half‑value layer of lead for this isotope?

a)
1.25 cm

b)
0.80 cm

c)
0.78 cm

d)
1.27 cm

e)
none of the above

23.
Two camera heads are alike except that the one employs a 10-inch
diameter scintillation crystal and the other a 15-inch diameter
detector. The collimators for the detectors are identical in all parameters
(length, focal length, etc). The counting rate obtained with the 10-inch
head from an extended source compared to that obtained with the 15-inch
head with comparable collimation is:

a.
1.5 times as great

b.
0.667 times as great

c.
the same

d.
2.25 times as great

e.
0.4444 times as great

24.
A radioactive source has a dose rate of 40 mR/hr at a distance of one
foot. At what distance from this source would a technician working 40 hours per
week for 50 weeks per year receive a total dose of 5,000 mR?

a.
10 feet

b.
6 feet

c.
4 feet

d.
3 feet