513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
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Morse potential

The bond between two atoms can be described by a Morse potential where U0 = 4 eV, r0 = 0.21 nm, and a = 0.105 nm.

U(r) = U0(e-2(r - r0)/a - 2e-(r - r0)/a)

For small deviations around r0, the force between the two atoms can be described by Hooke's law F = -k(r - r0). Here k is the effective spring constant. The relationship between the potential and the force is F = -dU/dr. What is the spring constant for this bond?

k = N/m

The atoms form a crystal 1 cm high, 1 cm wide, and 6 cm long. The crystal has a simple cubic structure and the bond between each pair of atoms can be described by the Morse potential given above. The crystal is stretched along the long axis. What is the spring constant of the crystal?

k = N/m