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the half life of colbalt-60 is approximently 5.25 days. find the amount of cobalt-60 left from a 30 gram sample after 42 days. round to the nearest thousandth of a gram.

 Apr 24, 2014

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 #3
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The expression for radioactive decay is N = N0e-ln(2)t/th  where N is the mass, at time t, N0 is the mass at the start (30grams) and th is the half-life (5.25days), so here: 

$${\mathtt{N}} = {\mathtt{30}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{ln}{\left({\mathtt{2}}\right)}{\mathtt{\,\times\,}}{\mathtt{42}}}{{\mathtt{5.25}}}}\right)} = {\mathtt{N}} = {\mathtt{0.117\: \!187\: \!500\: \!000\: \!000\: \!1}}$$ grams

To the nearest thousandth of a gram this is 0.117grams.

 Apr 24, 2014
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Guest Apr 24, 2014
 #2
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Hahaha, made my day!^^^

 Apr 24, 2014
 #3
avatar+33603 
+5
Best Answer

The expression for radioactive decay is N = N0e-ln(2)t/th  where N is the mass, at time t, N0 is the mass at the start (30grams) and th is the half-life (5.25days), so here: 

$${\mathtt{N}} = {\mathtt{30}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{ln}{\left({\mathtt{2}}\right)}{\mathtt{\,\times\,}}{\mathtt{42}}}{{\mathtt{5.25}}}}\right)} = {\mathtt{N}} = {\mathtt{0.117\: \!187\: \!500\: \!000\: \!000\: \!1}}$$ grams

To the nearest thousandth of a gram this is 0.117grams.

Alan Apr 24, 2014

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