A narrow, monoenergetic photon beam of intensity travels along the -direction through…

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

Life at Thermal Energy, Ch Radiation in tissue: interaction, dose and risk

Problem

A narrow, monoenergetic photon beam of intensity

I

travels along the

x

-direction through a uniform absorbing medium. In each thin layer of thickness

\mathrm{d}x

, a photon already in the beam has a constant probability

\mu\,\mathrm{d}x

of being removed from the beam (by absorption or by scattering out of it), independent of how far it has already travelled;

\mu

is the linear attenuation coefficient of the medium, in

\mathrm{cm^{-1}}

. ((a)) Starting from the removal probability per layer, write down the differential equation obeyed by

I(x)

and solve it for

I(x)

in terms of

I_0=I(0)

\mu

and

x

. ((b)) Define the half-value layer

\mathrm{HVL}

as the thickness that halves the beam and express it in terms of

\mu

. ((c)) Water at

60\,\mathrm{keV}

has

\mu/\rho = 0.206\,\mathrm{cm^2\,g^{-1}}

and density

\rho = 1.00\,\mathrm{g\,cm^{-3}}

. Compute

\mathrm{HVL}

for water at this energy.

Related theory

Nuclear Physics

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