Question

Question 1:

A sample containing 30% ZrSiO_{4 ,} 30% FeTiO_{3 ,} 30% TiO₂ And 10% Monazite with the chemical formula (Ce,La,Nd,Th)(PO₄,SiO₄) weights 10 kilograms. Calculate the radioactivity of the sample given the thorium content present. The result should be in Bq/gram.

Please show all steps with all formulas for the question to be worth any marks.

Answer 1

Molar mass of Zr SiO₄ =183.3071 g/mol

Molar mass of FeTiO₃ =151.7102 g/mol

Molar mass of TiO₂ = 79.866 g/mol

molecular weight of monazite=240.21 gm

Now the sample has 30 % mass of Zr SiO₄ ie 30 kg of it , and similary 3 kg ,3kg and 1 kg of respectively of FeTiO₃ , TiO₂ and 1 kg of monazite.

Now the number of molecules in 1 kg of monazite =1000/240.21 =4.16 This 4 units (the decimal value of the molecules is the presence of impurities in the mineral . Nonetheless it has no major effect on the radioactivity.

There are 4 atoms of thorium in 4 molecules of monazite.

half life of thorium -228 =1.9 yrs =5.9*10⁷

-(dN/N) =dt

=>dN/dt= -N

When N=4 ,=1/half life=0.16*10^-7 s

dN/dt=-0.677*10^-7

This is an initial decay

A_bq =(number of particles in initial stage *(ln 2/t_1/2 )=4*(ln 2/5.9* 10⁷)

   =4*0.69*0.68*10^-7

=1.88 *10^-7

Activity per 10 kg of sample=1.88*10^-11 bq/gm