Question

Quantum Mechanics (QM)

Attempt to sketch the contour plots of y and y² in a 2D box for:

n_x = 1; n_y = 2

n_x = 2; n_y = 2

Consider Benzene as fitting inside a square box of length a = b = 5.00Å.

Where would the maximum adsorption be for this molecule? Look up the actual l_max. How do they compare?

Choose two things that are totally wrong with using the PiB model on benzene, that is to say, what idea do we have about benzene, and it’s bonding, that is totally inconsistent with our model.

Answer 1

If the particle is in a 2-D box, then with n_x = 1, n_y = 2 then the corresponding wave function can be written as shown below.

= A Sin (1x/L) Sin (2y/L), where L = length of the 2-D box

The corresponding energy of the particle can be expressed as shown below.

E₁₂ = (1² + 2²)h² / 8mL² = 5h² / 8mL², where 'm' is the mass of the particle.

If the particle is in a 2-D box, then with n_x = 2, n_y = 2 then the corresponding wave function can be written as shown below.

= A Sin (2x/L) Sin (2y/L)

The corresponding energy of the particle can be expressed as shown below.

E₂₂ = (2² + 2²)h² / 8mL² = 8h² / 8mL² = h² / mL2