An alpha particle of mass 3727.4 x 10° eV/c² is trapped in a box of size L 0.000001 nm = 10nm (the size of a nucleus). Treat this as a 1D infinite square well. Find: (a) The n=5 wavefunction and probability density. Draw a graph. (b) The ground state energy and first excited state. (c) The wavelength of a photon emitted when the alpha particle transitions from the first excited state to the ground state. (Note that wavelengths between 0.001 nm to 10 nm are x rays and less than 0.001 nm are gamma rays.) (d) The probability that the alpha particle is in the range x= 0 to x= 2/SL for the n= 5 state. (e) The expectation value of the position of the alpha particle for the n=5 state. Iif by inspection, explain.

An alpha particle of mass 3727.4 x 10° eV/c² is trapped in a box of size L 0.000001 nm = 10nm (the size of a nucleus). Treat this as a 1D infinite square well. Find: (a) The n=5 wavefunction and probability density. Draw a graph. (b) The ground state energy and first excited state. (c) The wavelength of a photon emitted when the alpha particle transitions from the first excited state to the ground state. (Note that wavelengths between 0.001 nm to 10 nm are x rays and less than 0.001 nm are gamma rays.) (d) The probability that the alpha particle is in the range x= 0 to x= 2/SL for the n= 5 state. (e) The expectation value of the position of the alpha particle for the n=5 state. Iif by inspection, explain.