The time required for the decay of the radioactive element to one half of its original amount is calledHalf-Life Period. It is denoted by t_1/2.

Putting these values in equation (iii), we get

Thus it is evident that t_1/2 of an element does not depend on the initial amount of radioactive element but depends on the value of l.

The t_1/2 of a particular radioactive isotope is a characteristic constant of that isotope. Values of t_1/2range from millions of years

The disintegration rate is also referred to as activity. The SI unit of radioactivity is becquerel (Bq) named after Antoine Becquerel, which is equal to one disintegration per second. The older unit, curie, named after Marie Curie is still used, One Curie (Ci) is defined as the amount of radioactive isotope that give 3.7 x 10¹⁰ disintegrations per second. This is the activity associated with 1g of radium-225 with half - life of 1600 years).

Thus 1 Ci = 3.7 x 10¹⁰ disintegration s^-1

= 3.7 x 10¹⁰ Bq.

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Definition

Radioactivity: Spontaneous changes in a nucleus accompanied by the emission of energy from the nucleus as a radiation.

Radioactive Half-Life: A period of time in which half the nuclei of a species of radioactive substance would decay.

Half-life

Main article: Half-life

A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. This time is called the half-life, and often denoted by the symbol t_{1 / 2}. The half-life can be written in terms of the decay constant, or the mean lifetime, as:

When this expression is inserted for τ in the exponential equation above, and ln2 is absorbed into the base, this equation becomes:

Thus, the amount of material left is 2 ^{− 1} = 1 / 2 raised to the (whole or fractional) number of half-lives that have passed. Thus, after 3 half-lives there will be 1 / 2³ = 1 / 8 of the original material left.

Therefore, the mean lifetime τ is equal to the half-life divided by the natural log of 2, or:

.

E.g. Polonium-210 has a half-life of 138 days, and a mean lifetime of 200 days.

Exponential decay

From Wikipedia, the free encyclopedia

A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constants of 25, 5, 1, 1/5, and 1/25 for x from 0 to 4.

A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where N is the quantity and λ is a positive number called the decay constant.

The solution to this equation (see below for derivation) is:

Here N(t) is the quantity at time t, and N₀ = N(0) is the initial quantity, i.e. the quantity at time t = 0.

Solution of the differential equation

The equation that describes exponential decay is

or, by rearranging,

Integrating, we have

where C is the constant of integration, and hence

where the final substitution, N₀ = e^C, is obtained by evaluating the equation at t = 0, as N₀ is defined as being the quantity at t = 0.

This is the form of the equation that is most commonly used to describe exponential decay. Any one of decay constant, mean lifetime or half-life is sufficient to characterise the decay. The notation λ for the decay constant is a remnant of the usual notation for an eigenvalue. In this case, λ is the eigenvalue of the opposite of the differentiation operator with N(t) as the corresponding eigenfunction. The units of the decay constant are s^-1.

decay constant Radioactive decay involves only the nucleus of the parent atom, and thus the rate of decay is independent of all physical and chemical conditions (e.g. pressure, temperature, etc.). The decay was shown byRutherford to follow an exponential law. The fundamental equation describing the rate of disintegration may be written as: −(dN/dt) = λN, where λ is the decay constant, representing the probability that an atom will decay in unit time t, and N is the number of radioactive atoms present. It is a fundamental assumption in geochronology that λ is a constant and that the only alteration in the amount of daughter or parent in the system is due to radioactive decay. The constant λ is usually expressed in units of 10^-10 per year (e.g. ²³⁵U is 9.72, ⁴⁰K is 5.31, ⁸⁷Rb is 0.139, and ²³⁸U is 1.54). The total lifetime of a radioactive parent in a given system cannot be specified; in theory it is infinite. It is a simple matter, however, to specify the time for half of the radioactive parent atoms in a system to decay. This is called the ‘half-life’ (T), which is related to the decay constant by the expression T = 0.693/λ. See also DECAY CURVE.

