- (a) Explain why quantisation of energy occurs. What experimental evidence is [5]there to indicate that energy is quantised? The Boltzmann equation for the difference in population between two energylevels

is: \frac{n_{\text {uper }}}{n_{\text {lower }}}=\exp \left(\frac{-\Delta E}{k T}\right) where AE is the energy gap between the states (in J), k is the Boltzmann constant,and Tis the temperature. O Describe qualitatively the effects on the populations of the energy states of a six [4]level system, where the gap between each subsequent level is approximately2x102 J, on decreasing the temperature from 300 K to 100 K. In NMR spectroscopy, the energy gap between the ground and excited states is given by: \Delta E=\frac{h \gamma B}{2 \pi} where h is Planck's constant, yis the gyromagnetic ratio (which equals 42.58×10Hz Tesla for 'H), and B is the applied magnetic field (in Tesla). Calculate the population difference between the ground and excited states for 'H atB = 7 Tesla and 300 K, and hence comment on the sensitivity of NMR as a spectroscopic technique. Calculate the wavelength of the electromagnetic radiation that would be absorbed in the transition in part (c). In what part of the electromagnetic spectrum does this radiation lie? For electronic spectroscopy, deltaE =1.97 x 10 J. Comment on the consequences of this value for the spectroscopic technique. • Peaks observed in electronic spectroscopy are broad (Av = 1.6 MHz), where as those observed in NMR spectroscopy are very narrow (Av= 1.6 Hz). Explain this difference, and also explain how it affects the uses of the two spectroscopic methods.