10.10.2017 radio active decay rates
Radioactive decay rates Edit
The decay rate, or activity, of a radioactive substance is characterized by:
Constant quantities:
The half-life—t1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value; see List of nuclides.
The decay constant— λ, "lambda" the reciprocal of the mean lifetime, sometimes referred to as simply decay rate.
The mean lifetime— τ, "tau" the average lifetime (1/e life) of a radioactive particle before decay.
Although these are constants, they are associated with the statistical behavior of populations of atoms. In consequence, predictions using these constants are less accurate for minuscule samples of atoms.
In principle a half-life, a third-life, or even a (1/√2)-life, can be used in exactly the same way as half-life; but the mean life and half-life t1/2 have been adopted as standard times associated with exponential decay.
Time-variable quantities:
Total activity— A, is the number of decays per unit time of a radioactive sample.
Number of particles—N, is the total number of particles in the sample.
Specific activity—SA, number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.
These are related as follows:
{\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}
{\displaystyle A=-{\frac {\mathrm {d} N}{\mathrm {d} t}}=\lambda N}
{\displaystyle S_{A}a_{0}=-{\frac {\mathrm {d} N}{\mathrm {d} t}}{\bigg |}_{t=0}=\lambda N_{0}}
where N0 is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.
The decay rate, or activity, of a radioactive substance is characterized by:
Constant quantities:
The half-life—t1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value; see List of nuclides.
The decay constant— λ, "lambda" the reciprocal of the mean lifetime, sometimes referred to as simply decay rate.
The mean lifetime— τ, "tau" the average lifetime (1/e life) of a radioactive particle before decay.
Although these are constants, they are associated with the statistical behavior of populations of atoms. In consequence, predictions using these constants are less accurate for minuscule samples of atoms.
In principle a half-life, a third-life, or even a (1/√2)-life, can be used in exactly the same way as half-life; but the mean life and half-life t1/2 have been adopted as standard times associated with exponential decay.
Time-variable quantities:
Total activity— A, is the number of decays per unit time of a radioactive sample.
Number of particles—N, is the total number of particles in the sample.
Specific activity—SA, number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.
These are related as follows:
{\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}
{\displaystyle A=-{\frac {\mathrm {d} N}{\mathrm {d} t}}=\lambda N}
{\displaystyle S_{A}a_{0}=-{\frac {\mathrm {d} N}{\mathrm {d} t}}{\bigg |}_{t=0}=\lambda N_{0}}
where N0 is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.
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