Question #43098

A non-magnetic semiconductor has a temperature-dependent energy band gap given by $E_g(T) = E_0 - \alpha T$, where $E_0$ and $\alpha$ are positive constants and $T$ is the absolute temperature. The semiconductor is placed inside a blackbody cavity. At a specific equilibrium temperature $T_0$, the peak wavelength of the cavity's thermal radiation, given by Wien's displacement law ($\lambda_{max} T = b$), exactly matches the band-gap wavelength $\lambda_g = \frac{hc}{E_g(T)}$ of the semiconductor. For an electromagnetic wave of this peak wavelength propagating inside the semiconductor, the refractive index is given by $n = n_0 \frac{E_0}{E_g(T_0)}$, where $n_0$ is a dimensionless constant. Let $E_{0}$ and $B_{0}$ be the amplitudes of the electric and magnetic fields of this wave inside the semiconductor. Which of the following expressions correctly represents the ratio $\frac{E_{0}}{B_{0}}$ at temperature $T_0$? (Here $c$ is the speed of light in vacuum, $h$ is Planck's constant, and $b$ is Wien's constant).