Three separate laboratory tasks

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radiation interactions, detection and dosimetry

The Nucleus Resolved, Ch What it is used for: medicine, dating and analysis

Problem

Three separate laboratory tasks, worked in turn. ((a)) A

{}^{99}\mathrm{Mo}/{}^{99m}\mathrm{Tc}

generator has a parent activity of

40\,\mathrm{GBq}

{}^{99}\mathrm{Mo}

at the moment it is loaded (freshly eluted, so the daughter starts at zero). Take

T_{1/2}({}^{99}\mathrm{Mo}) = 66\,\mathrm{h}

T_{1/2}({}^{99m}\mathrm{Tc}) = 6.0\,\mathrm{h}

, and a branching fraction of

87.6\,\%

{}^{99}\mathrm{Mo}

decays feeding the isomer. Calculate the activity of

{}^{99m}\mathrm{Tc}

that is eluted

24\,\mathrm{h}

after loading. ((b)) A bone sample has a measured

{}^{14}\mathrm{C}/{}^{12}\mathrm{C}

ratio equal to

0.15

of the modern atmospheric ratio. Take

T_{1/2}({}^{14}\mathrm{C}) = 5730\,\mathrm{yr}

. The sample is known to have derived its carbon from a marine reservoir with an apparent age offset of

400\,\mathrm{yr}

relative to the atmosphere. Calculate the conventional radiocarbon age of the sample corrected for this reservoir effect (no calendar calibration curve is supplied or required). ((c)) A suspect residue is irradiated for

45\,\mathrm{min}

in a thermal neutron flux of

8.0\times10^{12}\,\mathrm{cm^{-2}\,s^{-1}}

to test for gold via

{}^{197}\mathrm{Au}(n,\gamma){}^{198}\mathrm{Au}

, with

\sigma_{n\gamma} = 98.7\,\mathrm{b}

and

T_{1/2}({}^{198}\mathrm{Au}) = 64.8\,\mathrm{h}

. Immediately after irradiation the sample is counted for

1.0\,\mathrm{h}

in the

412\,\mathrm{keV}

line (emitted in

95.6\,\%

of decays) with a detector of

3.0\,\%

efficiency for that line. A background count of

25

counts is recorded in the same

1.0\,\mathrm{h}

window, and a peak is judged detected only if the net counts exceed

3\sqrt{B}

above that background,

B

being the background count (a simpler and looser rule than Chapter 10's detection limit

L_D = 2.71 + 4.65\sqrt{B}

). Decay of

{}^{198}\mathrm{Au}

during the

1.0\,\mathrm{h}

count may be neglected, since it is only about

1\,\%

of the half-life. Calculate the minimum mass of gold detectable under these conditions.

Related theory

Nuclear Physics

Browse the problem library