4.17 The manganese content of a certain stainless steel is to be verified by an

Question

4.17 The manganese content of a certain stainless steel is to be verified by an activation measurement. The activity induced in a sample of volume V by neutron capture during a time t is given by exp A foil of area 1 cm and thickness 2 mm is irradiated in a thermal neutron flux of 3 x 10 s) for 2 h. Counts taken immediately yield an activity of 150 mCi for the induced (cm Mn-56, half-life 2.58 h. Assuming that the atom number density of the alloy is 0.087 in units of 1024 and that the cross section for capture in Mn-55 is 13.3 barns, find the percent of Mn in the sample.

Explanation / Answer

Activity, A(t) = dN/dt = P*(1-exp(-la*t))

Half-life, th = 2.58h
decay constant la = 0.693/th = 0.693/2.58 = 0.27h-1
irradiation time, t = 2h
Activity, A(t) = P*(1-exp(-0.27*2))=0.416*P
Production rate, P = sigma*phi*N
Activity, A(t) =0.416*sigma*phi*N

Given
Activity, A = 150mCi = 150E-3*3.7E10 = 555E7 dps
Cross-section, sigma = 13.3barns =13.3E-24cm2
Neutron flux, phi = 3E12 cm-2 s-1

No. of Manganese atoms, N = A/(0.416*sigma*phi)= 555E7/(0.416*13.3E-24*3E12) = 33.4E19

Nt = number of atoms in the alloy = 0.087E24

Mole % of Manganese = N/Nt*100 = 33.4E19/.087E24*100 = 0.38%

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