Lecture 10
Problem Set-3
 

Question-5

The β¯ emitter  28Al ( half life 2.30 min) can be produced by the radiative capture of a neutron by 27Al. The 0.0253 eV cross section for this reaction is 0.23 b. Suppose that a small, 0.01 g aluminum target is placed in a beam of 0.0253 eV neutrons having an intensity of 3 x 108 neutrons/cm2 , which strikes the entire target. Calculate (a) the neutron density in the beam; (b) the rate at which 28Al is produced, (c) the maximum activity (in curies) which can be produced in this experiment. (2.17 x 10-4 cm-3, 1.54X104 s-1, 4.16 X 10-7 Ci)

  • The speed of the neutron is computed by equating energy to kinetic energy
Mass of neutron(kg)
1.675E-27
energy(eV)
0.0253
energy(J)
4.05559E-21
Speed(m/s)
2200.567091
I(n/cm2-s)
3.000E+08
n(cm-3)
1.363E+05
  • Check if infinite mass approximation is valid

σ59IT < 0.01
  • This is about 4.6 x 106 years, which is too large. Hence the approximation is valid.
  • Production rate of Al28 can be computed as
Mass of Al(g)
0.01
A
27
density of Al(g/cc)
2.7
Number of nuclei
2.23074E+20
σ(cm2)
2.3E-25
Production rate(s-1)
1.54E+04
  • During activation the activity of aluminum will build and reach a maximum, when production rate is equal to decay rate

  • Therefore maximum activity = 1.54E+04 s-1

    =  4.16 x 10-7 Ci