chemistry

posted by .

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 -

    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
    so
    T = thalf/.6931
    NOW for this problem
    .25 = 2 e^-42/T
    ln (.125) = -42/T
    T = 20.2 days
    so
    thalf = .6931(20.2 = 14 days

    rough check
    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 -

    The same math but in slightly different format.
    k=0.693/t1/2
    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. half-life

    1. The half-life of a first-order reaction is 9.89 minutes. How many minutes will have elapsed after 27 half-lives?
  2. Chemistry

    What is used to tell different isotopes of a particular element apart?
  3. Chemistry

    A radioactive element has a half-life of 6.41 days. What percent of the original sample will be left after 15.0 days?
  4. statistics

    I have tried for days to figure out how to work this problem. Please help show me how to find the answer. A particular radioactive isotope decays from 210 mg to 182.7 mg in 15 days. Find the half life of the isotope.
  5. statistics - can someone please Help me

    I have tried for days to figure out how to work this problem. Please help show me how to find the answer. A particular radioactive isotope decays from 210 mg to 182.7 mg in 15 days. Find the half life of the isotope. I can not find …
  6. Chemistry. Half Life Problem. Help Plz

    If the half-life of iodine-131 is 8 day, how much would remain undecayed after 8 day if we started with 38 grams?
  7. abdul kabir

    the half life of an element is 5 days. if we have 10gram of the element initially. what is the mass of the element after 5days and 10days
  8. Chemistry

    A particular radioactive element has a half life of 10.0 days. How much is left after 30.0 days if the sample started with 345g?
  9. PRe calc story problem!!

    A radioactive element decays exponentially according to the function Q(t) = Q0ekt .If 100 mg of the element decays to 25 mg in 12 days, find the half-life of the element.
  10. chemistry

    Examine the information. Element A has a half-life of 10 days. A scientist measures out 200 g of this substance. After 30 days has passed, the scientist reexamines the sample.  How much Element A will remain in the sample 100g 12.5g …

More Similar Questions