I need help on E and F

Here we explore the statistical properties of particle translations: when they are quantized and when quantization effects are unimportant. Assume water molecules translate in one dimension.

A)

Calculate the average translational energy per molecule at T=1000K. 6.9010²¹ J

B)

Assume you can model the trasnslational energy of water molecules using the particle in a one dimensional box model. For what value of the quantum number n is the particle-in-a-box energy equal to the average translational energy that you calculated in Part A? Assume the box is one meter in length, i.e. L=1.00m. 6.1710^10

C)

Calculate the one dimensional translational partition function for water molecules at T=1000K. Assume L=1.00m. q = .710^10

D)

What is the probability that a water molecule at T=1000K in a box of length L=1.00m has a translational energy equal to the average translational energy that you calculated in part A? Give your answer as a number between 0 andf 1. P =7.810^12

E)

Suppose the box that contains the water molecule has a length that is only L=10.0 nm. Calculate the quantum number n that corresponds to the average translatioanl energy per water molecule at T=1000K. Assume again that the quantum mechanical energy is that of a particle in a one dimensional box..

n =

F)

Calculate the one dimensional translational partition function for a water molecule in a box of length L=10.0nm at T=1000K.

q=