Radioactive Emission: Determining Half-Life

In summary, a radioactive source emits electrons and the number of electrons emitted per second decreases according to dN/dt = −1.8 × 10−5N(t) where t is in seconds. If N = 12 electrons/sec at t = 0, it takes approximately 7 seconds for N to fall to 4.0 electrons/sec. The half-life of the radioactive source can be determined by finding the time it takes for the number of electrons emitted per second to drop from 12 to 6.
  • #1
henryc09
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Homework Statement


A radioactive source emits electrons. The number of electrons emitted per second
N(t) decreases with time according to the equation:

dN/dt = −1.8 × 10−5N(t) ,
where t is expressed in seconds. If N = 12 electrons/sec at t = 0, after what time t
has N fallen to the value 4.0 electrons/sec? [7]
What is the half-life of the radioactive source in seconds? [3]


Homework Equations





The Attempt at a Solution


I have the first part done, but am confused about the second part. How can you tell the half life of the material from the information given? N is just the amount of electrons given off per second, and the half life is the amount of time taken for the amount of substance to halve right? I don't see how they can be directly related. Any ideas?
 
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  • #2
One way is to just work out how long it takes for the number of electrons given off per second to drop from 12 to 6. That represents the half-life time.
 
  • #3
OK I was thinking that must be the only way. Thanks :)
 

1. What is radioactive emission and how is it measured?

Radioactive emission refers to the process by which unstable atoms release energy in the form of particles or waves. This process is measured by determining the half-life of the radioactive material, which is the time it takes for half of the atoms in a sample to decay.

2. What factors affect the half-life of a radioactive element?

The half-life of a radioactive element is affected by the atomic structure of the element, the type of radiation emitted, and the external environment. For example, certain elements may have a shorter half-life if they emit more energetic radiation, while the presence of other elements may slow down the decay process.

3. How is the half-life of a radioactive element determined?

The half-life of a radioactive element can be determined through experimental methods, by measuring the rate of decay over time. This involves counting the number of atoms that decay in a given period and using mathematical equations to calculate the half-life.

4. Why is understanding half-life important in studying radioactive emissions?

Understanding half-life is important in studying radioactive emissions because it allows scientists to predict and control the behavior of radioactive materials. It also helps in the development of medical treatments, as well as in monitoring and managing nuclear waste.

5. Can the half-life of a radioactive element be changed?

No, the half-life of a radioactive element cannot be changed. It is a property of the element itself and cannot be altered by external factors. However, the rate of decay can be influenced by changing the conditions of the environment, such as temperature or pressure.

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