In: Physics
A)Which of the following is NOT a valid boundary condition for a particle inside a 1D box of finite length L? For this problem, assume that the potential energy outside the box is infinite.
1-When x = 0, PHI = 0.
2-The particle can only be inside the box.
3-The wave function is complex.
4-If the wavefunction is normalized, the integral of the complex conjugate from 0 to L will be 1.
5-When x = L, PHI = 0.
B)Looking at the energy eigenvalues for a 1D particle in a box, which of the following can we conclude about the change in energy between levels?
1-Energy level spacing increases when the box becomes more confined.
2-Energy level spacing increases as Planck's constant increases.
3-Energy level spacing increases when particle mass decreases and when the box becomes more confined.
4-Energy level spacing increases when particle mass decreases.
5-Energy level spacing does not change with particle mass.
C)One argon molecule is confined in 1.0 m3 box at 298 K. The probability of the Ar molecule being in the ground state (n=1) is very small. Why?
1-The change in energy between levels is very small compared to kT.
2-The partition function for this molecule is very large.
3-The box is much larger than the de Broglie wavelength of argon.
4-All of these answers are correct.