Plutonium Alarm Clock

Classical Mechanics Level pending

Having just traversed the galaxy M31 in Andromeda, Dr. Von Dieemmon decided to enjoy a lie down to rejuvenate himself. Long ago, he had designed an alarm clock containing Plutonium-239. As his recent journey was so exhausting, he set it to 3.14. This means that he inserted 10 kilograms of Plutonium-239 into the clock and programmed it to ring when only 3.14 kilograms of the Plutonium remained. (Assume he was immensely tired and had an unfathomably long life span.) How long did he sleep until the alarm went off? (Half life of Plutonium-239 is 24,100 years.)

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