Problem: Decay of a 10.0-g sample of strontium-90 (t1/2 = 28.8 yr).The 10 ximes 10 grids show how much of the radioactive isotope remains aftervarious amounts of time.If we start with a 50.0-g sample, how much of it remains after three half-lives have passed?

FREE Expert Solution

In this problem, we are being asked to determine the mass of Strontium-90 remaining when after three half-lives have passed the 50.0 g of sample. 


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


ln[N]t=-kt+ln[N]0

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


k=ln 2t1/2


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Problem Details

The x-axis is time (year) ranging from 0 to 120 with intervals of 20. The y-axis is mass of strontium-90 (grams), ranging from 0 to 10.0 with intervals of 2.0. The data are described as follows; values are approximate. For a time of 0 years, the mass is 10.0 grams, and the portion of the 10 by 10 grid remaining is 100 percent. At 29 years, the mass is 5.0 grams with 50 percent remaining. At 58 years, the mass is 2.4 grams, with 25 percent remaining. At 85 years, the mass is 1.3 grams, and the percentage remaining is 12.
Decay of a 10.0-g sample of strontium-90 (t1/2 = 28.8 yr).The 10 x 10 grids show how much of the radioactive isotope remains aftervarious amounts of time.

If we start with a 50.0-g sample, how much of it remains after three half-lives have passed?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.