4. The half-life of lead-210 is about 22 years. How long will it take a sample t

Question

4. The half-life of lead-210 is about 22 years. How long will it take a sample to decay to 15% of its original amount? (Hint: You may use the results of the problem 3.) 5. The halflife of plutonium-238 is about 87.7 years. How long will it take a sample to decay to 30% of its original amount? (Hint: You may use the results of the problem 3.) 6. The half-life of carbon-14 is approximately 5,730 years. If an archeological sample has only 5% of the original amount of carbon-14 left, how old is the sample? (Hint: You may use the results of the problem 3.)

Explanation / Answer

4) standard form of exponential equation is

P = Po e^kt

1/2 Po = Po e^22k

ln 1/2 = e^22k

k = -.0315

time takes to decay to 15%

.15 = e^(-.0315 t )

ln (.15) = -.0315 t

t = 60.22

so, it takes 60.22 years to decay to 15%

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