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Problem 1:
Estimate the probability that a hydrogen atom at room temperature is in one of its first
excited states (relative to the probability of being in the ground state). Don't forget to
take degeneracy into account. Then repeat the calculation for a hydrogen atom in the
atmosphere of the star y UMa, whose surface temperature is approximately 9500K.

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Which one of the following statements about the exchange energy of the few lowest excited states of helium, in which the two electrons are in different subshells, is incorrect? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. b с d e In the absence of the exchange energy, the degeneracy between 1s¹2s¹ and 1s¹2p¹ configurations would only be lifted by relativistic corrections. For a given configuration and L the exchange energy favours (ie the energy is lower for) S-1 compared with S=0 O For a given configuration and L the exchange energy favours states that are spatially anti-symmetric The exchange energy gives larger shifts in the levels than relativistic corrections L, S remain good quantum numbers in the presence of the exchange energy
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The value of a partition function roughly represents the maximum energy of the states at a given temperature. O True False
Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v 2m dx² EV, with boundary conditions (0) = 0 and (1) = 0. Second, the Quantum Harmonic Oscillator (QHO) V = EV h² d² 2m da² +ka²) 1 +kx² 2 (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.