3.8. Detector Efficiency 215
Problems
1.Compute the total and primary charge pairs created percmin a mixture of
90% argon and 10% carbon dioxide.2.If the concentrations of argon and carbon dioxide as given in the previous
problem are reversed, how many charge pairs will be created percm.3.A gaseous detector is filled with 99% helium and 1% air (contaminant) at
standard temperature and pressure. Assume that incident radiation produces
6 eV electrons at a distance of 10mmfrom the collecting electrode. Compute
the percent loss of these electrons at the electrode assuming that their total
scattering cross section is 5× 10 −^14 cm^2.4.Determine the breakdown voltage for an argon filled chamber having electrode
separation of 0.3cmand first townsend coefficient of 100cm−^1 at standard
pressure. What will be the breakdown voltage if the filling gas is replaced by
helium?5.The first Townsend coefficient for an argon filled chamber is desired to be
around 300cm−^1 at a distance of 0.5mmfrom the anode. If the gas must be
kept at a pressure of 826torr, estimate the electric field.6.Determine the first Townsend coefficient for a gas at 0.01cmfrom the electrode
to achieve a multiplication factor in excess of 10^5. Also determine the second
Townsend coefficient at the same location.7.Derive the expression for Paschen minimum as a function of the Townsend
coefficient.8.Compare the Paschen minimum for helium filled chamber with that of an argon
filled chamber at 0.02cmfrom the positive electrode. Assume that the gases
in both chambers are kept at 1.6atmand the electric field intensity is 3× 104
Vcm−^1.9.A collimated source of 6.5MeV βparticles is placed in a vacuumed enclosure
in front of an argon filled ionization chamber having a depth of 1.7cm.The
window of the detector is made of 12μmthick mylar sheet. If the filling
gas pressure is 1.5atm, calculate the energy deposited byβ-particles in the
detector.10.A helium filled cylindrical chamber is operated under standard conditions of
temperature and pressure. The radii of the chamber and its anode wire are
3.5cmand 12μmrespectively. At what applied voltage you would expect this
chamber to work as a proportional counter having a multiplication factor of at
least 100?11.A GM detector having a dead time of 85μsmeasures count rates of 225s−^1
and 133s−^1 from two separate sources. If both the sources are placed in front
of the detector at the same time, what count rate you would expect the GM
counter to measure?