A sealed sample of radon gas initially consists of a pure isotope with mass number 222 and atomic number 86. In a short time interval the nucleus in one atom of this sample undergoes the following three decays in the exact order listed:
(a) Determine the mass number and atomic number of the daughter nucleus produced immediately after the first decay.
(b) Determine the mass number and atomic number of the nucleus that exists immediately after the second decay.
(c) Identify the nuclide (name or chemical symbol with mass number) that results after the third decay. Explain how conservation principles support your identification.