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

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### 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 \( k \).
Transcribed Image Text:### 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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