If you start at t = 0 a decay rate of r = 10,000 Cs -137 decays per second, how many decays per second would you expect to find after 70.0 s?
If you start at t = 0 a decay rate of r = 10,000 Cs -137 decays per second, how many decays per second would you expect to find after 70.0 s?
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If you start at t = 0 a decay rate of r = 10,000 Cs -137 decays per second, how many decays per second would you expect to find after 70.0 s?
![### Radioactive Decay Equation
The formula shown in the image represents the half-life (\( t_{1/2} \)) of a radioactive substance. The half-life is the time required for a quantity to reduce to half of its initial value. The equation is as follows:
\[ t_{1/2} = \frac{\ln(2)}{\lambda} \]
Where:
- \( t_{1/2} \) is the half-life of the radioactive material.
- \( \ln(2) \) is the natural logarithm of 2, which is approximately equal to 0.693.
- \( \lambda \) is the decay constant, which is a probability rate at which the substance decays per unit time.
### Explanation
This equation is fundamental in the field of nuclear physics and is used to determine how quickly a radioactive substance undergoes decay. The decay constant \( \lambda \) is key to understanding the rate of decay, and the natural logarithm of 2 is used since the half-life is based on the exponential nature of the decay process.
No graphs or diagrams are included in the provided image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F453e0d9b-179f-45b0-9ee9-778be53b8a42%2F979a043d-0af7-434d-9ce0-604b18f4bf2c%2Fmeq5wdh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Radioactive Decay Equation
The formula shown in the image represents the half-life (\( t_{1/2} \)) of a radioactive substance. The half-life is the time required for a quantity to reduce to half of its initial value. The equation is as follows:
\[ t_{1/2} = \frac{\ln(2)}{\lambda} \]
Where:
- \( t_{1/2} \) is the half-life of the radioactive material.
- \( \ln(2) \) is the natural logarithm of 2, which is approximately equal to 0.693.
- \( \lambda \) is the decay constant, which is a probability rate at which the substance decays per unit time.
### Explanation
This equation is fundamental in the field of nuclear physics and is used to determine how quickly a radioactive substance undergoes decay. The decay constant \( \lambda \) is key to understanding the rate of decay, and the natural logarithm of 2 is used since the half-life is based on the exponential nature of the decay process.
No graphs or diagrams are included in the provided image.
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