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Semmy [17]
2 years ago
11

How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed? [See Section 6.6 Example 13] Th

e decay equation is A(t)=A_0e^{Kt} , where t is the time for the decay, and K is the characteristic of the material. Suppose T is the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove that K= \frac{ln0.5}{T} . What is T for the uranium-235? Show the steps of your reasoning.
Mathematics
1 answer:
horsena [70]2 years ago
8 0

Answer:

From what I can see of the problem, you CANNOT solve for the half-life of U 235 AND then solve for the length of time to determine the 20% decay.

U-235 half-life is 704,000,000 years. (Wikipedia)

The elapsed time formula = half-life * [log (Beginning Amount / ending amount) / log 2]

elapsed time = 7.04 x 10^8 * [log (100 % / 80%) / log 2]

elapsed time =7.04 x 10^8 *  [log (1.25) / .30103]

elapsed time =7.04 x 10^8 *  [0.096910 / .30103]

elapsed time = 7.04 x 10^8 *  0.321928047

elapsed time = 226,637,000 years

Step-by-step explanation:

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You can clean up the 9/8 to be 1.125

Now what you want to do is find the answer to (9/8)^5 which is 1.8020324707

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The <em><u>correct answer</u></em> is:

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