(a) Examine the energy level diagrams in picture below. Indicate if the label is
ID: 964837 • Letter: #
Question
(a) Examine the energy level diagrams in picture below. Indicate if the label is correctly assigned to the diagram. if not, correct the mistake and assign the label to the correct diagram. Provide justification for each answer.
(b) After fixing any errors from part a, you still find that one of the diagrams does not have a label. Does it correspond to a quantum mechanical system? Which one and why, or why not?
Explanation / Answer
In the given energy level diagrams, diagram A and B possess energy levels with same energy gaps. In diagram C and diagram D contains energy levels with increasing gaps with their quantum number.
The rotational energies of molecules represent with the following equation. EJ = B J(J+1); here B is rotational constant and J is rotational quantum number. With increasing the value of J, the rotational energies are much increasing (for J= 0,1,2,3.....the rotational energies are 0, 2B, 6B, 12B........). So, in its (Rigid rotor) energy level diagram, the energy levels lies in increasing distances with rotational quantum number. It looks, either Diagram C or Diagram D is the appropriate representation to Rigid rotor.
Similarly in case of 1D-particle in a box, the equatin for their energies is, En = n2h2/8ml2; here n is the quantum number, h is the planks constant, l is the length of the box, m is the mass of the particle; except n, remaining parameters being constant for a particular particle and a specific box (supposed that h2/8ml2= A). Here also, with increasing quantum number the energies of particle increses in the square orders. for example, if n = 1,2,3..... the energies of particle in 1-D box are 1A, 4A, 9A....So, the energy levels in its diagram are much increasing then their quantum numbers. it mostly looks like the Diagram C or Diagram D.
In case of an harmonic oscillator, the enrgies obey the given equation, En= (n+1/2)hv, hv is the amount of photon/quantum. here with increasing n value, the energies are steadily increases (for n=0,1,2,3..... the enrgies of the harmonic oscillator are 1/2hv, 3/2hv, 5/2hv, 7/2hv.... The energy gap of any two successive levels is equal (hv). It is more likely explains by representing with either Diagram A or Diagram B.
the Diagram D, is perhaps the enrgy level diagram of regid rotor or 1D-partice in a box
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