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August 7th, 2008, 02:45 PM  #1 
Newbie Joined: Aug 2008 Posts: 1 Thanks: 0  Halflife problem. Please help :)
Guys, Could you please help me with this problem? "What is the halflife of a radioactive substance that has a decay rate of 25% per decade? Hint: Remember that the Rule of 70 does not give a good approximation to halflife when the rate is larger than 15%. We must use the actual formula here." Thanks a bunch.. 
August 7th, 2008, 03:06 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Halflife problem. Please help :)
Hi The total amount of radioactive material remaining in a decay is always given by where K is the starting amount and is some positive constant related to the rate of decay. If we measure t in years, then since after 10 years there will be 75% of the starting amount, we have the relationship so To work out the halflife, we need to find the value of t  call this  that corresponds to the time where the amount remaining is half the initial amount. This can be represented by the formula so or 
August 8th, 2008, 09:53 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
If the halflife is t years, (3/4)^(t/10) = 1/2, so t = 10ln(1/2)/ln(3/4) = 24.1 to 3 significant figures.


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