Question

Some quantum mechanical system has the following energy levels: E1 = 1.2 × 10−19 J, E2 = 1.5 × 10−19 J, E3 = 4.8 × 10−19 J.

1) Find all of the wavelengths of light that could be emmitted from this system (spectral lines)

2) For each spectral line, identify what part of the electromagnetic spectrum it lies in.

3) Suppose that there were 4 electrons occupying a set of molecular orbitals with the energies above; Find the lowest unoccupied molecular orbitals (LUMO) of this system when it is in ground state, then find its total energy when it is in that state.

4) What spectral lines would occur in the absorption spectrum of the previous system (4 electrons) when it is in its ground state

Answer 1

1)

transition from level 3 to level 2 :

E₃ - E₂ = (4.8 - 1.5) (10^-19) = hc/

(4.8 - 1.5) (10^-19) = (6.63 x 10^-34) (3 x 10⁸)/

= 602.7 nm

region : visible light

transition from level 3 to level 1 :

E₃ - E₁ = (4.8 - 1.5) (10^-19) = hc/

(4.8 - 1.2) (10^-19) = (6.63 x 10^-34) (3 x 10⁸)/

= 552.5 nm

region : visible light

transition from level 2 to level 1 :

E₃ - E₂ = (1.5 - 1.2) (10^-19) = hc/

(1.5 - 1.2) (10^-19) = (6.63 x 10^-34) (3 x 10⁸)/

= 6630 nm

region :infrared region