Question

A customer buys a “gold” chain from a jeweler that is advertised to be 10% pure gold. The customer issuspicious and irradiates one 25 mg link of the chain in a constant neutron source with a flux of 10^10 neutrons/s/cm^2 long enough for the gold activity to saturate (not change appreciably). The customer then measures the activity of the link to be 75,000 decays/s with a detector that has a detection efficiency of 12%.The neutron capture for gold is 99 barns. What is thepercent (by weight) of gold in the chain?

Answer 1

25 mg of gold contains 25.0E-3*0.602E+24/197 gold atoms

nuetron capture cross section of Au-197 = 99b

macroscopic cross section of the sample = 25.0E-3*0.602E+24/197 *99E-24

= 7.64E-5 /cm²  

This the effect area seen by the incident neutron beam of the nuetrons and neutrons effectively blocked by the sample. every nuetron blocked is captured and Au, atom is activated.

Inicident neutron beam conatains 1.0E+10 neutrons /s/cm²

rate of neutron interation = 7.64E-5 * 1.0E+10 = 7.64E+5 /s

This is the stauration activity of the sample if all the sample contains Au- nuclie

detector efficiency = 12% = 0.12

number of decays measured = 7.64E+5 *0.12 = 9.168E+4 = 91680 decays/s if the sample has 100% gold

deacys mesured = 75000 /s

% of gold in the sample = 75000/91680 *100 = 81.81%