# Properties of waves review and reinforce radioactive dating

While radioactive decay can be dangerous, it can be used in many medicines and begin to emit radiation, which is an energy wave moving out from an atom. Review of Monte Carlo simulations for backgrounds from radioactivity . understanding of the geochemistry, decay properties, and ingrowth kinetics of radium .. oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a. Elements and the Periodic Table • Review and Reinforce. Radioactive Elements Which diagram represents radioactive decay that leads to a decrease in atomic number? Guta katil consists of high-energy waves and always accompanies Uranium shows a property of being able to spontaneously emit radiation.

Moreover, the faster recoils reach the stopper in a shorter time and therefore contribute less to the area of the flight peak. Even though this effect has been known for a long time, it was often underestimated, resulting in wrong half-lives.

These problems stimulated efforts to improve the technique with respect to higher reliability and to make it more transparent so that the presence of possible systematic errors is revealed more easily. Some of these improvements are [ 3536 ]: The drawback is the need for longer beam time and many Ge-detectors. Gating as a means of reducing background is beneficial to the statistical precision only if it improves the peak-to-background ratio by a large factor.

Nanoseconds—microseconds Nano- and microsecond nuclear states are mostly measured electronically in delayed coincidence experiments or alternatively by time interval analysis. The radiation yielding the state of interest is detected to provide a start pulse for an electronic clock, and the radiation by which the state decays is detected in the same or another device to provide a stop pulse.

The half-life is derived from the analysis of the time difference between both signals. Using ultrafast scintillators plastic scintillator, LaBr3 CeBaF2the applicability range of the method has been extended down to picoseconds [ 37 ].

Also states of tens of milliseconds or even seconds are within reach, provided that the count rate is sufficiently low. Conventional experimental set-ups contain electronic modules, such as delay line amplifiers, timing single channel analysers TSCAtime-to-amplitude converters TAC and multi-channel analysers ADCbut they can also be replaced by programmable processors FPGA or software performing off-line data analysis of digitally acquired data saved in list files [ 38 ].

Common features of the delayed coincidence method are that time differences are stored in a spectrum, that the decay constant is derived from the slope of an exponential function fitted to a part of the spectrum and that account has to be taken for data not due to the intended parent—daughter pairs.

Random coincidences may be recorded due to background signals, decays from other states or closely spaced but unrelated parent and daughter events. The first two interferences can be significantly reduced if the experiment allows for energy selectivity, e. By means of energy selection, multiple half-lives can be derived from one experiment.

There exist different variants of how the data are recorded, each requiring a specific mathematical basis for the functional shape of the time spectrum. Two options are discussed below, based on different manners to collect and interpret time differences. Single delayed coincidence In a classical set-up, a timer is started whenever a parent decay is detected and stopped when a daughter decay is detected. Then the system is made sensitive again for parent decays. In doing so, all the parent events arriving before the first daughter event are ignored.

In this type of experiment, the time spectrum theoretically takes the following shape: This can be solved by means of an alternative time analysing circuit in which a parent decay starts the timer and not a single but multiple delayed coincidences are added to the time spectrum, one time value for every recorded daughter decay over a long period of time [ 40 ].

Using multiple delayed coincidences eliminates the spectral distortion effect, but at the price of an increased number of random coincidences. Time-interval distribution analysis method. Time-interval distribution analysis is a well-established method for measuring the activity of radiation sources [ 41 — 43 ]. For a simple decay, the probability density of the time interval between two successive disintegrations is given by the formula: For a large number of parent atoms N1, the probability of a given time interval between two successive disintegrations is given by: It shows that, at low time intervals, the shape of the curve has a term that depends not on the activity of the daughter nuclide, but on its half-life.

### The uncertainty of the half-life - IOPscience

The time-interval spectrum is obtained by binning the time differences between all events. It is possible to focus on one of the transitions separately by selecting regions in the energy spectrum mainly belonging to the parent-daughter sequence of interest. Time-interval distribution analysis yields comparable results to the delayed coincidence method [ 3843 ]. The half-life of the nuclide is usually derived from a least-squares fit of an exponential function to the measured time spectra.

