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.
+33661 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.
+33661 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.
