Homer enters the visitors\' chambers, and his Geiger beeper sounds. He shuts off
ID: 1437265 • Letter: H
Question
Homer enters the visitors' chambers, and his Geiger beeper sounds. He shuts off the beeper, removes the device from his shoulder patch, and holds it near the only new object in the room—an orb that is to be presented as a gift from the visiting Cartesians. Pushing a button marked "monitor," Homer reads that the device is reading a counting rate of 4235 counts/s above the background counting rate. After 10 min, the counting rate has dropped to 460 counts/s above the background rate.
(a) What is the half-life of the source?
Explanation / Answer
use the equation N = No e ^-LT
where L is decayc constant
T is time = 10 min = 10* 60 = 600 secs
N is the count after 10 mins = 460 C/s
No is initial count = 4235 c/s
so
e^-LT = 460/4235
-LT = ln (0.108)
-LT = -2.22
L = 2.22/600
decay constant L = 0.0037
now T1/2 = ln2/(L)
T1/2 = 0.693/0.0037
T1/2 = 187.3 secs or 3.12 mins (answer)
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