Isobars

Isotopes are chemically same and physically different. But the converse is true in isobars. That is isobars are elements, which are chemically different but physically same. So, isobars are atoms of different elements having the same atomic mass but different atomic number. Since their number of electrons is different, their chemical properties are different. The light nuclei have unstable isobars. Heavy nuclei have stable isobars and these occur in pairs. Suppose the number of protons of one isobar matches with that of another they are called as mirror-nuclides of each other.

Examples of isobars are

Since isobars are different elements they appear in different places in the periodic table.

Isotones

Isotones are elements having the same number of neutrons. Examples of isotones are Chlorine - 37 and Potassium - 39. Both have 20 neutrons in their nuclei.

Isotope

From Wikipedia, the free encyclopedia

For other uses, see Isotope (disambiguation).

Isotopes are different types of atoms (nuclides) of the same chemical element, each having a different number of neutrons. Correspondingly, isotopes differ in atomic mass and in mass number.^[1] The difference in the number of nucleons comes from a difference how many neutronsare in the atomic nucleus. The number of protons (the atomic number) is the same because that is what characterizes a chemical element. For example, carbon-12, carbon-13 and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13 and 14, respectively. Theatomic number of carbon is 6, so the neutron numbers in these isotopes of carbon are therefore 12−6 = 6, 13−6 = 7, and 14–6 = 8, respectively.

A nuclide is an atomic nucleus with a specified composition of protons and neutrons. The nuclide concept emphasizes nuclear properties over chemical properties while the isotope concept does the converse; for the neutron number has drastic effects on nuclear properties but negligible effects on chemical properties. Since isotope is the older term, it is better known, and it is still sometimes used in contexts where nuclidewould be more proper, such as nuclear technology.

An isotope or nuclide is specified by the name of the particular element (this indicates the atomic number implicitly) followed by a hyphen and the mass number (e.g. helium-3, carbon-12, carbon-13, iodine-131 and uranium-238). When a chemical symbol is used, e.g., "C" for carbon, standard notation is to indicate the number of nucleons with a superscript at the upper left of the chemical symbol and to indicate the atomic number with a subscript at the lower left (e.g. 32He, 126C, 136C, 13153I, and 23892U).

There are about 339 naturally occurring nuclides on Earth^[2], of which 288 are primordial nuclides and 269 are "stable"^[2]. To be precise, the nuclides termed "stable" are nuclides which have never been observed to decay. This qualification is necessary because many "stable" isotopes are predicted to be radioactive with very long half-lives.^{[citation needed]} Adding in the radioactive nuclides that have been created artificially, there are more than 3100 currently known nuclides.^[3]

Halflife The applet lists a "halflife" for each radioactive isotope. What does that mean? The halflife is the amount of time it takes for half of the atoms in a sample to decay. The halflife for a given isotope is always the same ; it doesn't depend on how many atoms you have or on how long they've been sitting around. For example, the applet will tell you that the halflife of beryllium 11 is 13.81 seconds. Let's say you start with, oh, 16 grams of 11Be. Wait 13.81 seconds, and you'll have 8 grams left; the rest will have decayed to boron 11. Another 13.81 seconds go by, and you're left with 4 grams of 11Be; 13.81 seconds more, and you have 2 grams...you get the idea. Hmmm...so a lot of decays happen really fast when there are lots of atoms, and then things slow down when there aren't so many. The halflife is always the same, but the half gets smaller and smaller. That's exactly right. Here's another applet that illustrates radioactive decay in action. Pick an isotope from the menu and click the "start" button. In the top picture, you'll see the atoms change color as they decay; the lower picture is a graph showing the number of atoms of each type versus time. Notice how the decays are fast and furious at the beginning and slow down over time; you can see this both from the color changes in the top window and from the graph. You'll also notice that the pattern of atoms in the top picture is random-looking, and different each time you run the applet, but the graph below always has the same shape. It's impossible to predict when a specific atom is going to decay, but you can predict the number of atoms that will decay in a certain time period.

