Rotational spectroscopy observe what type of molecule? What is
his energy range? Measured molecule properties.
vibrational spectroscopy observe what type of molecule? What is
his energy range? Measured molecule properties.
The vibrations of a bi-atomic molecule AB can be approximated as a harmonic oscillator with the potential energy of type V (x) = (kx^2)/2, x representing the spatial deviation of the relative position between those 2 molecules towards equilibrium. Calculate the vibrational energy of the H2 molecule knowing that k = 510N/m and the mass of a hydrogen atom is m0 = 1.66 ∗ 10−27 kg
Take an eigenfunction for the harmonic oscillator and the
corresponding energy eigenvalue, and substitute them into the
Schrodinger equation. Then prove that the equation is satisfied. Do
this for n =4, show how n is substituted.
A H2 molecule can be approximated by a simple
harmonic oscillator having a spring constant k = 1.1 ✕
103 N/m.
(a) How many different energy transitions are possible when the
H2 molecule decays from the third excited state down to
the ground state?
(b) Find the photon energies produced in these transitions and
their wavelengths. Enter 0 in any unused boxes.
relative energy
transition energy
wavelengths
lowest
eV
nm
middle
eV
nm
highest
eV...
Demonstrate that the WKB approximation yields the energy levels
of the linear harmonic oscillator and compute the WKB approximation
for the energy eigenfunctions for the n=0 and n=1 state and compute
with the exact stationary state solutions.
For the ground state of the Harmonic Oscillator and 2D Rigid Rotor
A. Give the time dependent wave function
B. Determine <x> and <p> for both the Harmonic
Oscillator and 2D Rigid Rotor
The potential energy shared by two atoms separated by a distance
r in a diatomic molecule is given by the Lennard-Jones function (?0
and ?0 are constants): ?(?) = ?0 [( ?0/?)^12 − 2( ?0/? )^6 ] (a)
Where is ?(?) = 0? (b) Show that the minimum potential energy is
−?0 and that it occurs at ?0. (c) Where is ?? = 0 ? (d) Sketch
?(?).