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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?

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.
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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