Physics and Engineering of Radiation Detection

2.7. Problems 143

2.7 Problems

1.The x-ray flux measured at a distance of 1.2mfrom an x-ray machine is

3. 6 × 108 cm−^2 s−^1. Compute the flux at a distance of 3.5m.

2.Compare the mean free paths of thermal neutrons in silicon and aluminum.

Assume the total cross sections for silicon and aluminum to be 2.35band 1.81

brespectively.

3.The mean free path ofN 2 ions in nitrogen gas at 273Kand 1.2atmis approx-

imately 10−^5 cm. Compute the relative change in mean free path if the gas is

brought to the standard conditions of 27^0 Cand 1atm.

4.A gas-filled detector is filled with 90%CO 2 and 10%CH 4 under atmospheric

conditions of temperature and pressure. Compute the radiation length of high

energy electrons passing through the detector.

5.Compute the maximum frequency of the photons emitted when an electron is

accelerated through a potential of 30kV.

6.The cut-off Bremsstrahlung wavelength of an x-ray machine is found to be 35

fm. Estimate the electric potential applied across its electrodes.

7.Compute the threshold energy anα-particle must possess to emit Cherenkov

radiation in light water withn=1.3. At what angle would the light be emitted

at this energy? Is it practical to build a Cherenkov detector for detectingα

particles?

8.In a liquid filled Cherenkov detector, the maximum angle of Cherenkov cone

ever observed was 48^0. Assuming that the particle emitting Chrenkov radiation

traveled at a velocity of 0. 9 c, estimate the refractive index of the liquid.

9.A fast moving electron in light water produces about 300 photons percmof

its travel path. Estimate the angle of the Cherenkov cone thus produced.

10.Compare the critical energies of electrons in lead and aluminum.

11.A photon beam of wavelength 80nmionizes hydrogen atoms. Compute the

energy of the emitted electrons.

12.Compare the cutoff wavelengths of cesium in metallic and free states for pho-

toelectric effect to occur. The ionization energy and work function of cesium

are 3.9eV and 1.9eV respectively.

13.A metal is illuminated with light of 290nm, which results in the emission of

electrons with a kinetic energy of 3.1eV. Compute the work function of the

metal.

14.A photon having an energy of 200keV scatters off of an atom at an angle of

350. Compute

the wavelength of the scattered photon,


the kinetic energy of the scattered electron, and