Calculate mass from activity?

FlipStyle1308

I was wondering what equations would be used to calculate the mass (in mg) of an isotope that gives an activity of 200 Ci.

cesiumfrog

You shouldn't start out intending to plug'n'chug. What does activity mean (eg. what units does it measure)?

FlipStyle1308

Activity has the units of decays/s, and it measures the rate of half-life.

daveb

From activity and half life, you can get the number of atoms in the sample. From that, you should be able to get the mass using Avogadro's number and the gram atomic weight

Astronuc

Using daveb's approach, one can calculate the specific activity or activity per unit mass. Activity divided by specific activity equals mass.

See this discussion on specific activity.

mpoesr

What if the element consists of two isotopes: example Stable Rb-85 and the radioactive Rb-87 with an abundance of 27.83%. How would you calculate the specific activity of natural rubidium chloride. I have figured the g.mol-1 for Rb-85=85.47g.mol-1 and 86.91g.mol-1 for the Rb-87, and M(r) =120.92g.mol-1?

Astronuc

Activity due to a particular radionuclide is simply the product of the decay constant and the number of atoms of the radionuclide present. In the case of a isotopic mix, if one know the mass and isotopic composition, then one can determine the fraction of atoms which are radioactive isotope.

Activity is measured - usually with a counter which interacts with the radiation.

In the case of a compound, e.g. RbCl, one subtracts the mass of the Cl, which gives the mass of Rb, then apply the isotopic ratio for the nuclide. Alternatively, know that there is one Rb atom for each Cl atom, determin the number of molecules of RbCl, which give the number of atoms, of which some fraction will be Rb-87. Rb-87 has a very long half-life, 4.81E+10 y, and consequently the beta energy is quite low, ~ 283.3 keV, so self-shielding would an issue for a large sample. A 4-pi or at least a 2 pi counter would be recommended for an accurate count.