4.10 Find the solid angle subtended by the circular end sur- face of a cylindric

Question

4.10 Find the solid angle subtended by the circular end sur- face of a cylindrical detector (diameter of 10 cm) for a point source located 20 cm from the surface along the cylindrical axis. 4.11 The diameter of the moon as seen from earth subtends an angle of about 0.5°. Find the probability that a laser beam aimed in a random direction from the earth's surface will stike the moon, 4.12 The detector of Problem 4.10 has an intrinsic peak effi- ciency at 1 MeV of 12%. The point source emits a 1 MeV gamma ray in 80% of its decays and has an activity of 20 kBq. Neglecting attenuation between the source and detector, calculate the number of counts that will appear under the 1 MeV full-energy peak in the pulse height spec- trum from the detector over a 100 s count.

Explanation / Answer

Solid angle = 2pi(1 - cos(theta))

cos(theta) = 0.2/sqrt(r^2 + 0.2^2)

r = 5 cm = 0.05

cos(theta) =0.2/sqrt(0.05^2 + 0.2^2) = 0.9701425

hence

Solid angle = 2pi(1 - 0.9701425)

= 0.18760 sterdian

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