33 Application and Examples: (The mean life of a radioactive nucleus) حل تطبيقات على التغير الأسي
Автор: Waleed AlFarra
Загружено: 2026-02-22
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39. The mean life of a radioactive nucleus Physicists using the radioactivity equation y = y0^(e-kt) call the number 1/k the mean life of a radioactive nucleus. The mean life of a radon nucleus is about 1/0.18 = 5.6 days. The mean life of a carbon-14 nucleus is more than 8000 years. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t = 3/k. Thus, the mean life of a nucleus gives a quick way to estimate how long the radioactivity of a sample will last.
40. Californium-252 What costs $27 million per gram and can be used to treat brain cancer, analyze coal for its sulfur content, and detect explosives in luggage? The answer is californium-252, a radioactive isotope so rare that only 8 g of it have been made in the Western world since its discovery by Glenn Seaborg in 1950. The half-life of the isotope is 2.645 years—long enough for a useful service life and short enough to have a high radioactivity per unit mass. One microgram of the isotope releases 170 million neutrons per minute.
a. What is the value of k in the decay equation for this isotope?
b. What is the isotope’s mean life? (See Exercise 39.)
c. How long will it take 95% of a sample’s radioactive nuclei to disintegrate?
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