Answer any two questions in this section.

  Total value of this section: 20 marks

1. The emission spectrum of has a line at a wavelength of 6.407nm. By trial and error (the method Rydberg used to obtain his famous equation), find the values of n for the two energy levels involved in this transition.
2. The entropy of solid aluminium oxide at 298K is and its melting point is 2300K. The specific heat capacity (in ) is given by the equation

   

   where T is in Kelvin. What is the entropy of solid aluminium oxide at the melting point?

3. Only a small number of quantum mechanical problems can be solved using the old quantum theory. We have seen two such problems in class (the particle in a box and hydrogenic atom models). Here is another: A particle of mass m is confined to a rigid, immobile circular ring of radius r. The particle has no potential energy.
   1. Relate the allowed de Broglie wavelengths to the radius of the ring. Show that a quantum number appears in this relation.
   2. Relate the kinetic energy to the de Broglie wavelength and thus to your quantum number.
   3. Calculate the angular momentum .  
   4. According to modern quantum mechanics, the angular momentum of a particle on a ring should be where and is an integer. How does this relationship compare with that derived in question 3c?
4. 1. The majority of compounds in thermodynamic tables have negative standard free energies of formation. For example, over 80% of the compounds listed in the Appendix of the course textbook have negative standard free energies of formation. Discuss briefly why this is not surprising.
   2. The standard free energies of formation of gaseous benzene ( ) and cyclohexane ( ) are, respectively, 129.66 and 31.76kJ/mol. One occasionally sees claims in otherwise respectable textbooks that cyclohexane is more stable than benzene because the free energy of formation of cyclohexane is lower. Explain why this is an inappropriate use of standard free energies of formation.
   3. For the reaction

      

      the entropy change is positive since excess gas molecules are produced. Since entropy is supposed to increase during spontaneous processes, this reaction should be spontaneous but it isn't. What's wrong?