View Full Version : Half-life equation
majehlover
Jun 14, 2009, 07:40 PM
Radium-226 has a half life of 1660 years.How many years does it take a radium sample to decay to 55% of the original amount. Round to the nearest year.
Please help me set up this equation!
Perito
Jun 14, 2009, 08:23 PM
here are some links:
Effective half-life - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Effective_half-life)
Radioactive decay - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Radioactive_decay#Decay_timing)
The equation you want is
\Large N = N_0 \,\times\, 2^{ \left( \frac {t}{t_{\frac 12} \right) (equation 1)
where N_0 is the original amount of material present. t is the time in the same units as the half-life, t_{ \frac 12 } is the half-life.
in your case \frac {N}{N_0} = 0.55
Divide both sides of equation 1 by N_0. Enter the data you have and solve for t.
Unknown008
Jun 15, 2009, 11:40 AM
I got a negative answer... I I got it, you missed a 'minus' sign in front of your power of two Perito...
What's happening to you today? Tired?
galactus
Jun 15, 2009, 01:20 PM
We can easily find k, the constant of proportionately, from the formula for half-life:
T=\frac{-1}{k}ln(2)
Since we are given the half-life is 1660, all we need to do is solve for k.
1660=-\frac{1}{k}ln(2)\Rightarrow \frac{-ln(2)}{1660}\approx -.00041756
Now we can sub this into the equation and solve for t:
.55A=Ae^{\frac{-ln(2)}{1660}t}
Solve for t.
bjones2379
Nov 5, 2010, 07:38 AM
Can u put this in simple terms for me
Unknown008
Nov 5, 2010, 07:42 AM
can u put this in simple terms for me
What do you mean? You want to know how to find the answer to this question on half life? :confused:
Or do you perhaps have another question?