A source contains two phosphorous radio nuclides ³²₁₅P (T_1/2 = 14.3d) and ³³₁₅P (T_1/2 = 25.3d). Initially, 10% of the decays come from ³³₁₅P. How long one must wait until 90% do so?

In a periodic table, the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are ²⁴₁₂Mg (23.98504u), ²⁵₁₂Mg (24.98584u) and ²⁶₁₂Mg (25.98259u). The natural abundance of ²⁴₁₂Mg is 78.99% by mass. Calculate the abundances of other two isotopes.

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei ⁴¹₂₀Ca and ²⁷₁₃Al from the following data:

m(⁴⁰₂₀Ca) = 39.962591 u

m (⁴¹₂₀Ca) = 40.962278 u

m (²⁶₁₃Al) = 25.986895 u

m (²⁷₁₃Al) = 26.981541 u

Under certain circumstances, a nucleus can decay by emitting a particle more massive than a α-particle. Consider the following decay processes:

Calculate the Q-values for these decays and determine that both are energetically allowed.

Consider the fission by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are ¹⁴⁰₅₈Ce and ⁹⁹₄₄Ru. Calculate Q for this fission process. The relevant atomic and particle masses are

m(²³⁸₉₂U) = 238.05079 u

m(¹⁴⁰₅₈Ce) = 139.90543 u

m(⁹⁹₄₄Ru) = 98.90594 u