Finding half-life from decay rates

In summary, the conversation discusses how the decay rate of a certain isotope decreases from 8339 decays/minute to 3037 decays/minute over a period of 4.50 days. The formula used to find the half-life is \frac{dN}{dt}=\lambda N, where the half-life is defined as the time it takes for the number of undecayed nuclei to decrease to half of its original amount.
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Measurements of a certain isotope tell you that the decay rate decreases from 8339 decays/minute to 3037 decays/minute over a period of 4.50 days. What is the half-life T_1/2 of this isotope in days?I know that i have to relate the ratio of decay rates to the ratio of undecayed nuclei present at each time, but i don't know which formula to use to find half life after that.
 
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So, the decay rate is simply proportional to the number of undecayed nuclei:

[tex]\frac{dN}{dt}=\lambda N[/tex]

The half life is defined as the time it takes for N to decease to N/2. Can you see where to go from there?
 

Related to Finding half-life from decay rates

1. What is half-life and why is it important in decay rates?

Half-life is the amount of time it takes for half of a radioactive substance to decay. It is important in decay rates because it helps us understand the rate at which a substance decays and how long it will take for it to become stable.

2. How is half-life calculated from decay rates?

The half-life can be calculated by using the decay constant, which is the probability that a specific atom will decay in a unit of time. The formula for calculating half-life is: half-life = ln(2) / decay constant.

3. Can half-life be used to determine the age of a substance?

Yes, half-life can be used to determine the age of a substance. By measuring the amount of a radioactive substance present and knowing its half-life, we can calculate how long it has been decaying and therefore determine its age.

4. Are all decay rates constant?

No, not all decay rates are constant. Some substances have a constant decay rate, while others may have a variable decay rate. This can depend on factors such as temperature, pressure, and the presence of other substances.

5. Is half-life the only factor that affects decay rates?

No, half-life is not the only factor that affects decay rates. Other factors such as external stimuli, such as radiation, can also affect the rate at which a substance decays. Additionally, the initial amount of a substance present can also impact the decay rate.

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