I sort of know what it is but I'm confused why I don't always get the right answer. Can someone explain to me how I can calculate half-life the right way?
2006-07-03 11:15:07 · 6 answers · asked by Etania 7 in Science & Mathematics ➔ Chemistry
radioactivity: N = No[exp(-lambda * t)] No = initial radioactivity
lambda = decay constant.
N/No = [exp(-lambda * t)]
now take the natural log of both sides (ln):
ln(N/No) = -lambda * t
using the properties of logarithims:
ln(No/N) = lambda * t
t = ln(No/N)/lambda
t½ = when N = No/2
t½ = ln[No/(No/2)]/lambda
t½ = ln(2)/lambda = 0.693/lambda
This last equation will get you the half life if you know lambda.
If you have 3 of 4 out of this equation: ln(No/N) = lambda * t
you can solve for the unknown quantity: i.e. I did an experiment in college where I "heated" a piece of indium up so it produced a radio isotope of it. As soon as I pulled it from the neutron source, I measured the CPS of the sample with a geiger tube. This gave me No. I waited several hours and remeasured. This gave me an n value. Since I knew N, No, and t (time between measurments) I calculated lambda
With lambda I was able to take 0.693/lambda and calculate the 1/2 life. BTW, I was able to get within less than 1% error of the textbook value! :^)
2006-07-03 15:50:12 · answer #1 · answered by cat_lover 4 · 2⤊ 1⤋
Halve lives are already calculated for you. You look up the half life and then you know in how many hours, days, or weeks it takes for that isotope to get to that half life. Once it reaches that half life, then you can calculate again when the activity will be halved, this time the activity will be one quarter the amount of the initial.
2006-07-03 18:22:36 · answer #2 · answered by mulderlx 2 · 0⤊ 0⤋
You can look up the correct half-lives of radio-isotopes in any good chemistry book. SImpley use the length of time you are given in the research question to calculate the correct half-life. The most common errors are purely mathematical, so take your time. You did not state whether the research questions indicate specific decay factors, shielding effects, moderators or other variables which affect theoretical half-lives. I am assuming that you are not in a nuclear engineering course, so assume straight and complete decay over the course of the period of time given.
2006-07-03 18:31:04 · answer #3 · answered by cake_eatingraccoon 1 · 0⤊ 0⤋
use the equation:1/2 life = ln2/(lambda)
Where ln 2 is the natural log of 2 and (lambda) is the decay constant for the particular substance you are looking at. It must be given in order to calculate for 1/2 life.
2006-07-03 20:33:49 · answer #4 · answered by Aaronkun 3 · 0⤊ 0⤋
Just ask the guy at Best Buy how much 'Half Life' costs. It's a great game, btw.
2006-07-03 18:20:00 · answer #5 · answered by Rob 5 · 0⤊ 0⤋
Don't try any shortcut; list each of the steps. That way, you will better understand what is required.
2006-07-03 19:51:03 · answer #6 · answered by flandargo 5 · 0⤊ 0⤋