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# The half-life of Radium-226 is 1590 years. If a sample contains

### Customer Question

The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

Hint: Recall P=P0ekt where P0 is the initial amount of such a substance, P is the amount at a given time t andk is the exponential rate of decay. What would it mean if P=.5P0?
Submitted: 3 years ago.
Category: Homework
Expert:  Ryan replied 3 years ago.
Hi,

Welcome! Thank you for using JustAnswer.

Since the half-life of Radium 226 is 1590 years we know that P = 0.5P0 when t = 1590 years. We can write the following equation:

0.5P0 = P0 * e^(k*1590)

Solving for k gives:

0.5 = e^(k*1590)

(1/2) = e^(k*1950)

ln (1/2) = k*1950

k = ln(1/2) / 1950

Now that we know the value of k, we can calculate the amount of Radium=226 remaining after 1000 years:

P = (200 mg)*e^[ (ln(1/2) / 1950) * 1000]

P = 200 e^-0.355460009

P = 200 * 0.70085091

P = 140.17 mg

Solution: After 1000 years the amount of Radium-226 remaining will be 140.17 mg.

Thanks,

Ryan
Customer: replied 3 years ago.
Expert:  Ryan replied 3 years ago.
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Ryan, Engineer
Category: Homework
Satisfied Customers: 7575
Experience: B.S. in Civil Engineering
Customer: replied 3 years ago.

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