The Big Ideas…                                                        Name Ghazwa Al-Doori   

                                                                                                    Jan 10, 09

Each time you learn a new topic in spectroscopy, be sure you can answer the appropriate questions below.  Some of the questions may not apply to every topic.

Topic  Thermal Energy                                                      

What is the range of energy involved in the process?

Molecules in the ground electronic state, two electrons are paired in a bonding orbital, the molecule would have no spin angular momentum, no orbital angular momentum, the molecule is in the lowest possible vibration energy state and has modest amount of rotational energy.

How is the Boltzmann distribution relevant in this process?

Ludwig Boltzmann developed an equation that yields the ratio of the number of molecules at two different energy levels, i and j, when the molecules are in thermal equilibrium. The equation is known as the Boltzmann distribution equation.

                                    N_i        =      g_i       e^-(ε_{i –} ε_j)/kt , g_i/g_j =1 because of degeneracy

                                   N_j                       g_j

Using the Boltzmann equation to verify that all twelve molecules will be found

In the state zero at T=0K.

e^{-(εi – εj)/kt} = e^-1/0 =e^-∞ =1/e^∞ = 1/∞ = 0, at T = 0, all molecules are at the lowest level zero.

Three of the twelve will be found at level one at T= 300K

e^{-(εi – εj)/kt} =0.333 = 3/9 ( N_i + N_j ) = 12, three molecules will be found at level one.

Half the number of molecules in level one at T = ∞