# Just needed help on this one

• Oct 24th 2008, 09:21 PM
dc52789
Just needed help on this one
I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
• Oct 24th 2008, 09:44 PM
Jhevon
Quote:

Originally Posted by dc52789
I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?

recall that $r = \frac {\ln 2}{\text{half life}}$

use that $r$ in the exponential decay formula: $N(t) = N_0e^{-rt}$

where $N(t)$ is the amount remaining after time $t$, $N_0$ is the initial amount, $r$ is the rate of decay

you want to find $N(2160)$
• Oct 24th 2008, 09:59 PM
dc52789
Quote:

Originally Posted by Jhevon
recall that $r = \frac {\ln 2}{\text{half life}}$

use that $r$ in the exponential decay formula: $N(t) = N_0e^{-rt}$

where $N(t)$ is the amount remaining after time $t$, $N_0$ is the initial amount, $r$ is the rate of decay

you want to find $N(2160)$

For r, would it be best if it's nearest to the hundredth or the thousandth?
• Oct 24th 2008, 10:06 PM
Jhevon
Quote:

Originally Posted by dc52789
For r, would it be best if it's nearest to the hundredth or the thousandth?

well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required
• Oct 24th 2008, 10:11 PM
dc52789
Quote:

Originally Posted by Jhevon
well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required

He asked to give the answer to the nearest thousandths of a gram.
• Oct 24th 2008, 10:16 PM
Jhevon
Quote:

Originally Posted by dc52789
He asked to give the answer to the nearest thousandths of a gram.

ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished
• Oct 24th 2008, 10:19 PM
dc52789
Quote:

Originally Posted by Jhevon
ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished

o k...I have 0.414 as my answer. Is it correct?
• Oct 24th 2008, 10:44 PM
Jhevon
Quote:

Originally Posted by dc52789
o k...I have 0.414 as my answer. Is it correct?

that's not what i got
• Oct 25th 2008, 05:12 AM
HallsofIvy
Quote:

Originally Posted by dc52789
I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?

You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.
• Oct 25th 2008, 08:00 AM
dc52789
Quote:

Originally Posted by HallsofIvy
You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.

wow...that helps a lot. Thanks.