Asked by Kelly
The mass of a radioactive substance decreases at a rate proportional to the mass at the time. The orginal mass is 700 grams and after 8 years it has decayed to 550 grams. Determine its half-life.
Answers
Answered by
oobleck
dm/dt = -km
dm/m = -k dt
ln m = -kt+lnc
m = ce^(-kt)
Since e is just some power of 1/2, we can change bases just by using a different k
m = c*(1/2)^(kt)
since (1/2)^0 = 1,
m = 700*(1/2)^(kt)
Since m(8) = 550,
700*(1/2)^(8k) = 550
k = 0.04349
That means that
m = 700*(1/2)^(0.04349t) = 700*(1/2)^(t/23)
so, the half-life is 23 years
dm/m = -k dt
ln m = -kt+lnc
m = ce^(-kt)
Since e is just some power of 1/2, we can change bases just by using a different k
m = c*(1/2)^(kt)
since (1/2)^0 = 1,
m = 700*(1/2)^(kt)
Since m(8) = 550,
700*(1/2)^(8k) = 550
k = 0.04349
That means that
m = 700*(1/2)^(0.04349t) = 700*(1/2)^(t/23)
so, the half-life is 23 years
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