Acertain ergodic system can only be in three possible energy states with energy values e1 = 300 kbk, e2 = 600 kbk, e3 = 900 kbk, where kb is the boltzmann constant and k is kelvin (temperature unit). first the energy state is not degenerate. the degeneration of the second energy state is g2 = 2. the degeneration of the third energy state is g3 = 6.
a) determine the probability that the system is in the third energy state of energy e3 at 300 k.
b) determine the mean energy of the system at 600 k.
c) plot the mean energy of the system as a function of temperature between 0 and 2000 k.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

You are traveling in a car going at a constant speed of 100km/h down a long, straight highway. you pass another car going in the same direction which is traveling at a constant speed of 80km/h. as measured from your car's reference frame this other car is traveling at −20km/h. what is the acceleration of your car as measured from the other car's reference frame? what is the acceleration of the other car as measured from your car's reference frame?

Determine the age of a fossil if it had only one eighth of its original carbon-14 content remaining?