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calc I... just need a super simple formula for 1/2 life and doubling time, that would be a HUGE help!!! thnx?

to be more specific here's the calc problem:

Suppose a radioactive spill occurs and the half-li fe of the spilled material is 1500 years. Environmentalists estimate that the material should be 99.99% degraded before it can be
safely returned to the environment. Consequently, the government decides to bury it in a cave in a protected container until it is safe to unbury it. How many years (approximately)
must this material remain buried in the cave until it is 99.99% degraded.?

This is the EXACT answer:

The half life formula is N(t) = No*e(-λt),
where N(t) is the # of atomic nuclei present at time t,
No is the initial number of atomic nuclei and
λ is the decay constant, which is ln(2)/t(1/2) for half life.
t(1/2) is the time for a half life in seconds.

Ok so in your problem:
t(1/2) = 1500 years = 4.7335*10^10s
"99.99% degraded" means when .01% = .0001 of the initial amount No remains. You want to solve for t when N(t)= .0001No.

N(t) = No*e(-λt)
.0001No = No*e^( -ln(2)/(4.7335*10^10) * t )
Reduces to:
.0001 = e^( -1.464*10^-11 * t )
Take ln of both sides:
ln(.0001) = -1.464*10^-11 * t
Divide out -1.464*10^-11 to solve for t:
t = ln(.0001) / [-1.464*10^-11]

t = 629,121,610,107.662 seconds

t = 19,936.0866 years

This is the APPROXIMATE answer which is simpler.
Let x = # half lifes
Solve for the # of half lifes that occur until .0001 of the initial amount remains:
(.5)^x = .0001
Take ln of both sides:
x ln(.5) = ln(.0001)
x = ln(.0001)/ln(.5) = 13.2877 half lifes

1500 years/ half life * 13.2877 half lifes =

19,931.55 years, not that off from the true time.

The reason for the difference is that the first way uses exponential decay, which means the rate of decay is constantly changing. The Approximate method says the rate of decay is always the same which is not true but still a good approximation.

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