Phys help, can someone answer these questions for me with explanation and detail

Question

Phys help, can someone answer these questions for me with explanation and detail thanks alot!

A neutron (m = 1u) is trapped inside a one dimensional box of length 17pm. (a) Calculate the Energies for the first FOUR energy levels of the box. (b) What wavelength photon would be required to be absorbed to promote the neutron from the first to the second energy level? What wavelength for the second to the third level, and what wavelength for the third to the fourth level? What do you notice about the energy spacing between the subsequent levels? (c) Sketch the probability function of the n = 3 state for this neutron in the box. Indicate where you are most likely to detect the neutron. (d) Following Bohr's atomic model, find the wavelength for the transitions from the first to second, second to the third and third to the fourth level for the hydrogen atom. Compare the change in required energy to that from part (b). (e) Calculate your de Broglie wavelength for your trip to uni today. Write down your assumptions.

Explanation / Answer

a) energies = 0.456 eV , 0.543 eV , 0.658 eV , 0.784 eV

b) wavelengths =   256 nm , 452 nm ,   654 nm

c) most likely to detect neutrons are around the nucleus .

d)   wavelengths =   872 nm , 546 nm ,   367 nm

e)   debroglie wavelength = h/mv

                                          = 2.652 * 10-8 m

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