Radioactive Dating: Calculating Half-Life & Remaining Mass

[toothpaste666]

Homework Statement

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

 

[Simon Bridge]

You calculated the amount of Pb210 after 17.5a, you were asked for the amount of Hg206

 

[toothpaste666]

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

 

[Simon Bridge]

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?

 

[toothpaste666]

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

 

[Simon Bridge]

What is the decay mode?

 

[toothpaste666]

i am pretty sure it undergoes alpha decay

 

[Borek]

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.

 

[epenguin]

Bit of a trick question IMHO. Firstly you misread it, but I'd call that a set trap. 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 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.

 

[toothpaste666]

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?