# Problem: In how many days will a sample of polonium 210 with a half-life of 138 days decay to one-fourth of the original amount?

###### FREE Expert Solution

We’re being asked to time it would take for a polonium-210 to decay to one-fourth the original amount.

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

$\overline{){\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{0}}}}$

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration.

###### Problem Details

In how many days will a sample of polonium 210 with a half-life of 138 days decay to one-fourth of the original amount?