2. Consider a He atom trapped in a 3-D cube (box with: length = width =...

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2. Consider a He atom trapped in a 3-D cube (box with: length = width = height = a = 1.0 m). The potential inside of the box is zero, and the potential is infinite outside of the box. The He atom's translational behavior is described by the wavefunction: 4(x,y,z) = siny a) 5pts. Is the wavefunction normalized? b) 5pts. Suppose the He atom is in its lowest energy translational state. What are the values of nx,ny, & n? c) 5pts. What is the kinetic energy of the He atom in its lowest energy translational state? d) 5pts. In the lowest energy translational state, compare the likelihood of finding the He atom in a cubic centimeter near the middle of the box to the likelihood of finding it in a cubic centimeter at one of the corners. (Hint: either use a qualitative argument based on the shape of the wave function, or use a quantitative argument with integration). e) 5pts. Now consider nx = n = n = 1 x 107: what is the kinetic energy of the He atom in this translational state? f) 5pts. For the translational state given in e), compare the likelihood of finding the He atom in a cubic centimeter near the middle of the box to the likelihood of finding it in a cubic centimeter at one of the corners. (Hint: either use a qualitative argument based on the shape of the wave function, or use a quantitative argument with integration). 2. Consider a He atom trapped in a 3-D cube (box with: length = width = height = a = 1.0 m). The potential inside of the box is zero, and the potential is infinite outside of the box. The He atom's translational behavior is described by the wavefunction: 4(x,y,z) = siny a) 5pts. Is the wavefunction normalized? b) 5pts. Suppose the He atom is in its lowest energy translational state. What are the values of nx,ny, & n? c) 5pts. What is the kinetic energy of the He atom in its lowest energy translational state? d) 5pts. In the lowest energy translational state, compare the likelihood of finding the He atom in a cubic centimeter near the middle of the box to the likelihood of finding it in a cubic centimeter at one of the corners. (Hint: either use a qualitative argument based on the shape of the wave function, or use a quantitative argument with integration). e) 5pts. Now consider nx = n = n = 1 x 107: what is the kinetic energy of the He atom in this translational state? f) 5pts. For the translational state given in e), compare the likelihood of finding the He atom in a cubic centimeter near the middle of the box to the likelihood of finding it in a cubic centimeter at one of the corners. (Hint: either use a qualitative argument based on the shape of the wave function, or use a quantitative argument with integration).