Half Life - Calculate Fraction Remaining

[jendrix]

Homework Statement

Carbon 14 has a half-life of 5730 years, what fraction will have decayed in 2300 years?

Homework Equations

Nf/No =e^-kt

The Attempt at a Solution

Nf/No =e^-1.21 x 10^-4 x 2300

=0.068585374

However if I use Nf =No(1/2)^2300/5730

I get 0.757125224

I appreciate that I'm looking for the fraction that has decayed but I'm unsure as to why this has produced 2 different answers, I thought either could be used for this problem.

Thanks

 

[Doc Al]

Nf/No =e^-1.21 x 10^-4 x 2300

=0.068585374

Redo this.

 

[gneill]

Recheck your math for the first formula.

EDIT: Doc Al beat me to it again.

 

[BruceW]

I agree with them guys. You got it right using the second method jendrix. But maybe just a mistake while calculating using the first method.

 

[jendrix]

Hi, I think I was using a wrong value for the decay constant but somehow wrote it down correct here.

My new answer is 0.77130147

I was wondering why there is a discrepancy albeit a small one depending on which formula I use, is it to do with the rounding of the constant?

 

[Doc Al]

Hi, I think I was using a wrong value for the decay constant but somehow wrote it down correct here.

My new answer is 0.77130147

I was wondering why there is a discrepancy albeit a small one depending on which formula I use, is it to do with the rounding of the constant?

You're still making an error somewhere. Just evaluate the formula you gave in your first post:

Nf/No =e^-1.21 x 10^-4 x 2300

That should give you the right answer.

 

[jendrix]

Thanks Doc Al, I now get 0.757069666 as opposed to 0.757125224 from the other formula.
Is this where rounding the constant has had an effect?

Now I have to find the fraction that was lost to decay, if i do 1 - 0.757069666 to give 0.242930334 would you consider this sufficient or should I call it 6/25?

 

[Doc Al]

Thanks Doc Al, I now get 0.757069666 as opposed to 0.757125224 from the other formula.
Is this where rounding the constant has had an effect?

Yes. (But round off your answers to a reasonable number of significant figures.)

Now I have to find the fraction that was lost to decay, if i do 1 - 0.757069666 to give 0.242930334 would you consider this sufficient or should I call it 6/25?

That decimal should be fine (rounded off, of course). (When they say 'fraction' they probably don't literally mean fraction, as in numerator/denominator.)

 

[jendrix]

Excellent, thanks for all your help guys