Physics

Problem

Which of the following gives the correct relation between the half-life

T_{1/2}

of a radioactive nuclide and its decay constant

\lambda

? a)

T_{1/2}=\dfrac{1}{\lambda}

T_{1/2}=\dfrac{\log_{10} 2}{\lambda}

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

T_{1/2}=\dfrac{1}{2\lambda}

Intuitive explanation

Half-life measures how long it takes for half a sample to decay, while the decay constant describes the rate at which decay happens at any moment. The key insight is that these two quantities are inversely related through the exponential decay law: when you set the remaining amount equal to half the original and solve for time, $\lambda$ and $T_{1/2}$ appear together in a simple, elegant formula. Understanding this connection lets you convert between "how fast" and "how long" for any radioactive material.

Intuitive explanation

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