We’re being asked to **determine how many alpha particles are emitted in 5.00 min by a 10.0 mg sample of ^{226}Ra**.

**Step 1. Calculate the decay constant. **

Recall that * half-life* is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{l}\mathbf{n}\mathbf{}\mathbf{2}}{\mathbf{k}}}$

where:

**t**_{1/2} = half-life

**k** = decay constant

Radium-226, which undergoes alpha decay, has a half-life of 1600 yr.

How many alpha particles are emitted in 5.00 min by a 10.0 mg sample of ^{226}Ra?

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