Given a sample of radioactives substance, if half the material takes 10 years to decay to a non radioactive material, what is the rate of decay?
Given 1 ton of material, how long until 0.1% remains.
2006-10-27 03:23:50 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Use equation A = A_0e^1-.000124t
2006-10-27 03:30:30 · update #1
For part 2, 0.1% of 2000 is 2.
Use the equation
2 = 2000(1/2)^(t/10)
solve for t
2006-10-27 03:42:55 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋
The rate of decay is approximately 6.6967% per year.
0.1% of 2000=2
2=2000(.933032991)^x
.001=.933032991^x
log 0.001/log 0.933032991=99.65784202
It will take 99.65784202 years for only 0.1% to remain.
2006-10-27 11:02:19 · answer #2 · answered by tamana 3 · 0⤊ 0⤋
if half life is 10y then 0.001=exp(-t*ln2/10y)==>ln(0.001)= -t*ln2/10y==> t = -10*ln0.001/ln2==> t=100 years till 0.1% remains. the rate of decay is: dm/dt = -m*ln2/10y= 0.069tons/y or 69kg per year
2006-10-27 10:40:50 · answer #3 · answered by okko 1 · 0⤊ 0⤋
0.5 = (R)^10
log 0.5 = 10 log R
log 0.5/10 = log R......R(growth rate)=.933..decay = 1-.933= 6.7%
2). .001 = (.933)^t
log .001 = t log .933
t= log.001/log.933 = 99.607 years
2006-10-27 12:15:11 · answer #4 · answered by davidosterberg1 6 · 0⤊ 0⤋