5. (a) The radioisotope ( { }_{83}^{212} mathrm{Bi} ) has two modes of decay - an alpha decay to an isotope of thallium and a beta decay to an isotope of polonium. (i) Write down the equation of each decay. Which type of beta decay did you write and why? (ii) Evaluate the energy released in each process. Given are the following atomic masses (choose carefully!): [ egin{array}{l} mleft({ }_{83}^{212} mathrm{Bi} ight)=211.991286 mathrm{u}, mleft({ }_{84}^{212} mathrm{Po} ight)=211.988868 mathrm{u}, mleft({ }_{84}^{208} mathrm{Po} ight)=207.981246 mathrm{u}, \ mleft({ }_{81}^{212} mathrm{TI} ight)=211.998340 mathrm{u}, mleft({ }_{81}^{208} mathrm{TI} ight)=207.982019 mathrm{u}, mleft({ }_{2}^{4} mathrm{He} ight)=4.002603 mathrm{u}, \ m_{e}=0.00054857 mathrm{u}, ext { and } 1 mathrm{u}=931.5 mathrm{MeV} / mathrm{c}^{2} . end{array} ] [3 marks] (b) Uranium isotopes: (i) Name and describe briefly the significance (for humanity) of the two primordial uranium isotopes and the key properties that set them apart. (ii) Which of the two has a longer half-life and what implications does that have for nuclear energy? The half-life of ( { }_{92}^{238} mathrm{U} ) is ( 4.468 imes 10^{9} mathrm{yr} ) - calculate its decay constant. (iii) The activity of ( { }_{92}^{238} mathrm{U} ) in a piece of rock is determined as ( 75 mathrm{kBq} ). How many atoms and what total mass of ( { }_{92}^{238} mathrm{U} ) does that correspond to?

m(83212Bi)=211.991286u,m(84212Po)=211.988868u,m(84208Po)=207.981246u,m(81212TI)=211.998340u,m(81208TI)=207.982019u,m(24He)=4.002603u,me=0.00054857u,and1u=931.5MeV/c2. [3 marks] (b) Uranium isotopes: (i) Name and describe briefly the significance (for humanity) of the two primordial uranium isotopes and the key properties that set them apart. (ii) Which of the two has a longer half-life and what implications does that have for nuclear energy? The half-life of 92238U is 4.468109yr - calculate its decay constant. (iii) The activity of 92238U in a piece of rock is determined as 75kBq. How many atoms and what total mass of 92238U does that correspond to