A Half-Life (of Strontium) Problem

[RSADancinQueen]

Here's the problem:
Strontium 90 has a half-life of 27 years. If the amount of Strontium 90 in an area is eight times the safe level, how much time would elapse to reach and acceptable level?

My biggest snag is where to start. I have the
Q=Qoe^(-0.000124t) equation, but it doesn't include the half-life anywhere. Help!

 

[galactus]

Half life is given by the formula:

\(\displaystyle T=\frac{-ln(2)}{k}\)

\(\displaystyle 27=\frac{-ln(2)}{k}\)

\(\displaystyle k=\frac{-ln(2)}{27}\approx -.025672117799\)

\(\displaystyle P=P_{0}e^{-.025672117799t}\)

Your formula has k=-.000124. That would mean the half-life is around 5590 years. More like Carbon-14.

What is the acceptable level?. I suppose we can assume it is the initial amount.

If the Strontium is initially at a level 8 times what it needs to be to be safe, then we can use

\(\displaystyle P=8Pe^{-.025672117799t}\)

\(\displaystyle 1=8e^{-.025672117799t}\)

and solve for t.

 

[Deleted member 4993]

Here's the problem:
Strontium 90 has a half-life of 27 years. If the amount of Strontium 90 in an area is eight times the safe level, how much time would elapse to reach and acceptable level?

My biggest snag is where to start. I have the
Q=Qoe^(-0.000124t) equation, but it doesn't include the half-life anywhere. Help!

You can do this without algebra!

How long it will take to come down to four times the safe level (half of eight times) ? 27 years

How long it will take to come down to two times the safe level (half of eight times and half again ) ? (27 + 27 =) 54 years

How long it will take to come down to the safe level ( and half again ) ? (27 + 27 + 27 =) 81 years

 

[BigGlenntheHeavy]

Good show, Subhotosh Khan, just common sense thinking.