19. For a particle in a box, show that the solutions satisfy the Heisenberg Uncertainty Principle (see equation sheet). Use an electron for the particle with box of length 10 Å, approximating the conjugation length relevant to retinal as the active chromophore in rhodopsin/visual response. Derive the relevant expressions for the n=1 solution, slowest possible particle velocity. (Wavefunctions would be given in the test. See notes or equation sheet on Quercus. You need to think about what the energy of the particle is..KE or U. The variance in v and x is what you are being asked, i.e., Av, Ax.)

How many values are there for the magnetic quantum number when the value of the angular momentum quantum number is 3?

Is it true that the smaller the azimutal quantum number the more penetrating the orbitals? If yes/no why?

For a particle in a cubic box, what is the degeneracy of the energy level 50 times the ground state energy? Include specifications for each state. For a set of permutation partners, it is sufficient to show one state and indicate the number of states in the set.

please answer #2