However, some complications have to be taken into account. Least squares fitting procedures imply the assignment of proper weighting factors to the stochastically distributed data involved. In the case of a Poisson distribution, the obvious choice of setting the weighting factor equal to the inverse of the measured value is prone to bias towards low values. Alternatively, using the inverse of the fitted value may turn out to be biased towards higher values, depending on the procedure followed.

Additional problems arise when also the possibility of zero counts has to be taken into account. An overview of the problems and possible solutions can be found in [ 4445 ] and references therein.

In fact, it is possible to perform unbiased least-squares fitting with Pearson's chi-square i. After each optimisation, it is set equal to the fit value Y obtained in the last iteration and a new fit is performed until convergence is reached [ 45 ]. There exist alternative estimators that allow using existing software for least-squares in a less biased way, with a minimal adaptation to the procedure.

### radioactive decay simulation: Topics by studiojul.info

For example, one can minimise [ 45 ] freely without the need for an iterative procedure, and obtain an unbiased result if the data are not too close to zero. To decay curves with a quasi purely exponential shape, another excellent method to derive an unbiased value for the decay constant is applying 'moment analysis'.

It is known that the 'first moment' i. If the moment analysis of the decay curve is restricted to a time interval t1,t2the following relationship can be derived between the half-life and the first moment [ 45 ]: The first moment, which is not a central moment, is sensitive to the time value assigned to each time bin. Central moments are insensitive to a linear translation of the time origin. The time spectrum is the convolution of the prompt peak the width of which shows the variation in the timing between truly coincident events and the slope generated by the lifetime of the nuclear level.

For relatively long half-lives, the width of the prompt peak is negligibly small and the half-life is extracted from a fit to the exponential slope.

If the half-life is short compared to the time resolution of the detection system, the time spectrum resembles the prompt peak of which the centroid has been displaced. The lifetime can be extracted from this shift [ 37 ].

The 'shift' method is less precise than the 'slope' method. Typical uncertainty components are: It is represented by the FWHM of the prompt time spectrum, which is generally a Gaussian distribution obtained by measuring simultaneous events in the two timing branches. Contributors to the FWHM are variances due to scintillator, photomultiplier and time pickoff.

## The uncertainty of the half-life

Photomultipliers are matched to the scintillator for maximum spectral response at the required wave length, large quantum efficiency, short rise time, transit time and transit-time spread. The development of ultrafast scintillators and multipliers have contributed most to improving the sensitivity of the fast timing technique down to the picosecond region.

These effects are considerably reduced by using constant fraction discrimination, resulting in a bipolar pulse of which the zero crossing is nearly independent of pulse height. This results in more precise time pickoff. Parent-daughter transitions should be correctly separated from random coincidences and interfering signals, while influences from the latter need to be accounted for in the uncertainty.

In spectra with low counting statistics and long slopes, the least-squares analysis underestimates the lifetime and proper fitting should be based on Poisson statistics [ 37 ]. Measurement of intermediate half-lives 4.

Decay curve Many radionuclides with practical implications and applications have half-lives varying between seconds and about years. This is a range of half-lives that can be measured directly by repeated activity measurements of a source.

The simplicity of the measurement principle has incited many authors to publish thus obtained half-life data, unsuspecting of hidden processes that inflate the measurement errors far beyond their uncertainty estimates. A common scenario is that an exponential decay curve is fitted to various activity values measured as a function of time and that the uncertainty on the decay constant is obtained from the least-squares minimisation algorithm.

This procedure is often faulty [ 48 ], as real measurement data may deviate in a subtle but systematic way from the theoretically assumed decay curve. The fitted decay constant is the value leading to the smallest residuals, which explains why an erroneous result seldom raises suspicion in the mind of the experimenter [ 1415 ]. Also other methods can be applied to extract the half-life from the data, such as moment analysis section 3. The sum of an exponential function superposed on a constant background is often assumed to model the temporal dependence of the measured activity: In reality, there is a less than perfectly linear relationship between the activity and the measured signal count rate or current in a detector.

