Radioactivity taken up by cells
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The following quantities appear in the problem:
Zeit \(t\) / Zerfallskonstante \(\lambda\) / Anzahl \(N\) / Verhältnis / Anteil \(\eta\) /
The following formulas must be used to solve the exercise:
\(\eta = \dfrac{a}{A} \quad \) \(N_t = N_0 \cdot \text{e}^{-\lambda t} \quad \)
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Exercise:
In a certain experiment AzO Ci.eBq of isotopeP half life TO is injected o a medium containing a culture of bacteria. After tO the cells are washed and a detector that is netO efficient counts netO percent of emitted upbeta rays records AO from all the cells. What percentage of the original isotopeP was taken up by the cells?
Solution:
Geg A_ AzO Az T TO T t tO t eta' netO net A_d' AO AQ GesPrecentageeta text no unit The injected Phosphor has an initial activity of A_ AzO Az. This activity decays with the half-life of isotopeP TO. After one hour no significant change in the activity is expected since this one hour is much less than the half-life. A short calculation can confirm that: A_t A_ mathrme^-fracln T t A_ ^-fractT Az mathrme^fracln T t At Observation of the cell culture shows AO i.e. A where only netO is registered. Hence there is a real activity of A_d fracA_d'eta' fracAnet Ad in the cell culture. This is only eta fracA_dA_t fracfracA_d'eta'A_ mathrme^-fracln T t fracA_d'eta' A_ mathrme^-fracln T t approx fracA_d'eta' A_ fracAdAt nta ntap of the theoretical expected activity which means that only .% of the Phosphorus was taken up by the cells. eta fracA_d'eta' A_ mathrme^-fracln T t nta ntap
In a certain experiment AzO Ci.eBq of isotopeP half life TO is injected o a medium containing a culture of bacteria. After tO the cells are washed and a detector that is netO efficient counts netO percent of emitted upbeta rays records AO from all the cells. What percentage of the original isotopeP was taken up by the cells?
Solution:
Geg A_ AzO Az T TO T t tO t eta' netO net A_d' AO AQ GesPrecentageeta text no unit The injected Phosphor has an initial activity of A_ AzO Az. This activity decays with the half-life of isotopeP TO. After one hour no significant change in the activity is expected since this one hour is much less than the half-life. A short calculation can confirm that: A_t A_ mathrme^-fracln T t A_ ^-fractT Az mathrme^fracln T t At Observation of the cell culture shows AO i.e. A where only netO is registered. Hence there is a real activity of A_d fracA_d'eta' fracAnet Ad in the cell culture. This is only eta fracA_dA_t fracfracA_d'eta'A_ mathrme^-fracln T t fracA_d'eta' A_ mathrme^-fracln T t approx fracA_d'eta' A_ fracAdAt nta ntap of the theoretical expected activity which means that only .% of the Phosphorus was taken up by the cells. eta fracA_d'eta' A_ mathrme^-fracln T t nta ntap