Two adjacent allowed energies of a neutron in a one-dimensional boxare 4.8Ã10-13 J and 7.5Ã10-13 J. What is the length (in fm) of thebox?
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The nucleus of an atom is 5.0 fm (fm = 1*10^-15 m) indiameter. Avery simple model of the nucleus is a one-dimensionalbox in whichprotons are confined. Estimate the energy of a protonin the nucleusby finding the first three allowed energies of aproton in a5.0-fm-long box.
What is the length of a box in which the difference between anelectron's first and second allowed energies is 1.30Ã10â19 J?
2 .6.4 Consider an electron in a three-dimensional cubic box ofside length Lz . The walls of the box arepresumed to correspond to infinitely high potentials.(i) Find an expression for the allowed energies of the electron inthis box. Express your result interms of the lowest allowed energy, E18 , of a particle in aone-dimensional box.(ii) State the energies and describe the form of the wavefunctionsfor the 4 lowest energy states.(iii) Are any of these states degenerate? If so, say which, andalso give the degeneracy associatedwith any of the eigenenergies you have found that are degenerate.