Various processes make measurement data deviate from the ideal decay curve, long-term instabilities being at the same time the most influential but least visible sources of error. Due to differences in uncertainty propagation, it is convenient to subdivide these process according to the frequency at which they occur [ 1415 ]: A typical example would be counting statistics: Poisson processes are characterised by an exponential distribution of the interval times between successive events.

By extending the measurement, one improves the statistical uncertainty on the actual count rate. Also ultra-high frequency instabilities, such as e.

They are partly cancelled, though, by the 'integrating' effect of the duration of the measurement. Normal statistical treatments including least squares fitting apply because of the preservation of randomness of the data. They include the so-called 'seasonal effects' e. Their effect on the fitted half-life is greatly underestimated if treated as just a random residual.

Moreover, a fit tends to minimise the residuals and partly covers up the true size of the medium frequency effects. Typical examples are the activity interference by radioactive impurities, reproducibility of the source-detector geometry, noticeable changes in the detector efficiency e. They remain practically invisible in the residuals, as the fit will compensate for this trend, hence erase it erroneously.

Common problems in this range are a non-linear detector response to activity charge recombination in ionisation chamber, discharge of a capacitor, non-linearity in an electrometer, pile-up and dead time in countersystematic errors in the background subtraction, under- or over-compensation of count loss by live-time systems double count loss through summing-out of piled-up events, hidden dead time due to unexpected behaviour of detector and electronic modules, pulse undershoot and overshoot, cascade effects of pile-up and dead time, effect of variation of dead time during measurement of short-lived nuclideslong-term drift of the counting efficiency and source degradation e.

In figure 1hypothetical residuals of a fitted decay curve to data with high, medium and low frequency instabilities are shown. The dark dots represent the deviations of the data from the 'true' decay curve, the light circles show the deviations of the data from the fitted decay curve and the solid curve is the difference between the fitted and true decay curve.

The observer that performs the fit perceives only the light points. Ever since then, more elements have been investigated for their radioactivity, and different isotopes of elements have different radioactive behavior. Many are used commercially and medically, and others are just nuisances.

I'll list some of the uses: Small amounts of radioactive materials can be ingested as "radiotracers" to see how certain chemicals are taken up by the body. If a health researcher is interested in how a certain element is distributed by the body after it is ingested, he can choose to use a radioactive isotope of a common element, mix it in, and then use sensitive radiaion detectors to see where it ends up in the body. These are often used in studies to see how medications are absorbed and transported within the body.

Thorium, a naturally ocurring radioactive element, is used in making mantles for gas and kerosene lamps because thorium oxide glows brightly when heated. The radioactive elements uranium and plutonium are used in the generation of electricity in nuclear power plants. Small radiactive sources of particles are used in many home smoke detectors. These elements are also used in the production of nuclear weapons.

One can propose that the presence of nuclear weapons has prevented war, but also that they have made the consequences of possible war much much worse than before. Depleted uranium, that is, naturally ocurring uranium with the U taken out, is mostly U, which is a bit less radioactive than the natural material.

This material is very dense and hard, however, and otherwise useless, so the army uses it to make bullets and other shells. These can pierce steel armor. Whether this is a good use or a bad use depends on which side of the gun you're standing on, I suppose.

Some radioactive elements glow because of their radioactive decays. They emit electrons or alpha particles, changing from one kind of element to another, and as the electrons in the atoms rearrange themselves to the new atom's configuration, they emit light. Radium was used for watch dials because it glows green. Tritium can also be used as a backlight in watches because it too glows green.

Tritium is still used in small quantities in small vials on watch hands and to mark the hour positions on watch dials. Radium isn't used anymore, however. Now for some negative effects: Radiation, even in small doses, can cause cancer in humans and other living things. Fast moving photons gamma rayselectrons beta rays and helium nuclei alpha particles can crash into other molecules and change their structure.

If this happens to a DNA molecule, it can damage the genetic information, and sometimes turn a cell cancerous. Radiation also causes burns, much like sunburn, in large doses over short amounts of time.

Usually you can walk away from radioactive substances, lowering your risk.

But if you ingest radioactive elements, they stay with you. Particulrly nasty radioactive elements include radon and radioactive iodine.