Answer all questions in this section.

1. 1. In relativistic dynamics, the kinetic energy is defined as the difference between the total energy and the rest energy . Suppose that an electron has a momentum of . Calculate the electron's kinetic energy using
      1. relativity theory, and
      2. classical mechanics.
      Is relativity theory required to treat the motion of electrons with a momentum of this magnitude? [6 marks]
   2. Suppose that the above electron's position is measured to an accuracy of , a distance equivalent to the radius of a small atom. What is the minimum uncertainty in the momentum after the measurement? Is the disturbance in the momentum significant? [3 marks]
   3. Calculate the de Broglie wavelength of the above electron. Could a beam of electrons of this kinetic energy be used to visualize the positions of atoms in a material sample? Explain briefly. [3 marks]
2. 1. Write down the ground-state electronic configuration of a germanium atom. [4 marks]
   2. Would a germanium atom be paramagnetic or diamagnetic? [2 marks]
3. An induction coil is a device which, when placed in a changing magnetic field, generates electricity. Reasonably large time-varying magnetic fields are produced by high-voltage power lines. Some years ago, a farmer whose property was crossed by high-voltage lines placed a large induction coil under the lines and supplied his farm with electricity from it. He was found guilty of theft. What was he stealing and from whom? Explain (briefly) the scientific basis of the case. [5 marks]
4. 1. During the calibration of a constant-volume calorimeter, a 1.0095g sample of benzoic acid ( ) is burned completely in an excess of oxygen. The temperature rises by . The heat capacities of reactants and products are negligible compared to the heat capacity of the calorimeter. What is the heat capacity of the calorimeter? The specific change in internal energy on combustion of benzoic acid is . [5 marks]
   2. A 1.1243g sample of solid sucrose ( ) is then burned in the same calorimeter. The temperature rises by . What is the specific energy of combustion of sucrose? [5 marks]
5. The ozone layer is approximately 20km above sea level. At this altitude, the mean temperature is 210K and the partial pressure of oxygen is 1.2kPa.
   1. Accurately calculate for the reaction

      

      at 210K. The standard enthalpy of formation of ozone at is 142.7kJ/mol. The standard molar entropies of ozone and of oxygen at the same temperature are, respectively, 238.82 and while the constant-pressure heat capacities are, respectively, 39.2 and . [10 marks]

   2. Calculate for the above reaction at 210K under the assumption that neither nor vary significantly with temperature. Is the result significantly different? [3 marks]
   3. Calculate the equilibrium pressure of ozone under the conditions prevailing at an altitude of 20km. [7 marks]

   Bonus:

   The above calculation gives a value for the partial pressure of ozone at 20km which is much, much too low. Why?

6. In 1885, Balmer discovered (by trial and error) that the wavelengths of the visible and near-ultraviolet lines of the hydrogen emission spectrum fit the following equation exactly:

   

   where A is a constant and Derive this equation and compute a value for the constant A. Explain the physical significance of the number 4 appearing in the above equation. [8 marks]

7. The normal air pressure in Lethbridge is about 0.9atm. Calculate the approximate concentration of sodium chloride required to raise the boiling point of water in Lethbridge to . What mass of salt would have to be dissolved in 1L of water to reach this concentration? The mole density of water at is 53.19mol/L. [13 marks]
8. The 1,1'-diethyl-2,2'-dicarbocyanine ion (Figure 1) absorbs light at 708nm.

    
   Figure 1: The 1,1'-diethyl-2,2'-dicarbocyanine ion. Cyanine dyes such as this one absorb strongly in the visible range and thus are brightly colored compounds. Accordingly, they have traditionally been used as dyes. This particular dye absorbs strongly at the red end of the spectrum, giving it a pleasant blue-green color.  
   

   This transition is due to the molecular orbital which follows the chain of conjugated bonds (alternating single and double bonds) between the two nitrogen atoms. This orbital can be treated as a one-dimensional box. In the ground state, electrons occupy all of the energy levels up to n=5 (the highest occupied molecular orbital, HOMO). Absorption is due to a HOMO to LUMO (lowest unoccupied molecular orbital) transition. Given this information, what is the length of the ``box''? The average length of carbon-carbon bonds in conjugated chains is 0.14nm. Is this data consistent with the results of your calculation and with the description of the orbital given above? [10 marks]