Radioactive Dating: Calculating Half-Life & Remaining Mass

In summary, the homework statement was that Pb has a slightly more dense than Hb, and that Hg undergoes alpha decay. N was calculated to be 4.36 g, but the correct answer was B. N0 was calculated to be 7.5 g, but the correct answer was A.
  • #1
toothpaste666
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Homework Statement



chemproblem.png

Homework Equations


N= (N_0) e^(-kT)
k = ln(2)/(T_1/2)

The Attempt at a Solution


N0 = 7.5g
T_1/2 = 22.3 years
T = 17.5 years

k = ln(2)/22.3 = .031

N = 7.5 e^(-.031 * 17.5)
N = 4.36 g

So I chose A, but the correct answer was B. can't figure out where I went wrong
 
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  • #2
You calculated the amount of Pb210 after 17.5a, you were asked for the amount of Hg206
 
  • #3
then wouldn't it be 7.5 - 4.36 = 3.14? because you start with 7.5 and end up with 4.36 and the rest was converted to Hg206. I am still doing something wrong though because I am supposed to end up with 3.09
 
  • #4
Do you think that after 22.5years, 7.5g of Pb will become 3.75g of Pb and 3.75g of Hg?
Does Hg have the same density as Pb?
 
  • #5
Pb is slightly more dense. I'm not sure how to include this in the calculation though. if at the beginning all 7.5 grams is Pb and after the time has elapsed 4.36 of the 7.5 is Pb then I have a hard time understanding how Hg won't be the remainder of the 7.5 grams
 
  • #6
What is the decay mode?
 
  • #7
i am pretty sure it undergoes alpha decay
 
  • #8
I would look for atomic numbers of isotopes mentioned.

But in general, if it is alpha decay, you can assume mass of the nucleus changes by 4.
 
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  • #9
Bit of a trick question IMHO. Firstly you misread it, but I'd call that a set trap.:devil: Then you made your calculation and, once you realize the first trap the result is clearly nearer one figure, D, than another one. But the second trap :devil: is there is a 2% difference due to the mass change (which was given in the problem).

It would be fair to ask questions as a quiz when it is possible to get answers by principles or ballpark reasoning. It would be fair to ask the question with no answers given, since you can eliminate some answers by ballpark, but you cannot choose between B and D without calculation. But they have set you up by two answers meant to confirm you in mistakes!

These people are evil. :devil: :devil:
 
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  • #10
yeah i like better when tests are not multiple choice and have partial credit. That way they can grade you on your method of solving instead of just running it through a scantron =\

so the reason its B) is because of the mass that becomes the alpha particle?
 

1. What is radioactive dating?

Radioactive dating is a method used by scientists to determine the age of a material or object by measuring the amount of remaining radioactive isotopes it contains.

2. How does radioactive dating work?

Radioactive isotopes decay at a known and constant rate, which is referred to as the half-life. By measuring the amount of remaining radioactive isotopes and comparing it to the initial amount, scientists can calculate how many half-lives have passed and determine the age of the material or object.

3. What is half-life?

Half-life is the amount of time it takes for half of the initial amount of a radioactive isotope to decay into a stable form. This rate is constant and unique to each radioactive isotope, making it a useful tool for determining the age of materials.

4. How is remaining mass calculated in radioactive dating?

The remaining mass of a radioactive isotope is calculated by multiplying the initial mass by the decay rate raised to the power of the number of half-lives that have passed. This calculation takes into account the amount of time that has passed and the rate at which the isotope decays.

5. What are some limitations of radioactive dating?

Radioactive dating can only be used for materials that contain radioactive isotopes. Additionally, it is only accurate for objects that are less than 50,000 years old, as the amount of remaining isotopes becomes too small to measure accurately after that time. Other factors such as contamination and the presence of other isotopes can also affect the accuracy of the results.

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