Reference no: EM132413032

We have seen in class that the energy stored in a classical vibrational mode is typically equal to k_BT. This is a classical result, which does not account for the discrete nature of the energy spectrum of the oscillator. ("Discrete" means here that the energy eigenvalues for the oscillator can only take particular values. Still, the expectation value of the energy could be anything so long as it exceeds the zero point energy.) The discreteness of the spectrum does not reveal itself when the energy spacing is less than, you guessed it, the thermal energy scale k_BT. The quantum nature of oscillations has an interesting consequence in solids: Below a certain temperature, called the Debye temperature, the heat capacity begins to decrease with lowering the temperature and vanishes at absolute zero, whereas the classical calculation would imply a temperature-independent k_B per bond irrespective of the temperature, as we discussed earlier in class. The Debye temperature T_D is defined as k_BT_D=hbar*omega, where omega is the (circular) vibrational frequency of the bond. Given that the Debye temperature of a hydrogen crystal is 122 K, what is the appropriate frequency of the oscillation, in SI units?