A sample of a radioactive substance decayed to 91.5% of its original amount after a year. What is the half life of the substance? Also have to find the amount of time for it to decay to 30% of the original amount.

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- October 21st 2008, 07:57 PMGreenandGoldRadioactive decay
A sample of a radioactive substance decayed to 91.5% of its original amount after a year. What is the half life of the substance? Also have to find the amount of time for it to decay to 30% of the original amount.

- October 21st 2008, 08:05 PMChris L T521
Radioactivity can be defined using this model:

, where

is the current amount of the substance

is the initial amount of the substance

is the decay constant

is the length of time

Now, we are told that we have after 1 year.

Thus,

Solving for k, we see that

Now, we can find the half life:

Half life is defined as , where

is the half life

is the decay constant

Thus,

Now, our decay model is

Can you find when ?

--Chris - October 21st 2008, 08:19 PMGreenandGold
take the natural log of both sides?

- October 21st 2008, 08:20 PMChris L T521
- October 21st 2008, 08:28 PMGreenandGold
I got -13 but i did something wrong. is it 7.803(ln(.3)/ln(2))

- October 21st 2008, 08:33 PMGreenandGold
ok i added a negative to the decay since its negative. so i got 1.35535

- October 21st 2008, 08:49 PMChris L T521
- October 21st 2008, 08:57 PMGreenandGold
ok i see now!!! thanks...