Determine the density of states D(E) for a 2D infinitewell (ignoring spin) in which
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Modern Physics
- List the quantum numbers of (a) all possible 3p states and (b) all possible 3d states.arrow_forwardCalculate the kinetic energy of free electron (π/a, 0, 3 π/a) in a 3D square lattice.arrow_forwardShow that if two equivalent hybrid orbitals of the form spλ make an angle θ to each other, then λ = ±(−1/cos θ)1/2. Plot a graph of λ against θ and confirm that θ = 180° when no s orbital is included and θ = 120° when λ = 2.arrow_forward
- Consider the original Stern–Gerlach experiment employing an atomic beam of silver, for which the magnetic moment is due entirely to the spin of the single valence electron of the silver atom. Assuming the magnetic field B has magnitude 0.500 T, compute the energy difference in electron volts of the silver atoms in the two exiting beams.arrow_forwardFor a one-electron atom or ion, spinorbit coupling splits all states except s states into doublets. Why are s states exceptions to this rule?arrow_forwardShow that the group velocity for a nonrelativistic free electron is also given by , where is the electron’s velocity.arrow_forward
- The valence election of potassium is excited to a 5d state, (a) What is the magnitude of the election's orbital angular momentum? (b) How many states are possible along a chosen direction?arrow_forwardGiven position-space lattice vectors a, b and c, show that the reciprocal lattice vectors (see figure) a* = 2pi b x c / a . (b x c), b* = 2pi c x a/ a . (b x c), c* = 2pi a x b/ a . (b x c) are such that a. a* = 2pi, a.b* = 0arrow_forwardWhat is the energy separation (ΔE) between the n = 4 and n = 5 states for an F2 molecule trapped within in a one-dimension well of length 3.0 cm? At what value of n does the energy of the molecule reach ¼kBT at 450 K, and what is the separation between this energy level and the one immediately above it?arrow_forward
- Why in 3D vibrational motion the energy due to the energy equipartition theorem is 2 (3/2 NKT) = 3NKT?arrow_forwardHow many electron states are there in the following shells: (a) n = 4, (b) n = 1, (c) n = 3, (d) n = 2?arrow_forward1000 molecules are bouncing between wells separated by enthalpy gaps H1= 1 ·10-20 J and H2 = 2 ·10-20 J. Considering multiplicities of each state write the partition function and calculate the occupancies of states 2 and 3 at 300K and 370K.arrow_forward
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