# The Naked Scientists Forum

#### fortengc

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« on: 28/02/2011 07:13:39 »
Suppose you begin with 2.0 mg of a pure radioactive substance and 4.0 h later determine that 0.50 mg remain. What is the half-life of the substance?

#### Geezer

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« Reply #1 on: 28/02/2011 07:25:01 »
I suppose I'd get the hell out of its vicinity.

#### Soul Surfer

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« Reply #2 on: 28/02/2011 08:30:45 »
That looks like a homework question and we should not give you the precise answer to that here.  The half life is the time it takes half of the substance to decay so if you had a specific amount of substance and you waited one half life half that amount would be left.  if you waited another half life half the remaining amount would be left and so on.  That should be plenty of information to enable YOU to work out the answer.

#### fortengc

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« Reply #3 on: 28/02/2011 08:56:19 »
This is how i solved it.

Ao=2
At=0.5
Ao/At=2^n
n=(In4/In2)=2

t=n T1/2
T1/2 = t/n= 4/2 =2 h per half-life

#### syhprum

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« Reply #4 on: 28/02/2011 15:20:15 »
Looks like pretty potent stuff your have there I trust it is well shielded.

#### Bored chemist

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« Reply #5 on: 28/02/2011 18:55:32 »
I'm sure this is a homework question and , as he has got the right answer (well done) I don't see any harm in pointing out that you can check the result.
If you start with 2 mg then after 1 half life (i.e. 2Hrs) you will have half as much, i.e. 1 mg.
After another 2 Hrs you will have just half of that so you would get 0.5 mg.

Here's another thought. Can you estimate some idea of how much power that radioactive material is dissipating?

#### syhprum

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« Reply #6 on: 28/02/2011 21:05:04 »
To get some ball park figures I looked up data on PuO2 pellets used as heat generators, Pu 238 has a half life of 88 years and the specification of the pellets is as follows.

SPECIFICATIONS FOR PUO2 FUEL PELLETS *
Diameter 0.494 ± 0.005 in.
Height 0.525 ± 0.015 in.
Density 81 to 85% of theoretical
Wattage 6.0 ± 0.05 W

This pellet would have a mass of about 15g giving a power output of .4 watts per gram.
A radioactive substance with a half life of 2 hours would have a vastly greater power
output per unit mass I estimate 300 watts for a 2mg sample and could not exist in solid form
« Last Edit: 01/03/2011 16:24:28 by syhprum »

#### Geezer

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« Reply #7 on: 28/02/2011 22:02:05 »
This reminded me of the time I had a bone scan. They injected something with a rather short half-life (a hour or so I think) into my bloodstream, then watched the scintillations when it went into my bone marrow. It was quite interesting to watch.

They told me there was nothing to worry about, but maybe that's because they were all wearing lead suits. (I made that last bit up!)