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Some isotopes are radioactive and decay by a specific type of emission, whereas others are stable indefinitely. The amount of radioactivity diminishes as time passes because less and less of the radioactive isotope is present.
The half-life is a fascinating and useful aspect of radioactive decay. In these half-life definition notes, we will learn the meaning of half-life definition and how to calculate the amount of radioactive substance left after a certain number of half-lives.
Half-life definition
The half-life of a chemical reaction is the time it takes for a particular reactant’s concentration to reach 50% of its initial concentration (i.e. the time taken for the reactant concentration to reach half of its initial value). It is commonly represented in seconds and is denoted by the sign ‘t1/2’. A radioactive isotope’s half-life is the length of time it takes for one-half of the isotope to decay. A radioactive isotope’s half-life is constant; it is unaffected by conditions and unchanged by the original amount of that isotope.
The phrase is also used to describe any form of exponential or non-exponential decay in general. The biological half-life of medications and other compounds in the human body, for example, is discussed in medical research. Doubling time is the inverse of half-life.
Consider the following illustration. Let’s pretend we have 100.0 g of 3H. (tritium, a radioactive isotope of hydrogen). It has a 12.3-year half-life. Half of the sample will have decayed to 3He by producing a beta particle after 12.3 years, leaving only 50.0 g of the original 3H. Another half of the remaining 3H will decay after another 12.3 years, for a total of 24.6 years, leaving 25.0 g of 3H. Another half of the remaining 3H will decay after another 12.3 years, for a total of 36.9 years, leaving 12.5 g of 3H. To understand how radioactive decay occurs, let us conduct an experiment with a large group of people because the statistical analysis will yield a reasonably obvious result.
Consider the following scenario: Nearly 1000 individuals are gathered in a hall, and each one is given a coin. The coin would represent the ability to decay, and each individual would represent a radioactive atom. Individuals can be requested to toss their money once every minute. If the toss result is heads, the person may be requested to leave the room (indicating atom disintegration), but if the outcome is tails, there is no need to do anything but wait one minute for another toss try.
The formula of half-life
As we discussed in these half-life definition notes, the half-life is the length of time it takes for one-half of the isotope to decay. Now, let’s look at the formula of half-life. It’s worth noting that the formula for a reaction’s half-life varies depending on the reaction’s order. The half-life of a zero-order reaction can be calculated using the mathematical calculation:
t1/2 = [R]0/2k
The half-life of a first-order reaction is calculated as follows:
t1/2 = 0.693/k.
The half-life of a second-order reaction is calculated using the formula:
1/k[R]0.
Where, The reaction’s half-life is t1/2
The initial reactant concentration is [R0] (mol.L-1 or M)
The reaction’s rate constant is k.
Important half-life definition notes
As per the Meaning of half-life definition, many people believe that a radioactive element’s half-life signifies the amount of time it is radioactive. In actuality, it is the time it takes for half of the element to decay radioactively, not all of it. However, in some cases, the daughter element is also radioactive. Thus its radioactivity must be taken into account.
An ionisation-type smoke detector (explained in the introductory article) has a 10-year estimated operational life. In that time, americium-241, which has a half-life of around 432 y, loses less than 4 percent of its radioactivity.
A half-life of 432 years may appear long to us, yet it is not very long in terms of half-lives. The most prevalent isotope of uranium, uranium-238, has a half-life of 4.5x 109 years, while thorium-232 has a half-life of 14×109 years. Some nuclei, on the other hand, have extraordinarily short half-lives, posing difficulties for scientists studying them. Lawrencium’s longest-lived isotope, 262Lr, has a half-life of 3.6 hours, while its shortest-lived isotope, 252Lr, has a half-life of 0.36 seconds. The largest atom ever discovered has an atomic number of 118, a mass of 293, and a half-life of 120 nanoseconds.
The half-lives of certain unstable atomic nuclei and the manner in which they decay are characteristics. The processes of alpha and beta decay are generally slower than gamma decay. Beta-decay has half-lives of up to one-hundredth of a second, while alpha decay has half-lives of up to one-millionth of a second. Although a wide range of half-lives for gamma emission has been observed, gamma decay half-lives may be too short to measure (about 10-14 seconds).
Conclusion
The half-life is an important concept in radioactive decay. The half-life of a chemical reaction is the time it takes for a particular reactant’s concentration to reach 50% of its initial concentration. Although many people mistakenly believe that a radioactive element’s half-life is the time it takes for half of the element to decay radioactively, it is really the time it takes for half of the element to decay radioactively, not the entire element. Thus, in these half-life definition notes, we have studied the meaning of half-life definition and formula.
