Half-life and radioactive dating mastering physics answers - Pawillion
Half-Lives and Radioactive Decay Kinetics Thus the half-life of a reaction is the time required for the reactant concentration to . Answer a. The radioactive decay half-life formula states that. N(t)=N0(12)tt12 To solve for half-life of a substance, rearrange the formula in terms of t We can easily answer this question by using the definition of Half Life and.
In addition to altering the chemical bonds, the half-life can be altered by simply removing electrons from the atom. In the extreme limit of this approach, all of the electrons can be ripped off of a radioactive atom. For such an ion, there are no longer any electrons available to capture, and therefore the half-life of the electron capture radioactive decay mode becomes infinite. Certain radioactive isotopes that can only decay via the electron capture mode such as rubidium can be made to never decay by ripping off all the electrons.
Other types of radioactive decay besides electron capture have also been found to have the decay half-life depend on the state of the surrounding electrons, but the effects are smaller. Lastly, the half-life of a radioactive material can be changed by bombarding it with high-energy radiation. This should not come as a surprise since radioactive decay is a nuclear reaction, and inducing other nuclear reactions at the same time as the decay can interfere with it.
However, at this point, you don't really have stand-alone radioactive decay.
Half-life and carbon dating (video) | Nuclei | Khan Academy
Rather, you have nuclear reaction soup, so this approach may not really count as "changing the half-life". When reference books list values for the half-life of various materials, they are really listing the half-life for the material when its atoms are at rest, in the ground state, and in a particular chemical bonding configuration.
Note that most changes to the half-life of radioactive materials are very small. Furthermore, large changes to a half-life require elaborate, expensive, high-energy equipment e.
Therefore, outside of specialized labs, we can say that as a good approximation radioactive decay half-lives don't change. For instance, carbon dating and geological radiometric dating are so accurate because decay half-lives in nature are so close to constant. Another possibility is spontaneous fission into two or more nuclides.
While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-lifeusually given in units of years when discussing dating techniques. After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide or decay product. In many cases, the daughter nuclide itself is radioactive, resulting in a decay chaineventually ending with the formation of a stable nonradioactive daughter nuclide; each step in such a chain is characterized by a distinct half-life.
In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter.
Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years e.
Half-Lives and Radioactive Decay Kinetics
It is not affected by external factors such as temperaturepressurechemical environment, or presence of a magnetic or electric field. For all other nuclides, the proportion of the original nuclide to its decay products changes in a predictable way as the original nuclide decays over time.
This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present. Accuracy of radiometric dating[ edit ] Thermal ionization mass spectrometer used in radiometric dating.
The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation. The possible confounding effects of contamination of parent and daughter isotopes have to be considered, as do the effects of any loss or gain of such isotopes since the sample was created.
It is therefore essential to have as much information as possible about the material being dated and to check for possible signs of alteration. Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron. This can reduce the problem of contamination. In uranium—lead datingthe concordia diagram is used which also decreases the problem of nuclide loss.
Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample.
For example, the age of the Amitsoq gneisses from western Greenland was determined to be 3. The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate.
This normally involves isotope-ratio mass spectrometry. For instance, carbon has a half-life of 5, years. After an organism has been dead for 60, years, so little carbon is left that accurate dating cannot be established.
Basic Physics of Nuclear Medicine/The Radioactive Decay Law
On the other hand, the concentration of carbon falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades. Closure temperature If a material that selectively rejects the daughter nuclide is heated, any daughter nuclides that have been accumulated over time will be lost through diffusionsetting the isotopic "clock" to zero. The temperature at which this happens is known as the closure temperature or blocking temperature and is specific to a particular material and isotopic system.
These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace.
As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy.
Radiometric dating - Wikipedia
At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. This temperature is what is known as closure temperature and represents the temperature below which the mineral is a closed system to isotopes.
Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature.
The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature. This field is known as thermochronology or thermochronometry. The age is calculated from the slope of the isochron line and the original composition from the intercept of the isochron with the y-axis.
The equation is most conveniently expressed in terms of the measured quantity N t rather than the constant initial value No. The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature.
This is well-established for most isotopic systems. So if you go back after a half-life, half of the atoms will now be nitrogen.
So now you have, after one half-life-- So let's ignore this. So we started with this.
All 10 grams were carbon. This is after one half-life. And now we have five grams of c And we have five grams of nitrogen Let's think about what happens after another half-life. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon So let me actually copy and paste this one.
This is what I started with. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here. Let me clean it up a little bit. After one one half-life, what happens? Well I now am left with five grams of carbon And by the law of large numbers, half of them will have converted into nitrogen So we'll have even more conversion into nitrogen So now half of that five grams.
So now we're only left with 2. And how much nitrogen? Well we have another two and a half went to nitrogen. So now we have seven and a half grams of nitrogen And we could keep going further into the future, and after every half-life, 5, years, we will have half of the carbon that we started. But we'll always have an infinitesimal amount of carbon. But let me ask you a question. Let's say I'm just staring at one carbon atom.
Let's say I just have this one carbon atom. You know, I've got its nucleus, with its c So it's got its six protons. It's got its eight neutrons. It's got its six electrons. What's going to happen?
- Radiometric dating
- Can the decay half-life of a radioactive material be changed?
- Half-life and radioactive dating mastering physics answers
What's going to happen after one second? Well, I don't know. It'll probably still be carbon, but there's some probability that after one second it will have already turned into nitrogen What's going to happen after one billion years? Well, after one billion years I'll say, well you know, it'll probably have turned into nitrogen at that point, but I'm not sure. This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon So after one half-life, if you're just looking at one atom after 5, years, you don't know whether this turned into a nitrogen or not.
Now, if you look at it over a huge number of atoms. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. I don't know which half, but half of them will turn into it. So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, and it has a half-life of two years. I'm just making up this compound. And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left.
And we want to know how much time has passed by. So 10 grams left of x. How much time, you know, x is decaying the whole time, how much time has passed? Well let's think about it.