When plotting,(how o plot a graph process) please use graph paper or a graphing program.
Additionally, be sure to label the axes properly.
1. [6 pts] Can we fully specify the position vector of a particle and the x-component of the particle’s angular momentum at the same time to any arbitrary precision? Show this. HINT: Use Cartesian coordinates.
2. [12 pts] Fluorine atoms have a 2p^(5) electronic configuration and have a doublet spin state. The two lowest electronic energy levels of F atoms are shown to the right: E = 404.1 cm^(-1) E = 0
a) Plot the partition function for this system as a function of temperature from 1 K to 2000 K. Explain the behavior 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 (p_(0)and p_(1)) 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 (Google Sheets is free). Please label the axes properly with units. (tell me the process --,E=404.1cm^(-1)
---,E=0)
3. [12] Consider the rotational energy levels of the ^(6)Li-^(1)H molecule, which has a bond distance of 0.91\angstrom .
a) Calculate and tabulate the populations of the first rotational 10 energy levels at 298 K assuming there are only 10 energy levels.
b) Plot the population as a function of the quantum number l.
c) Replot the populations, but with a bond distance of 1.7 Ă….
HINTS:
The energy of the rotational states is given by: E_(l)=l(l+1)(â„Ź^(2))/(2\mu r^(2)), l=0,1,2,... and the degenercy of the energy levels is given by g=2l+1. For a), show a sample calculation. It is recommended to use a spreadsheet (i.e. Google Sheets or Microsoft Excel), such that it can be easily recalculated and replotted for part c).
4. [4 pts] The molar absorption coefficient, \epsi ,for ethane is 40(c(m)/(b)ar )^(-1) at a wavelength of 12\mu m.
a) Calculate (I_(out ))/(I_(in )) in a 1.0-cm long absorption cell if ethane is present at a level of 2.0 ppm in one bar of air. ( 2 ppm means that 2 out of a million air molecules are ethane molecules. You can use this to calculate the partial pressure of ethane).
b) What cell length is required to make (I_(out ))/(I_(in ))=0.90 ? (help me with this problems as fast as you can)
$E = 404.1 cm^{-1}$
$E = 0$
