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Evaluate the maximum value of energy and momentum of a phonon (acousite quantum) in copper whose Debyed temperature is equal to 300K. |
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Answer» SOLUTION :The maximum energy of the phonon is `ħ omega_(m)= kTheta= 28.4meV` On substituting `Theta= 330K`. To get corresponding value of the maximum moment we must have the dispersion relation `omega= omega (vec(K))`. For small `(vec(k))` we know `omega=|vec(k)|` where `v` is the velocity of sound in the crystal. For an order of magnitude estimate we continue to use this RESULT for HIGH`|vec(k)|`. Then we estimate `v` from the values of the models of elasticity and density `v~sqrt((E )/(rho))` We write `E~ 100GPa, rho= 8.9xx109^(3)kg//m^(3)` Then `v~3xx10^(3)m//s` Hence `ħ|vec(k)|_(max)~( ħ omega_(m))/(v)~ 1.5xx10^(-19) gm cms^(-1)` |
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