Question

The Debye temperature $\Theta_D$ for Diamond is 1850K. The Debye frequency is:

• A. $2.42 \times 10^{13}$ Hz
• B. $12.42 \times 10^{13}$ Hz
• C. $14.42 \times 10^{13}$ Hz
• D. $16.42 \times 10^{13}$ Hz

Answer 1

The Correct Option is A

The Debye frequency is related to the Debye temperature as:
\[ f_D = \frac{k_B \Theta_D}{h} \]
Given $\Theta_D = 1850 \text{ K}$, $k_B = 1.38 \times 10^{-23} \text{ J/K}$, and $h = 6.626 \times 10^{-34} \text{ J s}$:
\[ f_D = \frac{1.38 \times 10^{-23} \times 1850}{6.626 \times 10^{-34}} \approx 2.42 \times 10^{13} \text{ Hz} \]