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 :)
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
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...
Math - You have just isolated a new radioactive element. If you can determine ...
chemistry - A radioactive sample contains 2.45g of an isotope wiht a half life ...
physics - if you have an element that starts out at 40g and has a half-life of ...
Chemistry - IF 80mg of a radioactive element decays to 10mg in 30 minutes, the ...