Question

What is the half-life for the first-order decay of phosphorus-32?\(_{{\bf{15}}}^{{\bf{32}}}{\bf{P}} \to _{{\bf{16}}}^{{\bf{32}}}{\bf{S + }}{{\bf{e}}^{\bf{ - }}}\)The rate constant for the decay is\({\bf{4}}{\bf{.85 \times 1}}{{\bf{0}}^{{\bf{ - 2}}}}{\bf{da}}{{\bf{y}}^{{\bf{ - 1}}}}\).

Short answer

The half-life is 14.3 days.

Step-by-step solution

Definition

The half-life of a sample is the time required for half of the sample to undergo the process.

First-order reaction half-life

The rate constant has an inverse relationship with the half-life.

A first-order reaction's half-life is specified as

\({t_{1/2}} = \frac{{0.693}}{k}\)

k is the rate constant of the given reaction, and this is the derived formula of half-life.

Calculation of Half-life

Replacing the values,

\(\begin{align}{t_{1/2}} &= \frac{{0.693}}{{4.85 \times {{10}^{ - 2}}}}\\{t_{1/2}} &= 14.3days\end{align}\)