Question

# Radium-$223$ decays with a half-life of $11.4$ days. How long will it take for a $0.240-\mathrm{mol}$ sample of radium to decay to $1.50 \times 10^{-2}$ mol?

Solution

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Half-life ($t_h$) is the time required for a quantity to reduce to half of its initial value. The formula for the half-life is:

$\textcolor{#c34632}{N=N_0\times(\dfrac{1}{2})^{\dfrac{t}{t_h}}},$

where $N$ is final amount, $N_0$ is initial amount, $t$ is time and $t_h$ is the half-life.