where A₀ is the radioactivity produced (disintegrations per cubic
centimeter per second); N is the number of target atoms per cubic
centimeter in the sample; φ is the neutron flux (neutrons per square
centimeter per second); σ is the cross section for the reaction (square
centimeters); λ is the disintegration constant[6] for the radioactive
atoms produced (number per second); the number “e” is the base of
natural logarithms; and t is the irradiation time in seconds. Note that
for short irradiation times (t very small), 1-e^{-λt} approximates λt,
while for long irradiations (t very large), 1-e^{-λt} approximates 1.
[Illustration: Graph: Decay scheme for manganese-56]
Maximum Energy % Betas
2.84 MeV 53
1.03 MeV 30
0.720 MeV 16
0.30 MeV 1
% Gammas
0.847 MeV 68
1.811 MeV 20
2.110 MeV 10
Other Energies 2
2.543 MeV
2.658 MeV
2.957 MeV
3.39 MeV
(avge~ 1.4 gammas per beta)
This summarizes what the decay scheme or energy level diagram shows in
terms of the relative amounts of betas and gammas emitted in the decay
of manganese-56. Thus, you could observe more than three times as many
gamma rays having an energy of 0.847 MeV than of 1.811 MeV, etc. Note
that while one, and only one, beta is emitted in the decay of one atom
of manganese-56, two gammas can sometimes be emitted in one decay.
Of course, when the target is removed from the reactor, the number of
radioactive atoms begins to decrease according to the characteristic
half-life of the nuclide. The mathematical expression that describes the
process of radioactive decay of a single nuclide is: