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NAA Quantification

The measured count rate (R) of the gamma rays from the decay of a specific isotope (110Ag) in the irradiated sample can be related to the amount (n) of the original, stable isotope (109Ag) in the sample through the following equation (1):

R = ε Iγ   A = ε Iγ n φ σ (1-e ti) ed


Equation 1

where:
R = measured gamma-ray count rate (counts per second)
A = absolute activity of isotope A+1Z in sample
ε = absolute detector efficiency
Iγ = absolute gamma-ray abundance
n = number of atoms of isotope AZ in sample
φ = neutron flux (neutrons·cm-2·sec-1)
σ = neutron capture cross section (cm2) for isotope AZ
λ = radioactive decay constant (s-1) for isotope A+1Z
ti = irradiation time (s)
td = decay time (s)

If the neutron flux φ, neutron capture cross section σ, absolute detector efficiency ε, and absolute gamma-ray abundance Ιγ are known, the number of atoms n of isotope AZ in the sample can be calculated directly. In most cases, however, a standard is irradiated and counted under similar conditions as the sample, and the mass of the element in the sample (Wsam) is found by comparing the measured count rates (R) for the sample and standard through the following equation (2):


Sample Mass Equation
Equation 2

where:
Wsam = mass of element in sample (g)
Wstd = mass of element in standard (g)
Rsam = gamma-ray count rate from the sample (counts per second)
Rstd = gamma-ray count rate from the standard (counts per second)
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