Question

It is found that it takes a 2.36-cm-thick piece of Pd metal foil (density 12.0 g/cm³) to reduce the intensity of a beam of thermal neutrons to exactly 10^-3 of its original intensity. Calculate the neutron capture cross section of Pd metal in units of barns.

Answer 1

Number of atoms n

= density x Avogadro number / molecular weight

= 12 g/cm3 x 6.023 x 10^23 / 106.4 g/mol

= 6.79 x 10^22 atoms/cm3

Thickness x = 2.36 cm

Cross section =?

intensity of a beam reduced = 10^-3 of original

I_x/I_o = exp(-nx)

10^-3 = exp (-6.79 * 10^22 * * 2.36)

ln 10^-3 = (-6.79 * 10^22 * * 2.36)

= (-6.91)/(-6.79 * 10^22 * 2.36)

= 4.31*10^-23 cm2 x 1 barn/10^-24cm2

= 43.1 barns