Question
problem 10
What is the atom densities in U-235, U-238, O? What is the enrichment of 235-U in weight- percent? In fission reactors one deals with neutrons having kinetic energies as high as 20 MeV. How much error is incurred in computing the speed of 20-MeV neutrons by using the classical expression rather than the relativistic expression for kinetic energy? A 1-MeV gamma ray loses 350 keV in a Compton scatter. Calculate the scattering angle. What are the gamma wavelengths before and after the scattering event? What is the kinetic energy of the recoil electron? What speed (m s^-1) and kinetic energy (MeV) would a neutron have if its relativistic mass were 20% greater than its rest mass? In a Compton scattering event, at what scattered photon angle is the photon energy loss minimum? What the scattered photon energy for that angle? What is the kinetic energy of the recoil electron? Repeat these three questions but now seek the maximum energy loss for the scattered photon. Derive for the Compton scattering process the recoil energy T_e, as a function of the incident photon energy E_gamma and the electron angle of scattering beta. Show that beta is never greater than pi/2 radians.
Explanation / Answer
10)
let the mass of netron is m0
mass of neutron , m = m0 * (1 + 0.20)
m = 1.20 * m0
let the speed of the neutron is v
1.20 * m0 = m0/sqrt(1 - (v/c)^2)
1.20 * m0 = m0/sqrt(1 - (v/c)^2)
solving for v
v = 0.552* c
v = 0.552 * 3 *10^8 = 1.656 *10^8 m/s
the speed of neutron is 1.656 *10^8 m/s
kinetic energy of neutron = (m * c^2 - m0 * c^2)/e
kinetic energy of neutron = (1.67 *10^-27 * 1.20 * (3 *10^8)^2 - 1.67 *10^-27 * (3 *10^8)^2)/(1.602 * 10^-19)
kinetic energy of neutron = 1.876 *10^8 eV
kinetic energy of neutron = 1876 MeV
