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31.5 Half-Life and Activity
Depending on how nuclide de-excites, there may be one or more s emitted.
Emission is common in radioactive decay.
The daughter nucleus is usually left in an excited state when decays.
Cancer therapy uses the cobalt rays, which come from nickel.
It is constructive to verify the laws for decay.
Nuclear decay is less common than other types.
Spontaneous fission is the most important form of nuclear decay because of its applications in nuclear power and weapons.
The next chapter covers it.
Some nuclides decay faster than others.
radium and polonium were discovered by the Curies.
They produce a greater rate of decay because they have shorter lifetimes.
The terms for lifetime and rate of decay are explored in this section.
Figure 31.21 shows how the number of radioactive nuclei in a sample decreases with time.
In the next half-life, half of the remaining nuclei decay.
In the following half-life, half of that amount decays.
If there is a large number, many half-lives pass before the nucleus decays.
Nuclear decay is an example of a statistical process.
A more precise definition of half-life is that each nucleus has a 50% chance of living for a time equal to one half-life.
Half of the original nuclei decay in one half-life if it is large.
A nucleus has a 50% chance of surviving through another half-life if it makes it through that time.
Even if it makes it through hundreds of half-lives, it still has a 50% chance of surviving through one more.
When you start counting, the probability of decay is the same.
Random coin flipping is what this is.
No matter what happened before, the chance of heads is 50%.
The number of radioactive nuclei is reduced by radioactive decay.
The number decreases to half of its original value in one half-life.
Half of what is left is decay in the next half-life.
The graph shows the number of nuclei present as a function of time.
The extent to which the nuclear force can depend on the combination of neutrons and protons is an indication of the shortest half-lives.
Particle physics will discuss the concept of half-life for other particles.
It applies to the decay of excited states in atoms.
The larger the value, the faster the exponential decreases.
Let's use the exponential in the equation to see how the number of nuclei decreases in one half-life.
You can divide the original number by 2 over and over again, instead of using the exponential relationship.
If ten half-lives have passed, we divide by 2 ten times.
The exponential relationship must be used for an arbitrary time.
Carbon-14 has a half-life of 5730 years and is produced in a nuclear reaction when solar neutrinos hit the atmosphere.
Radioactive carbon has the same chemistry as stable carbon, and so it mixes into the ecoosphere, where it is consumed and becomes part of the living organisms.
There is an abundance of 1.3 parts per trillion of normal carbon.
Carbon exchange with the environment ceases when an organisms dies.
It is possible to determine the artifact's age by comparing the abundance of living tissue with the abundance of mummy wrappings.
Carbon-14 dating is most accurate for younger samples since the amount of nuclei in them is greater.
There are no old biological materials at all.
Historical knowledge or tree-ring counting can be used to determine the date of an artifact.
The cross-references have confirmed the validity of carbon-14 dating and allowed us to calibrate it.
The American chemist who developed carbon-14 dating earned the 1960 Nobel Prize in chemistry for his work.
The relic was denounced as a fraud by a French bishop after it was first displayed in Turin.
The shroud's negative imprint resembles the image of Jesus, and so it remained controversial over the centuries.
When the process was refined to the point where only a small amount of material needed to be destroyed, carbon-14 dating was performed on the shroud.
Each sample was given four pieces of cloth and only one piece from the shroud, to avoid prejudice.
The shroud was first seen in the 14th century.
It is not known how the image was placed on the material.
The amount of living tissue found in the Shroud of Turin is less than the age of it.
Knowing that 92 percent of the remains means that.
The equation can be used to find something.
We know that the half-life is 5730 y, so we can use the equation to find and then find as we please.
We think that the decrease in is due to nuclear decay.
The equation can be used to find something.
The material in the shroud was found in the 1300s.
The year is rounded to 1300 because our calculation is only accurate to two digits.
The weighted average date was given by the values obtained at the three independent laboratories.
The small amount of living tissues, the amount of material available, and the amount of experimental uncertainties make the uncertainty typical of carbon-14 dating.
The date of the shroud is consistent with the first record of its existence and inconsistent with the period in which Jesus lived.
There are other forms of dating.
Rocks can sometimes be dated based on decay.
The ratio of nuclides in a rock is an indication of how long it has been since the rock solidified.
It is necessary to know the original composition of the rock with some confidence.
The technique can be verified by a consistent body of knowledge.
It is useful for dating only very old materials since it has a half-life of y.
The number of decays per unit time is high.
decays per minute or decays per year are examples of activity expressed in other units.
A becquerel is a small unit of activity.
Most radioactive sources, such as those used in medical diagnostics or in physics laboratories, are labeled in Bq or megabecquerel in Australia and New Zealand.
You would expect the activity of a source to depend on two things: the amount of radioactive substance present and its half-life.
The more radioactive the sample is, the more decay will occur per unit of time.
The longer the half-life, the more decays per unit time.
The activity should be proportional to the number of radioactive nuclei and their half-life.
Your intuition is correct.
The next two examples show how useful this relationship is.
The activity is calculated by the amount of carbon found in the living organisms.
The activity is expressed in units of Bq and Ci.
We need to know and use the equation to find the activity.
The half-life can be found in Appendix B.
We use the concept of a mole to find the number of nuclei in the carbon.
A mole of carbon has a mass of 12.0 g.
The equation has been used to find the activity.
We simply convert years to seconds to convert this to the unit Bq.
Our bodies contain a lot of carbon, and it's interesting to think that there are hundreds of decays per second in us.
Our bodies have naturally occurring radioactive substances in them.
The small number of decays per second found for a kilogram of carbon in this example gives you an idea of how difficult it is to detect in a small sample of material.
There are 0.25 decays per second in a gram of carbon in living tissue if there are 250 decays per second.
To reduce background noise, you must be able to distinguish decays from other forms of radiation.
It is impossible to do this with an old tissue sample since it contains less.
Human-made radioactivity has been produced for decades and has many uses.
Medical therapy for cancer, medical images and diagnostics, and food preservation by irradiation are some of the things that can be included.
In Medical Applications of Nuclear Physics, many applications as well as the biological effects of radiation are explored, but it is clear that radiation is hazardous.
Hundreds of thousands of people were directly affected by the release of several radioactive isotopes.
The total amount of radiation released is thought to be 100 millioncuries.
There will be thousands of deaths from radiation-caused cancer in the future, and more than 100 people died soon after its meltdown.
The clean up efforts were heroic, despite the accident being due to a series of human errors.
Firefighters and reactor personnel were the first to die.
If we can find the number of nuclei that have been released, we can calculate the mass released.
The half-life of the activity is found in Appendix B to be 30.2 y, so we can use the equation to find.
One mole of a nuclide has a mass of 137 g.
It is extremely radioactive since it only has a 30-year half-life, which is less than the amount of fuel in a power plant.
Six megacuries is an extraordinary amount of activity, but is only a small portion of what is produced in nuclear reactor.
The other isotopes were also released.
Although the chances of such a disaster seemed small, the consequences were extremely severe, requiring greater caution than was used.
In the next chapter, more will be said about safe reactor design, but it should be noted that Western reactor designs are fundamentally safer.
Activity decreases in time, going to half its original value in one half-life, then to one-fourth its original value in the next halflife, and so on.
The decay of radioactive nuclei is shown in this equation.
If a source has a 1.00-mCi activity, it will decline to 0.500 mCi in one half-life, to 0.250 mCi in two half-lives, to 0.125 mCi in three half-lives, and so on.
Sometimes the equation must be used to find.
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