The energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by ny E(nx, ny, nz) - 1²/0² (1²2² +22² +2²2²) 2m (a) Ten protons are confined in a box of dimension (a, 2a, a) on each side. Calculate the total energy of the ground state of these ten protons if we assume that the protons don't interact with each other. (b) If the ten protons are replaced by 10 neutral hydrogen atoms in the ground state, calculate the total energy resulting from the confinement. Again assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.

The energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by ny E(nx, ny, nz) - 1²/0² (1²2² +22² +2²2²) 2m (a) Ten protons are confined in a box of dimension (a, 2a, a) on each side. Calculate the total energy of the ground state of these ten protons if we assume that the protons don't interact with each other. (b) If the ten protons are replaced by 10 neutral hydrogen atoms in the ground state, calculate the total energy resulting from the confinement. Again assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.