An 8-cm diameter by 8-cm long NAI(TI) detector detects gamma rays of a specific energy from a point source of radioactivity. When the source is placed just next to the detector at the center of the circular face, 50 percents of all emitted gamma rays at that energy are detected. If the detector is moved to 1 meter away, the fraction of detected gamma rays drops to
A. 10−4
B. 2 ×10−4
C. 4 ×10−4
D. 8 ×10−4
E. 16 ×10−4
(GR0177 #14)
Solution:
The net power radiated by the source: P = I A
I = intensity
A = area of the surface
No power loss mentioned: P1 = P2
I1 A1 = I2 A2
A1 = area of circle with diameter 8 cm
r1 = 4 × 10−2 m
A2 = area of sphere with radius 1 m
The problem asks for the fraction, not how much the intensity is detected.
Thus, the fraction is just the ratio of the areas:
Answer: C
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