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expeople1 [14]
3 years ago
13

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 remain

s?
Chemistry
1 answer:
Elanso [62]3 years ago
4 0

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.

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