What is the difference between half-life and mean life?

Half-life ($T_{1/2}$) is the time required for half of the radioactive nuclei in a sample to decay. Mean life ($ au$), on the other hand, is the average lifetime of a radioactive nucleus. It's the total lifetime of all nuclei divided by the initial number of nuclei. The relationship between them is $ au = rac{1}{lambda}$ and $T_{1/2} = rac{ln 2}{lambda}$, which means $ au = rac{T_{1/2}}{ln 2} approx 1.443 T_{1/2}$. Mean life is always longer than half-life.

Does the half-life of a substance change if its temperature or pressure is altered?

No, the half-life of a radioactive substance is an intrinsic property of its nucleus and is entirely independent of external physical conditions such as temperature, pressure, or chemical environment. Radioactive decay is a nuclear process, meaning it involves transformations within the nucleus itself, which are not affected by the electron cloud or intermolecular forces that respond to changes in temperature or pressure.

If a radioactive sample has a half-life of 5 years, will it completely decay in 10 years?

No, it will not completely decay in 10 years. After 5 years (one half-life), half of the original sample will remain. After another 5 years (a total of 10 years, or two half-lives), half of the *remaining* half will decay, leaving one-fourth of the original sample. Radioactive decay is an exponential process, meaning the amount of radioactive material theoretically never reaches zero, though it becomes infinitesimally small over many half-lives.

How is half-life used in carbon dating?

Carbon dating utilizes the half-life of Carbon-14 ($T_{1/2} approx 5730$ years). Living organisms constantly exchange carbon with their environment, maintaining a constant ratio of Carbon-14 to stable Carbon-12. Upon death, this exchange stops, and the Carbon-14 begins to decay. By measuring the current Carbon-14 to Carbon-12 ratio in an ancient organic sample and comparing it to the known ratio in living organisms, scientists can determine how many half-lives have passed, thus calculating the sample's age.

Can half-life be used to determine the activity of a radioactive sample?

Yes, half-life is directly related to the decay constant ($lambda = rac{ln 2}{T_{1/2}}$), and activity ($A$) is defined as $A = lambda N$, where $N$ is the number of radioactive nuclei. Therefore, if you know the half-life and the number of nuclei, you can calculate the activity. Also, activity itself decays exponentially with the same half-life: $A(t) = A_0 left(rac{1}{2} ight)^n$, where $A_0$ is the initial activity.

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Half Life

Physics

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Version 1Updated 23 Mar 2026

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Half-life, denoted as $T_{1/2}$ , is a fundamental characteristic of a radioactive isotope, representing the time required for half of the radioactive nuclei in a given sample to undergo radioactive decay. It is a statistical measure, meaning that for any individual nucleus, the exact moment of decay cannot be predicted, but for a large ensemble of identical nuclei, precisely half will have decayed…

Quick Summary

Half-life ( $T_{1/2}$ ) is the characteristic time for half of a radioactive sample's unstable nuclei to decay. It's a constant for a given isotope, unaffected by external conditions. The decay process follows an exponential law, $N(t) = N_0 e^{-lambda t}$ , where $N_0$ is initial nuclei, $N(t)$ is nuclei at time $t$ , and $lambda$ is the decay constant.

The relationship between half-life and decay constant is $T_{1/2} = \frac{ln 2}{lambda} approx \frac{0.693}{lambda}$ . After 'n' half-lives, the number of remaining nuclei is $N = N_0 (1/2)^n$ . Activity, the rate of decay, also halves over each half-life period.

This concept is vital for applications like radiometric dating and medical diagnostics, providing a quantitative measure of radioactive decay rates.

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Key Concepts

Half-life (

T_{1/2}

)

Half-life is the most intuitive way to describe how quickly a radioactive substance decays. It's the time it…

Decay Constant (

lambda

)

The decay constant is a fundamental parameter that quantifies the probability of decay per unit time for a…

Radioactive Decay Law and Activity

The radioactive decay law, $N(t) = N_0 e^{-lambda t}$ , describes how the number of undecayed nuclei ( $N$ )…

Definition: — Time for half of radioactive nuclei to decay.

Symbol: —

T_{1/2}

Decay Law: —

N(t) = N_0 e^{-lambda t}

Remaining after 'n' half-lives: —

N = N_0 \left(\frac{1}{2}\right)^n

Relation to Decay Constant: —

T_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}

Relation to Mean Life: —

T_{1/2} = \tau \ln 2 \approx 0.693 \tau

Activity: —

A = \lambda N

, also decays exponentially

A = A_0 \left(\frac{1}{2}\right)^n

Independence: — Unaffected by T, P, chemical state.

Half-life Links Nuclei Decay Constantly.

Half-life:

T_{1/2}

Links:

\ln 2

Nuclei:

N = N_0 (1/2)^n

Decay Constantly:

T_{1/2} = \frac{\ln 2}{\lambda}

(Decay Constant

\lambda

)

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