what is half life period
Answers
Main article: Exponential decay
An exponential decay can be described by any of the following three equivalent formulas:
{\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}} {\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}}
where
N0 is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
N(t) is the quantity that still remains and has not yet decayed after a time t,
t1⁄2 is the half-life of the decaying quantity,
τ is a positive number called the mean lifetime of the decaying quantity,
λ is a positive number called the decay constant of the decaying quantity.
The three parameters t1⁄2, τ, and λ are all directly related in the following way:
{\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)} {\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}
where ln(2) is the natural logarithm of 2 (approximately 0.693).
Decay by two or more processes
Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1⁄2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation:
{\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}} {\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}}
For three or more processes, the analogous formula is:
{\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots } {\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots }
For a proof of these formulas, see Exponential decay § Decay by two or more processes.
Examples
Half life demonstrated using dice in a classroom experiment
Further information: Exponential decay § Applications and examples
There is a half-life describing any exponential-decay process. For example:
As noted above, in radioactive decay the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, and is usually determined experimentally. See List of nuclides.
The current flowing through an RC circuit or RL circuit decays with a half-life of ln(2)RC or ln(2)L/R, respectively. For this example the term half time tends to be used, rather than "half life", but they mean the same thing.
In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction the half-life of the reactant is ln(2)/λ, where λ is the reaction rate constant.
Half-life is the time required for a quantity to reduce to half its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay
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