Question

Many diatomic molecules have potential energy curves. In this problem you will use a model potential that approximates the potential energy curve of a diatomic molecule. The model PES is defined as follows:

V(x)= eternity symbol, if x<= 0

= 0, if 0<x<L,

= epsilon, if x>=L

Note that x is not r, the interatomic distance. If r0 is the shortest distance at which interatomic attraction and repulsion cancel out, you can think of x as r-r0; this choice makes the calculations simpler.

a) The total energy E is quantised when E < epsilon but not when E>= epsilon. Use physical arguments to account for this observation.

b) If m= 1.0 * 10E-26 kg., L=1.5* E-10 m., and epsilon= 7.0 * E-21 J, the wavefunction associated with E=1.2 *epsilon , the wavefunction associated is as shown.

i) Explain why the wave function features different wavelengths in the 0< x< L and x>= L regions.

ii) Determine the value of |p|, the module of the particle's momentum, in each of the 0,x,L and x>=L regions

Answer 1

a) When E<epsilon, potential energy, V(x)=-, so there would be no role of potential energy between x=0 to L. This is the feature of Particle in 1-Dimensional Box. In PIB, this energy between 0 to L is quantized and so an integral multiple of n².