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earnstyle [38]
3 years ago
12

The half-life of polonium-218 is 3 min. if you start with 16 mg, how long will it be before only 1.0 mg remains?

History
1 answer:
babymother [125]3 years ago
3 0
The decay equation is of the form
m(t) = m_{0} e^{-kt}
where
m(t) = the mass remaining after t minutes
m₀ =  the initial mass
k = constant

Because the half-life is 3 minutes, therefore
e^{-3k} = \frac{1}{2}
Therefore
-3k = ln(0.5)
k = ln(0.5)/(-3) = 0.231

Because m₀ = 16 mg, the time, t, for the mass to decay to 1.0 mg is given by
e^{-0.231t} =  \frac{0.1}{16} =0.00625 \\\\
-0.231t = ln(0.00625) \\\\ t =  \frac{ln(0.00625)}{-0.231} =21.97 \, min

Answer: 22 min (nearest integer)

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