2. In solids every atoms are vibrating rapidly about it equilibrium position (In

Question

2. In solids every atoms are vibrating rapidly about it equilibrium position (In this case the equilibrium is called Lattice points) . The frequency of this oscillations are very high 1013 Hz . This vibrations are causes of: electrical resistance, heat capacity and transportation of heat. Lets assume the amplitude of the oscillations are small and all are Simple harmonic oscillator( i.e Hook's Law is still valid.) Diamond are one of the hardest materials in nature (with very large Y value , as we discussed in elasticity, say diamond atoms (look up how diamond crystal look like! Why Diamond is transparent ? ) has force constant k 150 N/m , mass of carbon (yes diamond is made with carbon only) 12 amu or 1.9944235 × 10-23gm , what will its angular frequency of oscillation (a) 5.6 × 1012 rad/s (b) (a) 5.6 × 1013 rad/s (c) (a) 5.6x 1011 rad/s (d) none of them

Explanation / Answer

2. w = sqrt(k/m)

w = sqrt[ 150 / (1.9944235 x 10^-26 kg)]

w = 8.6 x 10^13 Hz ...Ans

total energy = k A^2 /2

=150(10^-11)^2 / 2

= 75 x 10^-22 J  

Ans(C)

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