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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?

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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=(0.693)/(t_1_/_2)

where
t_1_/_2 stands for half life.

Given half life is 3.0 minutes.

So,
k=(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((4.5g)/(40.0g))=-0.231min^-^1}


-2.18=-0.231min^-^1}


t=(-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.

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