The half-life of a species in a chemical reaction is the time taken for the concentration of the same substance to fall towards half of its initial value. For this example, rather than "half-life", the term half time tends to be used, but they mean similar. Here, ln (2) is a natural logarithm of 2 (approximately 0.693)įrom the equation given above, the current flowing through an RC or RL circuit decays with a half-life of ln(2) L/R or ln(2) RC, respectively. It differs based on the isotope and atom type and is usually determined as experimentally. There is a half-life that describes any exponential-decay process.įor example, in the radioactive decay case, the half-life is the length of time, after there is a 50% chance that an atom would have undergone nuclear decay. Half-life chemistry is demonstrated using dice in a classroom experiment. Several simple exercises can demonstrate probabilistic decay, such as running a statistical computer program or involving flipping coins. To define in other words, the radioactive atom probability decaying within its half-life is about 50% Instead, the half-life definition is defined in terms of probability as "Half-life is the required time exactly for half of the entities to decay on average". For example, if there is only one radioactive atom, and its half-life is just one second, there will not be "half of the atom" left after that one second. In that case, it doesn't work to use the half-life definition chemistry, stating that "half-life is the required time for exactly half of the entities to decay". Usually, Half-life chemistry describes the decay of discrete entities, such as radioactive atoms. Note the consequences of the law of large numbers - with more atoms the overall decay is more regular and predictable. The number at the top is that of how many half-lives have elapsed. The simulation of several identical atoms undergoing radioactive decay, beginning with either four atoms per box (towards the left) or 400 (towards the right). Probabilistic Nature of half-life Chemistry Therefore, the first-order half-life reaction is given by 0.693/k. The first-order reaction half-life equation is given by, The half-life of first-order reaction is given below on how it is derived, including the expression.įor a half-life of the first-order reaction, the constant rate can be mathematically expressed as follows. Substituting the value t = t 1/2, at which the point = 0 /2 (at the half-life of a reaction, the concentration of the reactant is half of the initial concentration)Īfter rearranging the above half-life equation chemistry, the half-life of zero-order reaction expression is found to be,ĭerivation of First-Order Reaction Half-life Formula And, an expression for a half-life of zero-order reaction's rate constant is given by, The half-life of a zero-order reaction is explained below on how it is derived, including the expression.įor the half-life of zero-order reaction, the units of the rate constant are mol.L -1. K is the rate constant of the reaction (unit - M (1-n) s -1, where ‘n’ is the order of reaction)ĭerivation of Half-Life Formula for Zero-Order Reaction is the initial reactant concentration (unit - mol.L-1 or M), and
T 1/2 is the half-life of certain reaction (unit - seconds) The mathematical expression can be employed to determine the half-life for a zero-order reaction is, t 1/2 = 0 /2kįor the first-order reaction, the half-life is defined as t 1/2 = 0.693/kĪnd, for the second-order reaction, the formula for the half-life of the reaction is given by, 1/k 0
The half-life formula for various reactions is given below. It is essential to note that the half-life formula of a reaction varies with the reaction's order. It is essential to make note that the half-life is varied between different types of reactions. The concepts of half-life play a vital role in the administration of drugs into the target, especially in the elimination phase, where half-life is used to discover how quickly a drug decrease in the target once it has been absorbed in a period of time (sec, minute, day) or the elimination rate constant ke (minute -1, hour -1, day -1 ). The half-life application is used in chemistry and in medicine to predict the concentration of a substance over time. The half-life chemistry or a half-life of a reaction, t 1/2, is defined as the specific amount of time required for a reactant concentration to decrease by half when compared to its initial concentration.