Age of Seashell: Calculating 14-C Half Life

[matt222]

Homework Statement

seashell HAVE 90% of 14-C as a livining shell of the same size half life is 5570 years, how old is it in years

how many yrs did it take for 14-C to diminish from its initial value to 99% of that?

Homework Equations

The Attempt at a Solution

for the first part of problem 90% N0=N0exp(-kt), where k is decay constant from this k=1.24x10^-4
so t=847 years

for the second part of the problem we have the same decay constant k, so 99%N0=N0exp(-kt)

so for t I got t=81.1years

I think the first part is ok but i am not sure i about the second one

 

[Delphi51]

Looks good to me. Is your 3 digit accuracy for k sufficient? If I were you, I would keep about 5 digit accuracy because exponent accuracy strongly affects the accuracy of the power.

 

[matt222]

but it confused me the second part I am not sure about it 81 years compared to 847 years

 

[Delphi51]

I get 80.8 rather than 81.1, keeping all the digits on my calculator until rounding the final answer. You don't say what you are confused about. If you mean losing 1% in one tenth the time it loses 10%, that seems almost too reasonable to be true. Normally you can't trust your intuition on non-linear functions. It might be worth graphing the decay function on your calculator or computer to see if the function is fairly linear in that range.

 

[rwisz]

Your calculations for the first part of the problem seem to be correct. The age of the seashell can be estimated to be approximately 847 years old based on the given information.

For the second part of the problem, your approach is correct but your calculation seems to be off. Using the same decay constant, k=1.24x10^-4, the time it would take for 14-C to diminish from its initial value to 99% of that would be approximately 4418 years. This can be calculated using the formula t = ln(0.01)/(-k), where ln is the natural logarithm.

I would also like to mention that these calculations are based on the assumption that the seashell has been in a constant environment and has not undergone any external changes that could affect the 14-C levels. Additionally, there may be some experimental error in the initial 14-C levels of the seashell, which could affect the accuracy of the calculations.