Posted by Ryan on Thursday, December 13, 2007 at 9:07pm.
How do you find the half-life of an element? Please explain and show me how to do this. I know the answer is 14.3 days, but I don't know how to work it. thank you!
the problem is:
After 42 days, a 2.0-g sample of phosphous-32 contains only 0.25g of isotope. What is the half-life of phosphorus-32?
- chemistry - Damon, Thursday, December 13, 2007 at 9:29pm
mass at t = mass at beginning times e^-t/T
where T is some decay time
m = mo e^-t/T
now when will m = 1/2 mo ?
1/2 = e^- thalf/T where I am calling thalf the half life
-ln (1/2) = thalf/T
but -ln(1/2) = .6931
T = thalf/.6931
NOW for this problem
.25 = 2 e^-42/T
ln (.125) = -42/T
T = 20.2 days
thalf = .6931(20.2 = 14 days
after 14 days I have (1/2)2 = 1 gram
after 28 days I have (1/2)1 = .5 gram
after 42 days I have (1/2)(.5)=.25 grams
well, amazing, it worked :)
- chemistry - DrBob222, Thursday, December 13, 2007 at 10:56pm
The same math but in slightly different format.
ln(No/N) = kt where No = beginning grams, N = ending grams, k is the constant from equation 1 and t is the time.
substitute from equation 1 into k in equation 2 to obtain
ln(No/N) = [0.693/t1/2*t]
Now substitute your numbers
ln(2/0.25) = [0.693/t1/2*42]
ln 8 = [0.693*42/t1/2]
2.079 = 29.1/t1/2
t1/2 = 29.1/2.079 = 13.997 which rounds to 14 days.
Answer this Question
More Related Questions
- statistics - I have tried for days to figure out how to work this problem. ...
- statistics - can someone please Help me - I have tried for days to figure out ...
- half-life - 1. The half-life of a first-order reaction is 9.89 minutes. How many...
- physics - If the physical half-life of sulfur-35 is 87.1 days, and the biologic...
- math - You have just isolated a new radioactive element. If you can determine ...
- Chemistry - A radioactive element has a half-life of 6.41 days. What percent of ...
- Chemistry - What is used to tell different isotopes of a particular element ...
- math - An unknown radioactive element decays into non-radioactive substances. In...
- chemistry - If there are 80 milligrams of a radioactive element decays to 10 ...
- Chemistry - Iron -59 has a half life of 45.1 days. How old is an iron nail if ...