Answer
The half-life of radium-230 is 92.98 minutes, though this can be rounded to approximately 93 minutes.
Work Step by Step
k = -$\frac{1}{t}$ln($\frac{N_{t}}{N_{o}}$)
k = -$\frac{1}{279 minutes}$ln ($\frac{0.25 mg}{2.00 mg}$)
k = -$\frac{1}{279 minutes}$(-2.08)
k = -$\frac{1}{279 minutes}$(-2.08)
k = $\frac{0.00745}{min}$
t$_{\frac{1}{2}}$ = $\frac{0.693}{k}$
t$_{\frac{1}{2}}$ = $\frac{0.693}{0.0075/min}$
t$_{\frac{1}{2}}$ = $\frac{0.693}{0.0075/min}$
t$_{\frac{1}{2}}$ $\approx$ 92.98 minutes
