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(a) Estimate the value of the force constant ? and the angular frequency ? for the...

(a) Estimate the value of the force constant ? and the angular frequency ? for the vibrations of the atoms in copper. Use that Young’s modulus Y = 130 GPa and that the cubic lattice constant is 0.36 nm (ignore that copper actually has an fcc structure instead of a simple cubic structure). (b) Estimate the angular frequency for the vibrations that correspond to the Debye temperature of 343 K and compare it to the result in (a). (c) Estimate the amplitude of the vibrations as a fraction of the lattice spacing at room temperature

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(a)Expression for force constant of the atoms in a crystal is (130 x 10% Pa) (0.36 x 104 m) -46.8 N/m s 47 N/m Angular frequency of vibrati on of atoms in the copper is M2 46.8 N/nm 1.055x10-3 kg s2.1x1013 Hz b)Relation between debye temperature and angular frequenecy is Angular frequency of the vibration corresponding debye temperature is, (343K) (1.38x10-23 J/K 1.055x10-* J.s -4.5x1011 Hz At mazimum amplitude,energy of oscillator is in the form of potential energy (1.38x10 JK) (300K) 46.8 Nim 1.33x10-11m

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