### Radioactive Decay Equation and Calculation ExampleRadioactive decay can be described by the following equation:\[ \ln A = \ln A_0 - kt \]where:- \( A_0 \) is the original amount of the substance,- \( A \) is the amount of the substance remaining after time \( t \),- \( k \) is a constant that is characteristic of the substance.For the radioactive isotope radon-222, \( k \) is \( 1.81 \times 10^{-1} \) days\(^{-1}\).#### Example Problem:If the original amount of radon-222 in a sample is 69.9 mg, how much time is needed for the amount of radon-222 that remains to fall to 37.8 mg?You need to calculate \( t \) (time in days).\[ t = \, \_\_\_\_ \, \text{days} \]To solve this, you will use the decay formula provided and input known values for \( A_0 \), \( A \), and \( k \).

Given : lnA = lnA0 - Kt where A = amount of substance remaining after time t = 37.8 mg A0 =…

Radioactive decay can be described by the following equation In A = In Ao – kt where Ao is the original amount of the substance, A is the amount of the substance remaining after time t, and k is a constant that is characteristic of the substance. For the radioactive isotope radon-222, k is 1.81 × 10-1 days. If the original amount of radon-222 in a sample is 69.9 mg, how much time is needed for the amount of radon- 222 that remains to fall to 37.8 mg? days

Radioactive decay can be described by the following equation In A = In Ao – kt where Ao is the original amount of the substance, A is the amount of the substance remaining after time t, and k is a constant that is characteristic of the substance. For the radioactive isotope radon-222, k is 1.81 × 10-1 days. If the original amount of radon-222 in a sample is 69.9 mg, how much time is needed for the amount of radon- 222 that remains to fall to 37.8 mg? days

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

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Question

### Radioactive Decay Equation and Calculation Example

Radioactive decay can be described by the following equation:

\[ \ln A = \ln A_0 - kt \]

where:
- \( A_0 \) is the original amount of the substance,
- \( A \) is the amount of the substance remaining after time \( t \),
- \( k \) is a constant that is characteristic of the substance.

For the radioactive isotope radon-222, \( k \) is \( 1.81 \times 10^{-1} \) days\(^{-1}\).

#### Example Problem:
If the original amount of radon-222 in a sample is 69.9 mg, how much time is needed for the amount of radon-222 that remains to fall to 37.8 mg?

You need to calculate \( t \) (time in days).

\[ t = \, \_\_\_\_ \, \text{days} \]

To solve this, you will use the decay formula provided and input known values for \( A_0 \), \( A \), and \( k \).

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