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# Solution: Barium-122 has a half-life of 2 minutes. You just obtained a sample weighing 10.0 grams. If takes 10 minutes to set up the experiment in which barium-122 will be used. How many grams of barium-122 will be left when you begin the experiment?a. 0.313 g remainb. 0.625 g remainc. 0.00 g remaind. 50.0 g remaine. 2.00 g remain

###### Problem

Barium-122 has a half-life of 2 minutes. You just obtained a sample weighing 10.0 grams. If takes 10 minutes to set up the experiment in which barium-122 will be used. How many grams of barium-122 will be left when you begin the experiment?

a. 0.313 g remain

b. 0.625 g remain

c. 0.00 g remain

d. 50.0 g remain

e. 2.00 g remain

###### Solution

We’re being asked to calculate the mass of barium-122 remaining from 10.0 g Ba-122 after 10 minutes. The half-life of Ba-122 is 2 minutes.

Since barium-122 has a half-life, it is a radioactive isotope. Recall that radioactive isotopes follow first-order kinetics.

The integrated rate law for a first-order reaction is as follows:

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

where:

[A]t = concentration at time t

k = rate constant

t = time

[A]0 = initial concentration

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