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November 5th, 2011, 01:26 PM   #1
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half life of radium question help

The half life of radium is 1690 years. If 200g is present now, how long (to the nearest year) till only 85g are present?

According to my worksheet example, I'm supposed to do
100=200e^r(1690)
1/2 = e^r(1690)
ln 1/2 = r(1690)
r = (ln 1/2) / 1690
but my calculator come up with weird # that doesn't look like an answer.

For second part, I'm supposed to do
85=200e^rx to get x for years but this r I've got above don't make any sense.
help..
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November 5th, 2011, 02:36 PM   #2
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Re: half life of radium question help

Quote:
Originally Posted by shin777
The half life of radium is 1690 years. If 200g is present now, how long (to the nearest year) till only 85g are present?

according to my worksheet example, I suppose to
100=200e^r(1690)
1/2 = e^r(1690)
ln 1/2 = r(1690)
r = (ln 1/2) / 1690
but my calculator come up with weird # that doesn't look like an answer

for second part i suppose to
85=200e^rx to get x for years but this r i've got above don't make any sense.
help..
I don't what your problem is. However, using the expressions you presented I get 2086 years, which looks perfectly reasonable.
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November 5th, 2011, 02:52 PM   #3
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Re: half life of radium question help

Can you explain how you did it for me?
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November 5th, 2011, 03:00 PM   #4
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Re: half life of radium question help

Your calculation for r is correct. Now solve 85 = 200 * e^(ln(1/2) * t/1690) for t. You should get 2086 as your answer.
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November 5th, 2011, 03:25 PM   #5
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Re: half life of radium question help

Oh, I get 2086 too on my calculator when I just put whole thing in. That's weird coz # I get from r by itself didn't make any sense to me.

How about 55 = 28(36/2^(t/5)?
How do you solve this for t?
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November 5th, 2011, 05:46 PM   #6
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Re: half life of radium question help

I have this in my head but do not know whether I am right or not
200/(2^(t/1690)) = 85
2^(t/1690) = 200/85
t = 1690*log( 200/85 ; base of log :: 2) = 2086.24627864657
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November 5th, 2011, 07:56 PM   #7
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Re: half life of radium question help

How come I get different answer?

1690 years is 1 half life , therefore from 200g to 100g used 1690 years

from 100g to 50g needs another 1690 years , so 50g : 1690 , 1g : 1690/50

1g : 33.8 years

from 200g to 85g = 1690 + ( 33.8 x 15 )


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November 5th, 2011, 08:02 PM   #8
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Re: half life of radium question help

You are assuming a linear decay, when it is actually an exponential decay. That is why your answer differs from the correct one.
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