Posted by **lolo** on Monday, August 22, 2011 at 8:49pm.

How long will it take for the 100mg of cesium-137 to decay to 6.25mg(1/16 the original amount)?

- chemistry -
**DrBob222**, Monday, August 22, 2011 at 8:58pm
2^{n} = 16

Solve for n = number of half lives.

- chemistry -
**lolo**, Monday, August 22, 2011 at 9:59pm
still i can't understand it

- chemistry -
**DrBob222**, Monday, August 22, 2011 at 10:31pm
Do you have the half-life given in the problem or are you allowed to look it up? If so there is an easier way to set it up.

To solve 2^{n} = 16, take the log of both sides.

log 2^{n} = log 16

n*log 2 = log 16

n*0.301 = 1.2 etc.

There is another way. Remember that half-life means the time it takes for 1/2 the material to disappear. So make a table like this. The periods are used for spacing.

amount......# half-lives

100 mg.........0

50 mg..........1

25 mg..........2

12.5 mg........3

6.25 mg........4

So whatever the half-life is, multiply that by 4 and you will have the time it takes to go through 4 half-lives.

- chemistry -
**Anonymous**, Tuesday, August 23, 2011 at 1:24am
thanks alot , this answer really helped me to understand this question

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