Calculating Radioactive Decay: Finding the Time for 80% Decay

[SETHOSCOTT]

Homework Statement

The half-life of a radioactive substance is 194 days. How many days will it take for 80% of the substance to decay?

Homework Equations

The Attempt at a Solution

I had to make 1/2ⁿ=1/5. I did this by finding log₂5=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.

 

[diazona]

There is absolutely enough information there. I could tell you the answer right now (but I won't, that's what you get to do ;-)

I'd advise you to go back and double-check that equation, though.

 

[HallsofIvy]

In one "half life", T, (1/2)C= Ce^kT. The Cs cancel, and you solve that for k. After you know that you can solve 0.8C= Ce^kt for t.

But you don't need to use "e". If T is the half life then $C(t)= C(0)(1/2)^{t/T}$ because every time "T" days, you multiply by1/2. Solve $.8C= C(1/2)^{t/194}$.

 

[diazona]

The Attempt at a Solution

I had to make 1/2ⁿ=1/5. I did this by finding log₂5=n. After this, I needed to only multiply by the number of days it took the half-life to occur, which was 194, and got 451 (approx.) as a reasonable answer.

Looks good...

 

[SETHOSCOTT]

=) omg! Thanks!