Calculation of specific activity when element consists of two isotopes

[mpoesr]

The element rubidium consists of two isotopes; the stable Rb-85 and the radioactive Rb-87 (abundance 27.83%). What is the specific activity of natural rubidium chloride? if you use A(r)=85.47 g.mol-1 for Rb-element, A(r)= 86.91 g.mol-1 for Rb-87, and M(r) = 120.92 g.mol-1 for RbCl.

 

[Astronuc]

Specific activity is simply activity divided by mass, and activity is simply the product of the decay constant and the number of atoms of particular radionuclide present.

So if one is measuring an alloy or compound of radionuclides and stable atoms, then the specific activity would be the ratio of the activity (∑λ_iN_i)/(∑A_jNj), where N is the number of atoms of a given isotope. The numerator includes on the activity of radionuclides, whereas the denominator includes the mass of all nuclides.

 

[sir-pinski]

The specific activity of natural rubidium chloride can be calculated by first determining the total activity of the sample, which is the sum of the activities of each isotope present. The activity of Rb-85 can be calculated using its abundance and the known specific activity of natural rubidium, which is 1.78 Bq/g. This gives an activity of 0.278 Bq/g for Rb-85.

The activity of Rb-87 can be calculated using its abundance and the specific activity of Rb-87, which is 9.85 Bq/g. This gives an activity of 2.73 Bq/g for Rb-87.

The total activity of the sample is then 0.278 Bq/g + 2.73 Bq/g = 3.01 Bq/g.

The specific activity of natural rubidium chloride can then be calculated by dividing the total activity by the mass of the sample. Using the given molar mass of RbCl, we can convert the mass of the sample to moles, which is 1 mole. Therefore, the specific activity of natural rubidium chloride is 3.01 Bq/mol.