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These definitions are for the lab exercise Natural Occurring Radioactivity

N = number of nuclides
D = disintegration rate (Bq, Ci, dimension s-1)
A = activity is disintegration rate D per unit of volume or unit of mass (dimension s-1)

We distinguish between two notions:
As(i) = specific activity is activity per unit of mass of that particular element the actual
radionuclide i belongs to. This notion is also used to express the activity of a
particular radiolabelled molecule in relation to the total mass of the same molecule
(labelled and unlabelled) in the sample (for instance when the inactive molecule is present
as a carrier).
Ac(i) = activity concentration is the activity of a special radionuclide i or all present
radionuclides (AcT = Ac(∑i) = total activity) per unit of volume or unit of weight of a radioactive
N,D and A may, in addition, have an index t (i.e. Nt, Dt and At). This denotes the parameter values at time t relative to a starting time t = 0.
R = counting rate (cps, cpm or generally cpt where t should be defined, dimension s-1)
S = number of counts
N, D, A, R and S may, in addition, have indexes B = background, T = total or N = net. The relations between them are: RN=RT - RB
SN =ST - SB. Other indexes may also be used, for instance SCr-51 in order to separate from SFe-59.
We consider the following three samples:
P1: 1 kg pure iron (Fe). This sample contains10 kBq of the radionuclide 59Fe.
P2: 1 kg steel consisting of 70 weight% iron and 10 weight% of each of the elements Cr, Ni and Mo. The sample contains 10 kBq of 59Fe and 10 kBq of 51Cr.
P3: A 1L aqueous solution with 100 g dissolved FeCl3 and 100 g dissolved CrCl3. This corresponds to 35 g dissolved Fe and 31.6 g dissolved Cr. The solution contains 10 kBq 51Cr and 10 kBq 59Fe.
For sample P1 we then have:
As(59Fe) = 10 kBq/kg Fe
Ac(59Fe) = 10 kBq/kg sample
For sample P2:
As(59Fe) = 10 kBq/0.7kg = 14.3 kBq/kg Fe
As(51Cr) = 10 kBq/0.1kg = 100 kBq/kg Cr
Ac(59Fe) = 10 kBq/kg sample
Ac(51Cr) = 10 kBq/kg sample
AcT = 20 kBq/kg sample
For sample P3:
As(59Fe) = 10 kBq/0.035 kg Fe = 285.7 kBq/kg Fe
As(51Cr) = 10 kBq/0.0316 kg Cr = 216.5 kBq/kg Cr
Ac(59Fe) = 10 kBq/1.2 kg sample = 8.33 kBq/kg sample and/or 10 kBq/l sample.
Ac(51Cr) = 10 kBq/1.2 kg sample = 8.33 kBq/kg sample and/or 10 kBq/l sample
AcT = 20 kBq/1.2 kg sample = 16.66 kBq/kg sample and/or 20 kBq/l sample.
Indexes may be omitted when the meaning of the parameters cannot be misunderstood.