[8] Consider a particle in a 1-dimensional box of length L. If we make the length L shorter and shorter, then we are localizing the position of the…

partition function at the limit of 0 K and 2000 K.

b) Plot the probabilities of occupancy of the ground and first excited state energy levels (p0 and p1) as a function of temperature from 1 K to 2000 K.

c) Plot the average energy, <E> in units of kJ/mol, of this system as a function of temperature from 1 K to 2000 K.

NOTE: You can use a spreadsheet to plot the graphs. Please label the axes properly with units.

5. [8] The molar absorption coefficient, for ethane is 40 (cm bar)-1 at a wavelength of 12 nm.

a) Calculate Iout/Iin in a 1.0-cm long absorption cell if ethane is present at a level of 2.0 ppm in one bar of air.

b) What cell length is required to make Iout/Iin = 0.90?