Question

PLZ HELP ...The half-life of polonium-218 is 3.0 minutes. If you start with 40.0 g, how long will it be before only 4.5 g remains?

Answer 1

Answer:-  9.4 minutes.

Solution:- Radioactive decay obeys first order reaction kinetics and the equation used to solve this type of problems is:

$lnN=-kt+lnN_0$

where, k is decay constant and t is the time. $N_0$ is the initial amount of the radioactive substance and N is the remaining amount.

Since the value of decay constant is not given, so we need to calculate it first from given half life by using the formula:

$k=\frac{0.693}{t_1_/_2}$

where $t_1_/_2$ stands for half life.

Given half life is 3.0 minutes.

So, $k=\frac{0.693}{3.0min}$

$k=0.231min^-^1$

Let's plug in the values in the first order reaction equation and solve it for t.

$ln4.5g=-0.231min^-^1(t)+ln40.0g$

It could also be written as:

$ln(\frac{4.5g}{40.0g})=-0.231min^-^1}$

$-2.18=-0.231min^-^1}$

$t=\frac{-2.18}{-0.231min^-^1}$

k = 9.4 min

So, the radioactive substance would take 9.4 minutes to decay from 40.0 grams to 4.5 grams.