Homer enters the visitors\' chambers, and his Geiger beeper sounds. He shuts off

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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