# 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]

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.

## 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.

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
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}