For geologic dating, where the time span is on the order of the age of the earth and the From the radioactive decay equations, an expression for elapsed time can be developed. The requirement of keeping the same number of nuclei gives. It turns out to be relatively well established, dating back more than it amusing that there's an equation for the 'optimal' age gap in love. Historically, a woman was to choose a man the same age, or five to 15 years older. According to internet lore, there's a mathematical equation that your own age: below the age of 14, by this rule, you shouldn't be dating at all.
In order to use this equation for decay over a given time period, we will need the solution of a first-order differential equation. Obtaining such a solution is beyond the scope and requirements of this class, though with years of calculus, you to could do the impossible.
The equation above is known as the decay equation. It shows that at any time t, the number of parent atoms, N, is equal to the number of original parent atoms at time zero N0 gives the number of parent atoms at time zeromultiplied by the natural exponent raised to the negative power of the decay constant l multiplied by the time t.
Relationship of l to half-life The decay equation can be used to show the relationship of the decay constant l to the half-life of any unstable isotope. I use the term "appropriate" in the sense that the specimen to be dated must obviously contain isotopes of a well known radioactive decay series, and be suitable for precise chemical analysis.
In the simplest ideal situation,the decay equation is utilized by making the following substitutions: Therefore, if we know the decay constant l and can accurately measure D and P, in principle, we can determine the absolute age. Accurate measurement of either the absolute or relative abundance of trace quantities of radioactive isotopes requires sophisticated instruments, known as mass spectrometers, and instrument operators who really know what they are doing.
The technique appears to be simple and straightforward, but is actually very difficult and time-consuming. It is not a trivial task! Starting the Radiometric Clocks 1.
Living organisms continually exchange carbon with the atmosphere through the process of photosynthesis. When the organism dies, however, exchange of carbon ceases and the carbon present in the organism becomes isolated.
This event death of the organism marks the effective starting of the C 14 clock. One of the most common types of material used in C 14 dating is charcoal e. These rocks form by the cooling and crystallization of hot silicate liquids magma or lava.
As cooling proceeds from high temperatures ca. A growing mineral may trap small amounts of a radioactive isotope within its crystal structure. When this occurs, the radioactive atoms become effectively isolated or trapped. The number of protons in the nucleus of an atom is called its atomic number. The sum of protons plus neutrons is the mass number. We designate a specific group of atoms by using the term "nuclide. The element potassium symbol K has three nuclides, K39, K40, and K Only K40 is radioactive; the other two are stable.
K40 can decay in two different ways: The ratio of calcium formed to argon formed is fixed and known. Therefore the amount of argon formed provides a direct measurement of the amount of potassium present in the specimen when it was originally formed. Because argon is an inert gas, it is not possible that it might have been in the mineral when it was first formed from molten magma.
Any argon present in a mineral containing potassium must have been formed as the result of radioactive decay. F, the fraction of K40 remaining, is equal to the amount of potassium in the sample, divided by the sum of potassium in the sample plus the calculated amount of potassium required to produce the amount of argon found.
The age can then be calculated from equation 1. In spite of the fact that it is a gas, the argon is trapped in the mineral and can't escape. Creationists claim that argon escape renders age determinations invalid. However, any escaping argon gas would lead to a determined age younger, not older, than actual. The creationist "argon escape" theory does not support their young earth model.
The argon age determination of the mineral can be confirmed by measuring the loss of potassium. In old rocks, there will be less potassium present than was required to form the mineral, because some of it has been transmuted to argon. The decrease in the amount of potassium required to form the original mineral has consistently confirmed the age as determined by the amount of argon formed.
See Carbon 14 Dating in this web site.Calculate Age from Date of Birth - Excel Functions and Formulas
The nuclide rubidium decays, with a half life of Strontium is a stable element; it does not undergo further radioactive decay. Do not confuse with the highly radioactive isotope, strontium Strontium occurs naturally as a mixture of several nuclides, including the stable isotope strontium If three different strontium-containing minerals form at the same time in the same magma, each strontium containing mineral will have the same ratios of the different strontium nuclides, since all strontium nuclides behave the same chemically.
Note that this does not mean that the ratios are the same everywhere on earth. It merely means that the ratios are the same in the particular magma from which the test sample was later taken. As strontium forms, its ratio to strontium will increase. Strontium is a stable element that does not undergo radioactive change. In addition, it is not formed as the result of a radioactive decay process.
The amount of strontium in a given mineral sample will not change. Therefore the relative amounts of rubidium and strontium can be determined by expressing their ratios to strontium These curves are illustrated in Fig It turns out to be a straight line with a slope of The corresponding half lives for each plotted point are marked on the line and identified.
It can be readily seen from the plots that when this procedure is followed with different amounts of Rb87 in different minerals, if the plotted half life points are connected, a straight line going through the origin is produced. These lines are called "isochrons".
The steeper the slope of the isochron, the more half lives it represents. When the fraction of rubidium is plotted against the fraction of strontium for a number of different minerals from the same magma an isochron is obtained.
If the points lie on a straight line, this indicates that the data is consistent and probably accurate. An example of this can be found in Strahler, Fig If the strontium isotope was not present in the mineral at the time it was formed from the molten magma, then the geometry of the plotted isochron lines requires that they all intersect the origin, as shown in figure However, if strontium 87 was present in the mineral when it was first formed from molten magma, that amount will be shown by an intercept of the isochron lines on the y-axis, as shown in Fig Thus it is possible to correct for strontium initially present.
The age of the sample can be obtained by choosing the origin at the y intercept.
Note that the amounts of rubidium 87 and strontium 87 are given as ratios to an inert isotope, strontium However, in calculating the ratio of Rb87 to Sr87, we can use a simple analytical geometry solution to the plotted data.