Positrons, Alpha Particles, and Gamma Rays What happens when an atom doesn't have enoughneutrons to be stable? That's the case with beryllium 7, 7Be4. Click on it in the applet and see what happens. It decays to lithium 7--so a proton turns into a neutron. That makes sense...but how do you deal with the electric charge problem now? Going from Be to Li, you lose charge; emitting an electron would just make things worse. Right...so instead you emit a positron--a particle that's just like an electron except that it has opposite electric charge. In nuclear reactions, positrons are written this way: 0e1. So the reaction looks like this: 7Be4 => 7Li3 + 0e1 Good. The applet will show you many other decays that produce either electrons or positrons; it's easy to tell which, by the "direction" in which the decay moves. Sometimes it even takes more than one decay to arrive at a stable isotope; try 18Ne or 21O, for example. So all radioactive isotopes decay by giving off either electrons or positrons? No, there are other possibilities. Some heavy isotopes decay by spitting out alpha particles. These are actually helium 4 nuclei--clumps of two neutrons and two protons each. A typical alpha decay looks like this: 238U92 => 234Th90 + 4He2 There's also a third type of radioactive emission. After alpha or beta decay, a nucleus is often left in an excited state--that is, with some extra energy. It then "calms down" by releasing this energy in the form of a very high-frequency photon, or electromagnetic wave, known as a gamma ray. Click on the advanced button for more information about why this happens.

Beta Decay

I'm going to illustrate how radioactive decay works with the help of an isotope table applet, which should now be open in a separate window. If it isn't, click here: to open it now.

There are several ways in which radioactive atoms can decay. Here's one example: suppose an atom has too many neutrons to be stable.That's the case with tritium, ³H₁.

Does it just kick out one of the neutrons?

No, it can't do that; the neutrons are stuck too firmly where they are. What it can do...well, I'll let you see for yourself. In the applet, click on the button labeled H3 (for hydrogen 3, or tritium).

The neutron turns into a proton! ³H₁ becomes ³He₂.

Right. An unstable isotope of hydrogen has converted itself into a stable isotope of helium. You'll notice that ³H₁ and ³He₂ have the same mass number, which is good, because mass has to be conserved.

There is a problem, though. Electric charge also has to be conserved.

Hydrogen has only one proton, and helium has two, so you'd end up with twice as much positive charge as you started with. How do you get around that?

When ³H metamorphoses into helium 3, it also gives off an electron--which has hardly any mass, and is endowed with a negative charge that exactly cancels one proton. This process is known as beta decay, and the electron is called a beta particle in this context.

You can write out the nuclear reaction involved in the beta decay of tritium by giving the electron a "mass number" of 0 and an "atomic number" of -1: 3H1 => 3He2 + 0e-1 Notice that the mass numbers on each side add up to the same total (3 = 3 + 0), and so do the charges (1 = 2 + -1). This must always be true in any nuclear reaction.

Isotopes

Atoms of the same element can have different numbers of neutrons; the different possible versions of each element are called isotopes. For example, the most common isotope of hydrogen has no neutrons at all; there's also a hydrogen isotope called deuterium, with one neutron, and another, tritium, with two neutrons.

Hydrogen		Deuterium		Tritium

If you want to refer to a certain isotope, you write it like this: ^AX_Z. Here X is the chemical symbol for the element, Z is the atomic number, and A is the number of neutrons and protons combined, called the mass number. For instance, ordinary hydrogen is written ¹H₁, deuterium is²H₁, and tritium is ³H₁.

How many isotopes can one element have? Can an atom have just any number of neutrons?

No; there are "preferred" combinations of neutrons and protons, at which the forces holding nuclei together seem to balance best. Light elements tend to have about as many neutrons as protons; heavy elements apparently need more neutrons than protons in order to stick together. Atoms with a few too many neutrons, or not quite enough, can sometimes exist for a while, but they'reunstable.

I'm not sure what you mean by "unstable." Do atoms just fall apart if they don't have the right number of neutrons?

Well, yes, in a way. Unstable atoms areradioactive: their nuclei change or decay by spitting out radiation, in the form of particles or electromagnetic waves.