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DescriptionChemistry 344: Physical Chemistry II for Biochemists
Total: 10 pts
1. (2.5 pts) A spin-1 particle has three spin angular momentum states, 11, 10 and 1-1. All
three have a spin quantum number, L, of 1, and each eigenstate has a polar spin quantum
number ‘m’ of either 1, 0 or -1. What is the orientation with respect to the z-axis, the polar
angle, for the angular momentum vector of these 3 eigenstates?
2. (2.5 pts) The deuterium nucleus, 2H, is a spin-1 particle. In a magnetic eld, B0, the
Hamiltonian for the eigenstates are represented below, in which as a real constant for
deuterium. Even though there are 3 di erent energy levels, only one transition or one peak
is observed in the spectrum. Why?
̂ lm = − γB0ℏm ϕlm

3. (2.5 pts) Derive the commutator between the Lx and Ly operators, [Lx, Ly].
4. (2.5 pts) A spin-1/2 particle, like an electron, is collapsed to the eigenvalue Lz = +


What are the ranges of possible values for Lx and Ly?
/ 2.

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